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76-5630

ROBBINS, Lynn Wayne, 1946WAREHCUSING AGRICULTURAL INPUTS IN MICHIGAN:
AN ECONOMIES QF SIZE AND LOCATION ANALYSIS.
Michigan State University, Ph.D., 1975
Economics, agricultural

Xerox University Microfilms # Ann Arbor, Michigan 48106

WAREHOUSING AGRICULTURAL INPUTS IN MICHIGAN:
ECONOMIES OF SIZE AND LOCATION ANALYSIS
By
Lynn Wayne Robbins

A DISSERTATION
Submitted to
Michigan State University
in p a rtia l fu lfillm e n t of the requirements
fo r the degree of
DOCTOR OF PHILOSOPHY
Department o f A gricultural Economics
1975

AN

ABSTRACT
WAREHOUSING AGRICULTURAL INPUTS IN MICHIGAN:
ECONOMIES OF SIZE AND LOCATION ANALYSIS

AN

By
Lynn Wayne Robbins

The Michigan Farm Bureau Services' Farm Supply Division predicts
that demand on th e ir warehousing system fo r a g ric u ltu ra l input supplies
w ill increase markedly over the next fiv e years.

This estimate pre­

sents the Farm Supply Division with a potential problem because th e ir
expansion p o s s ib ilitie s are somewhat lim ited and they suspect th at the
current warehousing f a c ilit ie s may be approaching maximum capacity.
The Farm Bureau contracted th is research to compare projected
future assembly, d is trib u tio n , and warehouse cost functions fo r the
current system to those of a one-warehouse system at each of seven
proposed a lte rn a tiv e s ite s .

They feel th at these comparisons w ill

provide them with the information necessary to decide whether to invest
in a one-warehouse system, and where the ideal s ite fo r th at system
might be.
The research contract provided an opportunity to apply
theoretical constructs to applied agribusiness problems w ithin r e a lworld constraints using a unique combination of research techniques.
A modified lockset model was used in conjunction with an economicengineering systems-simulation technique to discover values required
to calculate internal rates of return.

Lynn Wayne Robbins

Transportation costs were separated and analyzed as assembly and
d is trib u tio n costs.

The modified lockset model was used to calculate

d is trib u tio n costs fo r the seven proposed one-warehouse locations once
i t could adequately duplicate the current system's behavior structure.
Costs fo r assembling products from other than backhaul suppliers were
drawn from manufacturers' fre ig h t rate schedules.
Warehouse operating costs fo r the one-warehouse system were
synthesized by constructing a model o f its expected behavioral design.
Required construction parameters included storage, delays, ordering
in te rv a ls , and other factors dynamic by v irtu e of th e ir memory or
feedback c h a ra c te ristic s.

A systems simulation model was used to

estimate these parameters because of its advantage, re la tiv e to other
techniques, in estimating dynamic in te rre la tio n s h ip s .

The remaining

exogenous parameters were obtained from Farm Bureau Management and
manufacturer estimates.
The economic-engineering systems-simulator that resulted was
validated when i t demonstrated its c a p a b ility to s a tis fa c to rily trace
the costs and related behavioral characteristics exhibited by the
existing warehouse system.

The one-warehouse system's operations

model was constructed by updating parameters in the existing system's
model to r e fle c t differences predicted fo r a one-warehouse f a c i l i t y .
F in a lly the transportation and warehousing analyses were
evaluated together with a range of investments that would lik e ly be
required fo r the one-warehouse system by calculating internal rates
of return.

The product o f this process provided Farm Bureau with

Lynn Wayne Robbins

information that w ill assist them in th e ir decision to accept or re je c t
the one-warehouse system.
The fin a l investment decision should depend on how well the
calculated internal rates of return compare to Farm Bureau's cost of
c a p ita l.

The study did show, however, a cost advantage fo r a one-

warehouse system that provides service equivalent to that available
in the existing system.

This e n tire advantage stems from labor,

inventory, and related variable cost-savings.
Transportation cost calculations exhibited an advantage fo r
the one-warehouse system in assembling products, but demonstrated an
o ffs e ttin g disadvantage fo r d is trib u tin g products to dealers.

Models

of the seven proposed one-warehouse locations displayed essen tially
equivalent transportation costs which leaves resource a v a ila b ility and
management preference parameters with re la tiv e ly more importance in
s ite selection than would have otherwise been the case.
Lim itation on current warehouse expansion was shown to be a
problem.

Major modifications w ill be required in the current system

before 1980 unless the Farm Supply Division accepts substantially
higher stock-out rates than they have in the past.
Despite the fa c t that capacity lim ita tio n s w ill be a problem
fo r the current system in the fu tu re , the model demonstrated a possible
savings in the present fo r the existing system by reducing inventories.
A general inventory reduction of 15 to 20 percent would reduce inventory
carrying costs more than i t would increase costs of lo st sales.

Lynn Wayne Robbins

Other findings include:
1.

Despite inventory consolidation, the one-warehouse system would
not assemble larg er quantities of products than would be
assembled in the current system, under s im ilar demand conditions.

2.

Demand predictions in d o lla r terms did not necessarily re fle c t
equivalent percentage increases in volume terms.

F in a lly , the results give strong indications th at the economic
advantages of a one-warehouse system ju s t if y the required investment.

ACKNOWLEDGMENTS

F ir s t, thanks go to my thesis supervisor, Dr. Stephen B. Harsh
fo r his personal in te re s t and guidance throughout th is research e ffo r t
I want to thank Dr. Jack A llen , my major professor, who gave valuable
assistance and direction during my e n tire graduate program.

I am

especially indebted to Dr. John Ferris who encouraged me to pursue
graduate studies in A gricultural Economics.

Thanks also go to Drs.

Larry Connor and George Dike fo r serving as members of my thesis
committee.
A special thanks go to my mother and fa th e r-in -la w , Mr. and
Mrs. Edward B. Merchant, who gave loyal support throughout my graduate
tra in in g .
To my parents, Mr. and Mrs. Berlyn Robbins, thank you fo r your
unwavering confidence, support, and assistance throughout my education
and l i f e .
F in a lly , a very special acknowledgment and thank you is given
to my w ife Mary.

Without her s a c rific e s , understanding, and cheerful

encouragement th is endeavor would not have been possible.

TABLE OF CONTENTS

LIST OF TABLES

....................................................................

V

LIST OF FIGURES

....................................................................

ii

INTRODUCTION .............................................................

1

Problem Setting ................................................
General Needs Analysis ....................................
Expected Needs ............................................
Current Needs ............................................
General Problem Statement ............................
Research Objectives ........................................
Nature of This Study ........................................

1
2
3
5
8
10
10

THEORETICAL BACKGROUND AND LITERATURE REVIEW

13

E fficiency Considerations ............................
Formulation of a Theoretical Framework . .
Length of Operation, Rate of Output, and
Scheduling Variables ....................................
Assembly and D istribution Cost Functions .
Continuous Analysis ................................
Discontinuous Analysis ............................
Estimation of Plant Cost Relationships . .
Descriptive Analysis ................................
Economic Engineering . . . ....................
Systems Simulation ....................................

13
15

Chapter
I.

II.

III.

19
23
24
29
35
35
37
41

........................

43

Variable D istribution Costs ........................
H istorical Description ............................
The Model ....................................................
Model V e rific a tio n ....................................
Results ........................................................
1979-1980 Analysis ....................................
1979-1980 Results ............................................
Variable Assembly Costs ................................
Total Variable Transportation Costs . . .

44
44
48
50
53
56
58
60
64

VARIABLE TRANSPORTATION COSTS

iii

Chapter

Page

IV. VARIABLE IN-WAREHOUSE COSTS

..........................................................

69

The Nature of the S im u la t o r .....................................................
The Modeling Procedure .................................................................
Fundamental D a t a .....................................................................
General Model Description .................................................
Analysis Process .....................................................................
Model V e r if ic a t io n .........................................................................
R e s u l t s .............................................................................................
Inventory Strategy Costs.......................................................
Estimated Parameters .............................................................
The One-Warehouse System......................................................
The 1979-1980 Simulator .....................................................
Simulator Results With Projected Demands .............................
Warehouse Size A lternatives .....................................................
Construction Timing .....................................................................

69
73
75
79
82
87
91
91
96
96
101
102
Ill
115

V. INVESTMENT ANALYSIS

V I.

..........................................................................

118

Cash F lo w s ....................................................................
Evaluation Interval .....................................................................
Return on Investment .....................................................................
S e n s itiv ity Analysis .....................................................................

119
129
131
135

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

..............................

139

Surrenary.............................................................................................
C o n c lu s io n s .....................................................................................
Recommendations .............................................................................

139
144
145

Appendix
A.

DEALERSHIPS AND BACKHAUL POINTS

..................................

B.

EXISTING ROUTE STRUCTURES

.............................................. . . . .

151

C.

PRODUCTS BY PRODUCT GROUP

..............................................................

156

D.

WEEKLY AVERAGE SEMIANNUAL DEALER DEMAND IN CUBIC FEET

. .

159

E.

GENERATED ROUTE CONFIGURATIONSFOR SEVEN PROPOSED
ONE-WAREHOUSE LOCATIONS .................................................................

160

BIBLIOGRAPHY .............................................................................................................

iv

149

169

LIST OF TABLES

C la s s ific a tio n of Yearly Fixed and Variable
Transportation Costs fo r the Michigan Farm Bureau

. . .

Weekly Cost and Capacity Averages: A Comparison
fo r V e rific a tio n with 1972-73 Fiscal Year Data ................

52

Modeled Weekly Variable D istrib u tio n Costs fo r
1972-1973 .........................................................................................

55

Projected 1979-80 Warehouse Demands in Cost of
Sales Dollars .................................................................................

57

Modeled Weekly Variable D istribu tio n Costs fo r
1979-1980 .........................................................................................

59

Predicted Farm Bureau Product Demand Increases in
Cubic Feet from 1972-73 to 1979-80 ........................................

61

Products with Variable Inbound Freight Rates ....................

62

Variable Inbound Michigan Freight Rates

............................

63

Total Variable Transportation Cost Comparison,
1972-1973.... .........................................................................................

65

Total Variable Transportation Cost Comparison,
1979-1980.... .........................................................................................

66

I n i t i a l Simulator Parameters fo r the 1972-1973,
1979-1980 Farm Bureau Systems' Models ................................

76

Warehouse Operating Cost C lassificatio ns fo r
Farm Bureau's 1972-1973 System .................................................

83

Monthly Inventory Levels, 1972-1973

.....................................

88

Desired Inventory Levels fo r the Jenison
Warehouse, 1972-1973 .....................................................................

89

Annual Variable Cost Comparison, 1972-1973 Data

90

v

. . . .

Table

Page

16.

Inventory Strategy Cost Comparison, 1972-1973

......................

92

17.

Chemical Order Size Comparison Between a Oneand Two-Warehouse System Using 1972-1973 Data

.....................

100

Inventory Strategy Costs by Capacity and Percent
of Desired Inventory Level Projected 1979-1980 ....................

103

Annual Warehouse Cost Comparisons Between a Oneand Two-Warehouse System a t Approximately Equivalent
Performance Levels or Stock-Out Rates .....................................

107

One-Warehouse Capacity Requirements fo r Performance
To Be Acceptable U ntil 1987 fo r Two Performance
Levels and Two Demand Projections .............................................

115

Construction Timing fo r the Proposed One-Warehouse
System .....................................................................................................

117

Warehouse Cost Comparisons Between the Current and
Proposed Warehouse Systems as Predicted fo r 1979-1980

. .

120

Estimated Additions to Cost from Higher Inventory
Carrying Costs in a One-Warehouse System .................................

123

Estimated Savings from Lower Net P ro fits Lost in
a One-Warehouse System .....................................................................

123

Annual Cash Flows A fter Taxes fo r a $397,600.00
I n i t i a l Investment Through 1985-1986 .........................................

132

Internal Rate o f Return and S e n s itiv ity Calculations
Through 1985-1986 fo r a One-Warehouse System ........................

134

18.
19.

20.

21.
22.
23.
24.
25.
26.

vi

LIST OF FIGURES

Figure
1.

Page
Total monthly sales through the Michigan Farm Bureau
warehouses fo r fis c a l year 1972-1973 .........................................

17

2.

Warehousing stages .............................................................................

18

3.

A cost surface fo r producing a single productby varying
both rate and time of operation.....................................................

21

4.

Assembly route organization and road travel

26

5.

Location of impound points in supply band 1,
5,000 pounds per square mile per year density level . . .

28

6.

S tollsteim er's model .........................................................................

30

7.

A conceptual S tollsteim er approach ............................................

34

8.

Michigan Farm Bureau dealerships and backhaul points . . .

45

9.

Sample of lockset derived routes ................................................

54

.................

10.

The general warehouse Model

........................................................

74

11.

Zilwaukee strategy costs fo r 1972-1973 ....................................

93

12.

Jenison strategy costs fo r 1972-1973 ........................................

94

13.

End-to-end strategy costs fo r 1972-1973

95

14.

Zilwaukee strategy costs and capacity requirements
fo r 1980 .................................................................................................

104

Jenison strategy costs and capacity requirements
fo r 1980 .................................................................................................

105

The one-warehouse system's strategy costs andcapacity
requirements fo r 1980

106

15.
16.

Figure

17.

Page

New warehouse inventory strategy costs: predicted
costs versus true v a lu e s ................................................................

110

18.

New warehouse capacity selection......... ..........................................

112

19.

Estimated additions to cost fromhigher inventory
carrying costs in a one-warehouse system
.........................

122

Estimated savings from lower net p ro fits lo st in
a one-warehouse system .....................................................................

124

Net p ro fits l o s t .................................................................................

126

20.
21.

v iii

CHAPTER I

INTRODUCTION

Problem Setting
The Michigan Farm Bureau Services' Farm Supply Division is a
$33 m illio n a year operation.

This sales figure represents 20 percent

of Michigan's input supplies market.

The d is trib u tio n of this $33

m illio n is divided almost equally between Farm Bureau-owned o u tle ts ,
cooperatives on management contract, and independent dealers.

Sim­

i l a r l y , the $6 m illio n in sales of farm supplies that flow through
the two Farm Bureau warehouses is equally divided between the three
d iffe re n t o u tle t types.
The warehouses are located a t Zilwaukee near Saginaw and
a t Jenison near Grand Rapids.

At one time the Farm Supply Division

had as many as seven warehouses, but has since found the current twowarehouse system to be more economical.

The warehouses are supplied

prim arily from the Chicago area except fo r instate supplies and a
few supplies such as baler twine that currently come through the St.
Lawrence Seaway to Zilwaukee.

Both warehouses account fo r 35 percent

of th e ir sales in hardware and building supplies.

Feed, the next

largest portion of sales, makes up 31 percent of the movement at
Zilwaukee but only 24 percent at Jenison.

1

The feed moved through

2

the warehouses is mostly specialty feeds such as pet food and feed
additives from the B attle Creek plant.

Each warehouse runs one e ig h t-

hour s h ift per day and has a fiv e -u n it truck f le e t d is trib u tin g supplies
to dealers three or four days of the week.
The purposes of the warehouse operation are:

(1) to give basic

support to dealers who cannot economically ju s t ify d ire c t shipments
from manufacturers, (2) to act as a back-up source of supply fo r those
dealers who receive the m ajority of th e ir supplies from d ire c t shipments,
and (3) to break down and reship large orders.
The Michigan Farm Bureau doubts th at the two existing ware­
houses are s u ffic ie n t to f u l f i l l the needs that they have projected
fo r the next fiv e years.

Because of the potential fo r savings in a

one-warehouse system and because of res tric tio n s upon expansion within
the existing f a c i l i t i e s , they feel an economies of size and location
analysis would provide the information required to make fin a n c ia lly
sound decisions with respect to these a lte rn a tiv e s.
S p e c ific a lly , Farm Bureau Management questions whether one
large warehouse would be an improvement over the current arrangement
and, i f so, which of th e ir proposed locations is most desirable.
General Needs Analysis
The Michigan Farm Bureau doubts the current system's c a p a b ility
to f u l f i l l the needs projected fo r the next fiv e years.

A detailed

scru tin izatio n of those needs w ill provide a more precise d e fin itio n
of the Farm Bureau problem.

An important question relates to whose

3

needs are being determined.

Needs w i l l , th erefo re, be c a re fu lly

labeled as to th e ir source.
A to ta l d is trib u tio n system is required fo r agricu ltu ral
factors of production marketed by the Farm Supply Division of Michigan
Farm Bureau.

Participants in the system include farmer-consumers of

Farm Bureau products, dealers, warehouse employees, central management,
suppliers o f conmodities th at are backhauled, input suppliers, and
affected society.
The Farm Bureau is a cooperative structured prim arily to serve
member-consumers.

Farmer-consumer, dealer, and central management needs

are, therefo re, interdependent and in te rre la te d .

For th is reason, a

combined analysis of these three p a rticip a n ts' a c tiv itie s should lead
to a discovery o f what they require from the system.
Expected Needs
F ir s t, a look at expected p artic ip a n t a c tiv itie s should be
in s tru c tiv e [ 2 0 ] . 1

I t is iro n ic that while agriculture in Michigan

and in the nation w ill be shrinking in terms o f to ta l farms and land
in production, never has there existed a heavier demand fo r farm
products.

Consequently, Michigan farmers are motivated to increased

productivity in a ll enterprise areas in order to meet expanded market
demand fo r food, and to remain competitive with ag ric u ltu ra l products
from surrounding states and countries.
^he following section is taken from Farm Bureau Supply
D ivision's "Five Year P rojectio n --Ju ly 1, 1974 to June 30, 1979"
which includes s ta tis tic s and projections from Project 80 + 5.

Examples of this emphasis upon increased productivity is
observed in liv e s to c k, po ultry, dairy products, and crop production.
There are fewer milk cows, but greater milk production; less acreage,
but higher crop y ie ld s ; fewer layers, but more eggs per hen.

The

trend toward a reduction in the to ta l number of farms w ill continue,
but individual farm operations w ill increase in size and complexity,
thus

requiring greater c a p ita liz a tio n and sp ecializatio n .
C urrently, the Farm Bureau organization can provide better

q u a lity or lower cost marketing services to farmers than farmers could
provide fo r themselves.

As farms continue to increase th e ir size and

c a p ita liz a tio n , comparative advantages may s h ift from the cooperative
to the farmer and vice versa.

The cooperative must recognize the

p o s s ib ility of such s h ifts and adjust to meet them.

Despite these

s h ifts in comparative advantage, the expected increased output from
a ll farm operations w ill provide s ig n ific a n t opportunities fo r a growth
in product volume and services in a ll departments of the Farm Supply
D ivision.

There w ill be increased demands fo r f e r t i l i z e r m aterials,

pesticides, feed products, and building m aterials.

In th is connection,

a major objective of the Farm Supply Division w ill be to capture a
greater share o f the expanding farm supply market by increasing market
penetration through improvements in the cooperative's d is trib u tio n
system while maintaining the cooperative purpose.
The Farm Bureau's tra d itio n a l means o f moving farm supply inputs
to farmers through local elevators w ill continue as the primary system
of d is trib u tio n .

However, as individual farm operations increase in

5

size and scope, there w ill be an economic and competitive necessity
to serve these farmers on a d ire c t basis with major inputs.

I t is

expected th at feed concentrates, super-concentrates, and complete
feeds w ill move d ire c tly from the feed m ill to farmers; and that
farmers w ill be equipped to handle f u ll truckloads of f e r t i l i z e r
from manufacturing sources.
Projections to 1980, therefo re, indicate that the market fo r
farm supplies w ill continue to expand the potential of Farm Bureau
Services.

As a re s u lt, Farm Bureau expects a s im ila r increase in

demand fo r the products and services provided through it s warehousing
system.
Current Needs
Requirements or needs arising out of predicted situations have
been discussed.

The more current needs, those reflected by the existing

system, have yet to be presented.
Supplies are stocked in warehouses and dealerships or ordered
as customers need them.

Goods may be shipped d ire c tly to dealers

e ith e r on Farm Bureau carriers or on suppliers' c a rrie rs .

Goods may

move to warehouses where they are la te r transported on Farm Bureau
trucks to dealerships.

Warehouse shipments are also used as backup

sources of supply fo r those dealers who are mainly d ire c t shippers.
F in a lly , warehouses act as layover points where large orders are
disassembled, reassembled, and reshipped.
Other Farm Bureau a c tiv itie s not previously discussed reveal
some additional p articip an t needs.

For seasonal or infrequently

6

purchased supplies, farmer-consumers buy inputs from Farm Bureau
dealers on an order basis.

Regularly required items, on the other

hand, are usually on stock in stores.

Farmers, therefo re, expect

easy a c c e s s ib ility to dealers, no unreasonable delays in order
d e liv e ry , stocking o f reg ularly required items, competitive prices,
as well as good q u a lity merchandise and service.

Farm Bureau's role

in th is system is one of fa cto r-su p p lier and competitor.

They estab­

lis h dealerships in rural areas in order to create a competitive
atmosphere th at hopefully w ill lead to reasonable prices.
Because dealers are the means used by Farm Bureau to serve
th e ir consumer-members, Farm Bureau's needs w ill r e fle c t farmers'
needs.

Dealerships, therefo re, must be d istrib uted so as to be

accessible to Farm Bureau members.

They need satisfacto ry tran s­

portation services fo r assembly and d is trib u tio n .

They require

disassembly, storage, and reassembly marketing functions as well as
methods fo r contending with p a rtia l or nondirect shipment dealers.
Dealerships have been referred to in th is discussion as i f
they and Farm Bureau were one and the same.

Although most dealerships

are v e rtic a lly integrated with Farm Bureau through ownership or contract,
some dealers are completely independent.

These dealers would, there­

fo re , have needs in addition to those already mentioned.
with Farm Bureau because of the market mechanism.

They deal

They must feel that

Farm Bureau can supply them with merchandise at a lower p ric e , with
b etter service, or with some other favorable combination.
then, require a re lia b le source o f supply.

Independents,

Here is a point where the

7

p articip ants' needs may c o n flic t i f a radical change is made in the
existing system.

For example, i t may be that those independents

who come to the current warehouse location fo r supplies cannot be
economically included in a delivery route, should changes in warehouse
locations be implemented.
S im ila rly , warehouse employees, backhaul suppliers, input
suppliers, and affected society are participants whose needs, although
overlapping to a great extent, may c o n flic t with Farm Bureau's
management should a move be req u ire d .2
Employees need jobs and job security which

is a cost th at may

not be continually ju s t ifia b le in the eyes of Farm Bureau.

Backhaul

suppliers are those firms who happen to produce goods required within
the system and who happen to be located near a delivery route so that
Farm Bureau c a rrie rs do not have to return empty.

They could easily

have needs and, therefo re, po licies th at would c o n flic t
Bureau System's need to backhaul rather randomly.
holds fo r input suppliers.

with the Farm

A sim ilar statement

Input suppliers, of which backhaul suppliers

are a p a rt, are those firms who supply Farm Bureau with commodities to
market.

Participants found a t the interface between Farm Bureau and

the rest of the system have been c la s s ifie d as affected society.
2This is not to say th at management, dealers, and consumers
would not also have c o n flic tin g needs. I t does imply, however, that
th e ir c o n flic ts are lik e ly to be less re s tric tiv e to eventual imple­
mentation of a system a lte rn a tiv e than those of independent dealers,
input suppliers, and warehouse employees.

8

This group includes those regions w ithin Michigan whose needs to
maintain th e ir employment and income, c o n flic t with Farm Bureau
needs.3
Although a number of the needs discussed are outside the
immediately researchable scope o f th is study, they are not to be
ignored.

To do so

strateg ies.

might invalid ate otherwise sound system-improvement

This research w ill model the obvious Farm Bureau needs.

Border needs w i l l , however, have a major impact in determining the
constraints w ithin which the model must work.
The heu ristic nature of the needs analysis must also be
stressed.

As the research progresses, new needs may appear th at are

not at f i r s t apparent.

Constantly recycling the analysis process

w ill provide a vehicle fo r discovering the central issues in the crux
o f Farm Bureau's problem.

When the crux of the problem is revealed,

more appropriate solutions w ill n a tu ra lly follow .
General Problem Statement
The problem is to discover a low cost, highly e ffic ie n t
technology fo r the assembly, storage, and d is trib u tio n o f ag ricu ltu ral
inputs that w ill expand the throughput capacity of the existing Farm
Bureau system.

Total discounted costs and investments must be kept low

without losing, and hopefully gaining, market share and to ta l discounted
sales volume.

Simultaneously, dealer prices must remain competitive

3For example, the moving of a warehouse by Farm Bureau would
c o n flic t with employees' needs as well as the needs of the p a rtic u la r
region being abandoned.

9

from month to month and year to year, avoiding soaring costs due
to inventory mixes not being compatible with consumer tastes and
preferences.
I f these conditions can be met, farmers should be able to
increase th e ir productivity and remain competitive.

At least Farm

Bureau can keep th e ir sector of the input supply market from con­
trib u tin g to a lessening of th at competitive position.

As a con­

sequence o f achieving th is desired s ta te , Farm Bureau should be
rewarded with an improved competitive position in the Michigan
a g ric u ltu ra l input market.
I t is also important to study the potential of the existing
system, although th is a lte rn a tiv e does not meet the central objective
of increasing the system's throughput.

Indeed, i f the existin g system

did meet the objective of increasing throughput, the problem, as i t was
previously described, would not e x is t.

Because, however, the "expecta­

tion" o f increased demand is the motivation behind the need fo r an
analysis rather than a "current" f e l t need, i t is quite possible that
the existing system could exh ib it increased throughput.

On the other

hand, i t is not obvious th at i t would be the best a lte rn a tiv e a v a ila b le .
Knowledge is needed fo r planning future contingencies.
might more appropriately be stated as:

The question

Is the existing system s u f f i­

cient to f u l f i l l expected needs, and i f not, what superior a ltern atives
exist?

10

Research Objectives
These objectives outline the major accomplishments to be
achieved by this research.
1.

Determine the cost of d is trib u tin g supplies to the 96 dealers
placing the highest demand on Farm Bureau warehouses while
backhauling supplies from the 11 most active backhaul points
(a) from the two existing warehouses and (b) from each o f the
seven proposed one-warehouse locations.

2.

Comparethe assembly cost structures fo r the existin g f a c ili t ie s
to each of the seven proposed one-warehouse locations.

3.

Calculate operating cost structures (a) fo r the existing
f a c ilit ie s in 1972-73 and (b) fo r the existin g f a c ilit i e s
as well as a one-warehouse f a c i lit y in 1979-80.

4.

Conduct an investment analysis comparing the current system
to the proposed one-warehouse system.
Nature of This Study
Although numerous doctoral theses use a company-specific data

base, few are b u ilt d ire c tly around contracted research.

Although th is

process imposes additional restrain ts on the researcher, i t is possible
that research applied to actual business situations can re s u lt in an
e ffe c tiv e means o f demonstrating the usefulness and v a lid ity of theory.
Dobson and Matthes, fo r example, describe un iversity research
as inadequate because i t is often e ith e r too technical to be in te rp reted ,
or not tim ely enough to be useful.

This research project is confronted

11

by both of these problems.

Results, as well as a ll other information

communicated to managers, must be clear and straightforward.

This

means keeping to a minimum o f mathematical formulae and d is cip lin ary
jargon.

I t also requires constant surveillance o f le g a l, p o lit ic a l,

so c ia l, and physical fe a s ib ilit y with respect to research and social
implementation.

Without this surveillance, th e o re tic a lly v alid solu­

tions may be proposed that are not r e a lis t ic a lly v a lid .

I t may be,

fo r example, th at the elim ination of many marginal Farm Bureau dealer­
ships would lead to cost minimization fo r the warehouse operation.
P o litic a lly , however, this solution would be in feasib le fo r an
ag ricu ltu ral cooperative whose goals emphasize member service.
The importance o f the timeliness facto r was demonstrated
by two Farm Bureau requests fo r r e la tiv e ly rough approximations rather
than waiting fo r the fin a l resu lts.

Such requests require schedule

readjustments th at allow concentration on areas th at were e ith e r
previously not scheduled or set fo r a la te r time.
Grayson extends Dobson and Matthes1 argument fo r increased
firm -u n iv e rs ity intimacy by rela tin g his experience as Chairman of
the Price Commission.

In his opinion, "Managers and management

scientists are operating as two separate cultures each with its
own goals, languages and methods.

E ffective cooperation and even

communication between the two is ju s t about minimal" [1 2, p. 41].
He points out that management scientists want to help managers produce
more e x p lic it decision-making through s c ie n tific methodology.

Managers,

on the other hand, "make and implement decisions larg ely by rough rules

12

of thumb and in tu itio n " [12, p. 42 ].
not compatible.

These positions obviously are

Grayson discovered what he thought were the reasons

fo r th is in co m p atib ility.

When "putting together the Price Commission,

[he] used absolutely none of the management science tools e x p lic itly "
[12, p. 4 3 ].

He found he couldn't use them because of shortage of

tim e, in a c c e s s ib ility of data, resistance to change, long response
time, and in v a lid atin g s im p lific a tio n s .
I t seems, th erefo re, th at the agribusiness industry and related
departments in our colleges and u n iversities have two random sets of
nearly nonoverlapping a c tiv itie s .

This research w ill attempt to

adjust economic, marketing, and management tools from the university
to industry problems w ithin the industry constraints.

This should be

possible, because, unlike firm managers, the university researcher is
free to contend with technique inadequacies without interference from
the firm 's day-to-day re s p o n s ib ilitie s .

Once implementation techniques

are developed, however, managers should be able to apply them in the
face o f constraints such as those suggested by Grayson.

CHAPTER I I

THEORETICAL BACKGROUND AND LITERATURE REVIEW

The theory and lite r a tu r e related to this research is presented
in three parts.

Because this study is concerned with Farm Bureau's

assembly and d is trib u tio n functions as well as th e ir warehouse opera­
tio n s , the theory and lite r a tu re related s p e c ific a lly to those functions
is discussed separately.

In addition to the specific operations, points

o f importance pertaining to the system as a whole are also reviewed.
These more encompassing considerations w ill be presented p rio r to the
points s p e c ific a lly re la tin g to e ith e r product transportation or
warehouse operations.
E fficiency Considerations
Equating marginal revenue product and marginal facto r cost
determines the combination of inputs that w ill most e ffic ie n tly y ie ld
the greatest output in terms of price.

Neoclassical economics often

assumes th a t price or a llo c a tiv e effic ie n c y is calculated using a
production function th a t, w ithin environmental constraints, w ill y ie ld
the greatest output fo r any set of inputs.

The best existing

produc­

tio n function in these terms is said to be technically e f f ic ie n t 1*
"These e ffic ie n c y d e fin itio n s come from Ben French's review of
ag ricu ltu re production lite r a tu re whose framework o f approach is loosely
followed in th is and the next section.
13

14

[10, p. 3 ].

Firms fa ilin g to equate marginal revenue products and

facto r prices could be technically e f f ic ie n t , but would not be a llo c a tiv e ly e ffic ie n t.

Applied economists should not forget that the

objective is to discover a llo c a tiv e optima by using the most highly
e ffic ie n t production function in technical terms.

I t follows then

that the researcher's f i r s t concern should be with d efin itio n s of
production functions that are a t or near technical effic ie n c y .
Technical e ffic ie n c y is of prime importance especially in
the warehouse cost portion of this study.

The search w ill be fo r

technical as well as a llo c a tiv e optima.
Another Farm Bureau concern is warehouse s ize.

French

[10, p. 3] has shown that i t is possible to calculate a llo c a tiv e
optima with a nontechnically e ffic ie n t production function.

He also

points out that i t is possible to calculate a llo c a tiv e effic ie n c y on
tech nically e ffic ie n t production functions fo r nonoptimally-sized firm s.
This research seeks results that w ill help the Michigan Farm Bureau move
closer to optimums in technology, facto r a llo c a tio n , and size.

This

intention was expressed e a r lie r as a desire to discover a low cost,
highly e ffic ie n t technology fo r the assembly, storage, and d is trib u tio n
o f ag ricu ltu ral inputs th at w ill expand the throughput capacity of the
Farm Bureau system.
Although the Farm Bureau is interested in improving effic ie n c y
with operations th at approach optimal s iz e , they must do so within
boundaries defined by other economic facto rs.

Factors such as non­

homogeneity of product, q u a lity of management and labor input, and

15

personal preferences are not eas ily measurable but constrain improvement
more than would i n i t i a l l y appear to be the case.
This study is especially concerned with the assembly, storage,
and d is trib u tio n operations within the warehousing enterprise.

Although

i t would seem desirable to optimize the e ffic ie n c y in each of these
operations separately, a systems approach may d ic ta te d iffe r e n tly .
The systems approach "focuses on the performance of to ta l systems,
with clear recognition that the optim ization process may require some
trad e-o ffs in e ffic ie n c y among subsystems" [10, p. 3 ],

Because the

assembly,distribution,and warehouse cost functions are lik e ly to be
calculated, using independent research techniques, a good deal of
subjective judgment w ill be required to avoid excluding the important
n o nlin earities th a t may e xist between them.
Formulation of a Theoretical Framework
Within the Farm Bureau organization, there are variables of
importance other than input and output rates.

Time, space, and form

dimensions are also important and cannot be ignored.

Farm Bureau

transforms the products of input manufacturers into intermediate
products characterized by changes in form, to some degree, but mostly
by changes in location and timeliness of a v a ila b ility .
The Farm Bureau marketing system d iffe rs from a purely manu­
facturing process in that its d e fin itio n of the product emphasizes time
flow of inputs and outputs.

The product o f the Farm Bureau Warehouse,

therefo re, is almost e n tire ly service.

When nearly a ll of a product

16

is in the form o f convenience of location and a v a ila b ility , output
becomes d i f f ic u l t to measure.

Input-output flow is important because

of the seasonality of demand (see Figure 1) and the n o n va riab ility of
labor.

Because Farm Bureau's unionized labor force is paid fo r time

on the job , not time worked, and because the range of labor v a r ia b ility
is small a t each level of employment due to union p o licy , any contin­
uous cost function must be regarded as an approximation of the exact
cost-output relationships adopted fo r ease of manipulation.
I f stages and production lines are approximately
defined to be independent except fo r the flow of
m aterials between them, each may be thought o f as
having its own production function [10, p. 12].
What is required is a stage
by stage examination of
a lte rn a tiv e techniques and a selection of a set of tech­
niques which minimize costs of producing any volume of
marketing services, given the environment w ithin which
the firm must operate. Aggregation over stages then
defines the optimum combination of factors [10, p. 14].
[see Figure 2J.
In re la tio n to th is aggregation process i t is important to
point out something that French may

have implied but did notovertly

reveal.

may not be optimized whenthe

Total warehouse e ffic ie n c y

optimal functions from each stage are aggregated because a bottleneck
may occur th at would be more costly than combinations that include
some nonoptimal technique-using stages.

For example, the technique

that optimizes input-output relationships in the unloading stage may
cause in e ffic ie n c ie s when combined with the optimum stowing technique.
This might occur i f the firs t-s ta g e flow was much fa s te r than th at in
the second.

Combining these stage flows could e as ily lead to product

17

1,000
950

In Thousands of Sales Dollars

850

750

650

550

450

350

250
July Aug
1972

Sept Oct

Nov

Dec

Jan Feb
1973

Mar

Apr

Figure 1.

Total monthly sales through the Michigan Farm Bureau
warehouses fo r fis c a l year 1972-1973.

Source:

Statement of operations and margins.

May

June

18

Truck

Rail

Stage I

N

Stw
Stage I I
Str
N
X

f

□

= Stage

Q = Stage v a ria te

Stage I I I

D = Temporary storage

0

=

Substage

^ = Merchandise flow
i
1

U = Unloading
C = Checking
Stw = Stowing
Str = Storing

Stage IV

R = Replenishment
S = Selecting
L = Loading

Figure 2.

Warehousing stages.

19

stacking that would slow the stowing and possibly the unloading
process.

By remaining continually aware o f possible n o n lin e a ritie s ,

the stage-level production and cost functions can be o f use given
n o nlin earities that are e ith e r measurable or obviously in s ig n ific a n t.
In the above example, a systems approach would help to
a lle v ia te such a problem by examining the tra d e -o ff between using
the optimum stage technique a t a slow rate or a slower unloading
technique.

This slower technique could be nonoptimizing fo r the

stage alone but optimizing fo r the firm as a whole.

The approach

should also help to uncover other interdependencies.

I t may not,

fo r example, be appropriate to tre a t the unloading and loading
functions as separate e n titie s .

In r e a lit y , a loading technique

may e x is t that would increase both loading and unloading productiv­
itie s by leaving the men less fatigued a fte r completing the loading
process.
Length o f Operation, Rate of Output,
and Scheduling Variables
Firms change th e ir rate o f operation by increasing the operating
speed o f the existing technology or by adopting fa s te r techniques.

It

is also possible, however, to work at a constant rate but fo r a longer
period of time to achieve increased output.

This length o f operation

v a ria b le, often not o ve rtly discussed in neoclassical economic theory,
is important in empirical work.

Length o f operation is o f crucial

importance in determining short-run cost functions and optimal plant
size.

20

Analysis o f the length o f operation variable has not been
ignored in economic lite r a tu r e .

French, Sammet, and Bressler [1 1 ],

point out th a t length of operation may have a lin e a r cost function,
while output rate is more conventionally c u rv ilin ea r (see Figure 3 ).
This implies that managers should adjust length of operations while
holding rate a t its cost minimizing le v e l.
N o nlinearities in the cost functions with respect to length
of operation might, but would not necessarily, occur because of fatigue
or union re s tric tio n s on minimum pay or overtime.

At Farm Bureau ware­

houses, lengthening operations may also introduce no nlin earities
between the warehousing and the d is trib u tio n or assembly functions.
More tra c to rs , t r a ile r s , and other d is trib u tio n equipment may be
required i f , fo r example, the rate or length of operation in the
d is trib u tio n phase cannot be increased to handle increased warehouse
output.

A s im ila r situ atio n is also possible in assembling products

into the warehouses.

The e n tire system, including suppliers and

dealers, might have to adjust to such a change but not be able to
make th at adjustment in the form of increasing th e ir own length of
operation.
A systems approach is important when looking at the in te r ­
relationships between stages of production.

French refers to this

need in terms of the interrelatio n sh ip s between time periods of
production.

He states th at in terrelatio n sh ip s in the state of the

marketing system between periods may r e s tr ic t output v a ria tio n .

0

Figure 3

A cost surface fo r producing a single product by varying
both rate and time o f operation. Storage costs are
assumed zero. [Source: 6, p. 560.]

"Thus, the optim alization process must be developed with respect to
a sequence of decisions, rather than independently fo r each period"
[10, pp. 23-24].
In theory, the various size plants on an envelope curve are
assumed to operate a t a uniform rate of output.

With seasonal demand

fo r services, however, the same quantity of services cannot be produced
with each time period.

With the constant length of run that is also

normally assumed, theory often cannot explain such a problem.

Firms,

however, may be able to adjust th e ir short-run length o f operation in
order to maintain a uniform output ra te .
I f a constant length s h ift is desired, a firm may decide not
to change its length of operation.

A constant rate of output can be

maintained, however, because of the importance of timing or scheduling.
Scheduling is a th ird variable beyond rate of output and length of
operation.

I t has a t its base an in te rre la tio n s h ip between time

periods th a t requires the related optim ization process to be developed
with respect to a sequence o f decisions.

The scheduling variable not

only requires optim ization over a set of fixed length time periods but
also the optim ization with respect to the length of each time period.
Warehouse workers during periods of high demand w ill work
almost e n tire ly a t the basic functions of unloading, stowing, selecting,
and loading products.

In slack demand periods they w ill work on non-

basic operations such as rearranging products and cleaning up s p ills .
The length and timing of each task is varied, not the length of the
to ta l d a ily operation.

23

Again, i t is possible to manage a constant output rate because
of nontime specific or nonbasic tasks.

Operations o f th is type,

including overall management, some record keeping, cleaning, and
maintenance, are those tasks not organized sequentially around
m aterials flow .

These tasks need not be completed a t a specific

point in tim e, instead, they need only be completed within some
reasonable time span.
In essence, the scheduling variable changes the shape of
the production function.

To maximize over th is variable is to search

fo r the optimal combination of sequential and nonsequential tasks each
day.
Assembly and D istribu tio n Cost Functions
The discussion thus fa r has been in terms of theory and its
empirical application to the problem as a whole.
now s h ift to the transportation system.

The emphasis w ill

The overall transportation

problem concerns d is trib u tio n and assembly patterns, technologies,
and plant location.
Assembly and d is trib u tio n cost functions which address these
issues have been analyzed using many operations research techniques.
Among the several approaches found in the lite r a tu r e , lin e a r programs
and dynamic programs such as the transshipment model [2 , 13] and
Locksett method [23] abound.

No one single approach, however, has

been found to adequately handle the combination o f complexities unique
to th is study.

Problems of (1) tracking trucks so they w ill fin is h

24

d is trib u tin g near a backhaul point or warehouse, (2) irre g u la r dealer
demand, (3) sending p a rtia l loads, and (4) not being able to assume
away fra c tio n a l truck loads are some o f the more troublesome to this
research.
French perceives the general problem when he indicates th at
"because o f s t i l l unresolved d if f ic u lt ie s in handling the more complex
routing problems, solutions in practice have ty p ic a lly been o f a t r ia l
and e rro r nature" [10, p. 37].
I f he can make

th is statementin general without d ire c t

reference to the Farm Bureau com plexities, one is inclined to believe
that some optimizing simulator or Monte Carlo technique may be required
in th is research.
B asically, however, the transportation problem has been
approached in two waysby researchers.Models solve th is

type of

problem by e ith e r assuming continuity or discontinuity of space.
In th is case, a continuous space assumption would indicate that the
volume demanded from Farm Bureau Warehousing Service is d istrib uted
evenly over Michigan [1 8, 1, 6, 26, 21].

On the other hand, i f a

discontinuous demand was assumed, the exact location o f the volume
demanded would become important [15, 17].
Continuous Analysis
As a representative of the group th a t takes the continuous
approach, a selective review o f J. P. Williamson, J r . , "The Equilibrium
Size of Marketing Plants in a Spatial Market" should be in s tru c tiv e .

25

The in te n t of his paper is to show "how the equilibrium size of
marketing plants located in a spatial market depends upon market
density" [26, p. 9 5 3 ].5
Three assumptions th at he makes are crucial fo r analyzing the
usefulness of th is approach in th is study.

F ir s t, i t is assumed that

uniform marketing exists in each producing area [26, p. 953].

To

re in te rp re t th is in d is trib u tio n rather than assembly terms would be
to say th a t uniform demand exists over each dealer a re a .6

In the more

general cases th at these authors are dealing w ith , th is assumption
seems necessary and reasonable.

To make th is assumption in Farm

Bureau's case would defeat the purpose of th is transportation analysis
because dealerships are not evenly d istrib u ted and demand by those
dealers fo r warehouse service fluctuates widely.
Another assumption pointed out in a footnote [2 6, p. 954],
is th a t a constant relationship exists between a ir distance and road
mileage.

Again, the re la tiv e unimportance of any e rro r from th is

assumption in a general study becomes r e la tiv e ly more important in
th is more specific research.
Under these and other assumptions th at Williamson makes,
"and ignoring nonuniformity of te rr a in , assembly [d is trib u tio n ] costs
w ill be minimized by assembling [d is trib u tin g ] any given quantity of
commodity from [to ] a c irc u la r supply [demand] area" [26, p. 964].
sThe volume of business per u n it of market area.
6French points out the appropriateness of th is reversal when
he speaks of "approaches used by . . . Williamson [26] [and others]
. . . , w ill be in terms o f assembly but can be reversed to apply to
d is trib u tio n a c tiv itie s as w ell" [10, p. 37].

26

A short review o f two more continuous space applications
should s u ffic e to round out the description of the techniques used
with respect to th is approach.

Boutwell and Simons [ 5 ] , applied the

following formula fo r calculating route miles (RM) once the aforemen­
tioned c irc le has been constructed.
r
0 + 2 S

RM = r +
cos

x tanG

X =1

where r = radius, R = the number o f routes to be served, and 0 = the
angle described by lines of length r dividing the c irc le into r equal
segments.7

Figure 4.

Assembly route organization and road tra v e l.

7Roads are assumed to follow paths s im ilar to the arrowed lin e
in Figure 4 [source: 7, p. 843]; and another point made by these
authors relevant to the Farm Bureau research, but not necessarily
relevant to th is part o f our discussion, is th at marginal and average
costs fo r route assembly may be constant over a considerable range of
plant volume. "Route assembly can re s u lt in constant marginal and
average assembly costs i f addition o f customers does not s ig n ific a n tly

27

Henry and Burbee present "a synthetic analysis o f space
relationships designed to determine the net effects on assembly costs
of change in (1) firm s iz e , (2) supply density, and (3) transport
distance" [14, p. 3 ].

They determine the size and number of crew-

truck complements to achieve minimum labor inputs fo r each plant size
from assembly matrices.

They study location of b ro ile r growing u n its,

truck productivity in liv e bird tran sportation, labor productivity in
loading liv e birds,
As in other
with a c irc le .

The

and truck unloading time at the plant.
continuous studies, they enclose th e ir supplyarea
area is enclosed to produce exactly the amount of

poultry th at w ill allow the centralized

plant to run at capacity. They

then assume th a t the poultry fo r eachday's pick-up w ill be from one
flock or gathered a t an impound point from many flocks.

This impound

point is such th at
a ll the poultry in a given supply band is assumed to be
located a t impound points on a c irc le which is a certain
distance inside the band. . . . Since the b ro ile rs are
located evenly over the surface of the supply band, the
problem is to locate a c irc le w ithin the supply band which
divides the area o f the band (and the quantity of poultry)
in h a lf [14, p. 38].
Therefore, in a supply c irc le with a radius o f 16.3 miles and impound
point calculated to be on an inner c irc le with an 11.5 mile radius
(see Figure 5 ), each day's route miles are calculated as being some
function of the impound point radius.
change the route structure and i f a plant can avoid completecoverage
of the area by selecting only those customers which can be added to
the route conveniently" [5 , p. 847].

r
28

■16.3 m i l e s — &)*-11.5mjles

Figure 5.

Location of impound points in supply band 1,
5,000 pounds per square mile per year density
le v e l. [Source: 14, p. 3 9 .]

I t should be noted that the problem of plant location is
e s s e n tia lly assumed away in the continuous approach.

Once the market

c irc le is constructed, a one-plant firm or industry would fin d its
optimal location a t the center of that c ir c le .

The m ultiplant solution

fo r optimal plant location becomes only s lig h tly more d i f f ic u l t .
The continuous approach is not suited fo r th is research because
demand density is not uniform and demand areas are not regular and
continuous in shape.

The Farm Bureau has also lim ited the number of

r e a lis tic choices of e ffic ie n t locations and the warehouse cost func­
tions may not be independent o f these locations.

These two missing

ingredients are essential i f the continuous approach is to be used
[10, p. 88].

29

When taking a ll relevant assumptions and conditions into
account, the a d a p ta b ility o f the continuous approach is doubtful.
The following discussion and review o f discontinuous studies adds
reinforcement to the in f e a s ib ility o f th is approach fo r the proposed
study.
Discontinuous Analysis
One of the early studies th a t f i t s th is discontinuous clas­
s ific a tio n was presented by S to llsteim er.

S to llsteim er's model was

developed to answer questions s im ila r to those in th is study.
warehouses should there be?
should they be?

Where should they be located?

How many

How large

Stollsteim er admits th a t his model does not simul­

taneously consider assembly, processing, and d is trib u tio n costs.

It

w ill only handle processing and e ith e r d is trib u tio n or assembly cost,
not both when the two la t t e r functions are d is tin c t [24, p. 632].
The essence of S to llsteim er's model can be conceptualized
graphically as in Figure 6.
He calculates minimum to ta l processing (or plant) costs (TPC)
and to ta l transportation (assembly or d is trib u tio n ) costs (TTC) and
sums of them.

He presents two cases o f economies o f scale; one with

plant costs independent of plant lo catio n , another where plant costs
vary with location and two sim ila r cases without economies o f scale.
Stollsteim er then goes on to report the effec ts o f technical change
and output expansion on the optimum number, s iz e , and location of
pear marketing f a c i l i t i e s in a C a lifo rn ia pear producing region.

r
30

TPC + TTC

TPC

TTC
l
1

2
3
4
Number of Plants

Figure 6.

S to lls te im e r's model.

L

31

The model has since been modified by Chern and Polopolus,
Ladd and Halvorson, and Warrack and Fletcher among others.

Chern

and Polopolus [8 ] modified the model by substituting a discontinuous
plant cost function fo r a continuous function, by drawing an e x p lic it
d is tin c tio n between plant numbers and plant locations, by using th e ir
maximum plant size concept and by measuring excess plant capacity in
optimal solutions.

Indications were th at these modifications show

th a t the origin al model underestimated to ta l plant cost.

Warrack and

Fletcher [25] introduced a way to solve large problems using the
Stollsteim er model by incorporating a suboptimization technique.
Ladd and Halvorson [16] present procedures fo r determining the
s e n s itiv ity of a Stollsteim er model solution and the effe cts of
continuous change in the parameters on the minimum cost solution.
Because S to lls teim er's model does not handle separate assembly
and d is trib u tio n cost functions, the transshipment model is used where
the incorporation o f both functions is important or necessary.

As

Logan and King f i r s t described i t , the basic "transportation model
is modified by specifying each production and consumption area as a
possible shipment or transshipment point" [15, p. 97 ].

These authors

were among the f i r s t to apply th is transshipment approach to ag ricu ltu re
in th e ir beef slaughter problem.
Because of important variables lik e backhauling and seasonality,
a r e la tiv e ly simple transshipment lin e a r program mushrooms into a bulky
and cumbersome mixed integer one.

Indeed, the branch and bound tech­

nique generally used in integer lin e a r program algorithms are o f such

32

a nature that th e ir cost becomes p ro h ib itiv e as soon as they acquire
any size.
The Locksett approach presented by Schruben and C lifto n [23]
is another discontinuous approach used to calculate assembly or d is ­
trib u tio n costs.

I t allows accounting fo r irre g u la r demand as well as

p a rtia l loads but as o rig in a lly defined i t does not force trucks to
fin is h d is trib u tin g near a backhaul point.
A fter assuming an i n i t i a l solution o f one round t r ip to each
delivery point,
the f i r s t step in the Locksett method is to compile a l i s t
o f a ll possible pairs o f points not involving the plant
for o r ig in ). . . . The second step is to compute the DSC
(distance-saved c o e ffic ie n t) fo r each p a ir. . . . The th ird
step is to consider join ing the p a ir with the largest DSC
on the same route. . . . The next step is to te s t the
revised route fo r f e a s ib ilit y . The te n ta tiv e pairing
must meet four tests:
a. Each stop must have a t lea st one leg connected
to the o rig in .
b. Each stop must previously have been on a d iffe re n t
route.
c. A c a rrie r o f s u ffic ie n t size must be ava ilab le
to carry the combined load.
d. A c a rrie r capable o f trav elin g the required
distance must be availab le [23, pp. 862-863].
Steps three and four are then repeated with the next largest DSC u n til
a ll DSC pairings have been considered.
Of the discontinuous approaches reviewed only the Stollsteim er
technique included the plant cost function o v e rtly .

This does not

obviously preclude, however, the calculation o f each cost function
separately.

Assembly, processing, and d is trib u tio n cost functions

could be calculated with the most appropriate methods av ailab le and,

33

f in a lly , aggregated in a manner almost exactly lik e the one used by
S tollsteim er (see Figure 7 ).

This would require existing n o n lin earities

to be obviously in s ig n ific a n t or q u an tifiab le so that the fin a l analysis
could be adjusted to include them.
Although the discussion o f the transportation cost functions
is equally v a lid fo r assembly and d is trib u tio n , the major concern in
th is study w ill be with the d is trib u tio n side.

More s p e c ific a lly , the

concern is with simultaneous minimization of d is trib u tio n and backhaulassembly costs.
The ju s tific a tio n fo r de-emphasizing the remaining assembly
variables is found in the variables' c la s s ific a tio n s .

D istribu tio n

variables are fo r the most part endogenous and c o n tro lla b le , whereas,
once the warehouse location is established, assembly variables are
almost exclusively exogenous and uncontrollable from Farm Bureau's
point of view.
I t should also be emphasized that assembly's c la s s ific a tio n
as primary exogeneous and uncontrollable is not a detriment to the
research but rather an advantage.

Once warehouse demand is determined,

assembly cost calculation becomes a straightforward task.

Prices

specific to lo c a tio n , product, volume, and timing can be extracted
from manufacturers' fre ig h t rate schedules.

r
I

34

TPC + TAC + TDC

TPC
+■>

in
o
<_>

<o

-M

O

TAC (Assembly)

TDC (D is trib u tio n )
1

2

3

4

Number of Plants
Figure 7.

A conceptual Stollsteim er approach.

35

Estimation o f Plant Cost Relationships
Approaches to estimating plant cost and e ffic ie n c y
relationships may be grouped in to :

(1) descriptive analysis of

accounting data which mainly involves combining point estimates
of average costs into various classes fo r comparative purposes,
(2) s ta tis tic a l analysis o f accounting data which attempts to
estimate functional relationships by econometric methods, and (3)
the economic engineering approach which synthesizes production and
cost relationships from engineering data or other estimates of the
components of the production function [10, p. 44].
S ta tis tic a l analysis o f accounting data w ill not be used
because data are only availab le fo r the two existing warehouses.
A sample o f two is nowhere near the number required to do s ta tis tic a l
estim ation, especially when they are very s im ilar in size and design.
A s u ffic ie n t sample would require data from numerous warehouses of
various sizes.
Descriptive Analysis
Analyses of accounting data d es crip tively are popular fo r four
reasons, y e t, are lim ited in a t le a st three ways in French's viewpoint
[10, pp. 44-49].

Descriptive analyses are popular because they are:

(1) r e la tiv e ly inexpensive, (2) e a s ily understood by plant managers,
(3) real costs not fabricated ones, and (4) inputs to more general
studies once published.

36

This type o f analysis is lim ited because d iffe r e n tia l
accounting methods e x is t th a t may f o il comparison or simply mislead
a reviewer.

Should this p a rtic u la r technique be used fo r the study,

any data that has a potential fo r being misleading or m isinterpreted
could be reworked fo r the sake of c la r it y .

In these cases, the anal­

ysis w ill go beyond mere description and become re in te rp re ta tio n .
Accountants, fo r example, can depreciate capital investments on an
equal yearly basis or with a technique th at depreciates away more of
the equity in e a r lie r years.

In e ith e r case i t is possible to have

an item o f equipment with s ig n ific a n t market value being used in a
firm long a fte r i t is o f f ic ia lly 1isted a t zero or salvage value on
the books.
Descriptive analyses are also lim ited because they don't
c le a rly id e n tify individual factors th at have influence upon the cost
function.

Other study techniques could, however, be used th a t would

id e n tify in flu e n tia l facto rs.

The lim ita tio n does hold, however, fo r

descriptive analyses alone.
L astly, descriptions are lim ited because they are snapshots
that give no parametric measures of functional relation ship s.

Again,

th is is a lim ita tio n th at would hold i f the descriptive technique was
to be used alone.

The use of th is procedure in conjunction with other

less r e s tric tiv e standard an aly tical techniques would allow insights
into parametric, fu n ctio n a l, and dynamic relationships th at could not
be discovered using the descriptive approach alone.

37

Economic Engineering
The economic engineering approach fo r use where accounting data
are not availab le was originated in the early 1940's by R. G. Bressler,
Jr.

The o rig in al studies are lis te d and summarized in his book, City

Milk D istrib u tio n [ 6 ] . 8
The nature of the approach is described by French [10, pp. 6772], as consisting of four steps.

The f i r s t step is systems description,

where the various plant stages, th e ir nature, and sequence of operation
are determined through the use of process flow charts and job descrip­
tions.

Once th is is accomplished, a lte rn a tiv e production techniques

are specified.

In th is p a rtic u la r study, the task would not lik e ly be

arduous because the range of possible technologies fo r th is type of
warehousing is lim ite d .

Farm Bureau managers are well versed in those

warehousing techniques th a t can be operationalized with a good proba­
b i l i t y of success.

Once reasonable, a lte rn a tiv e technologies have

been discovered, the th ird step is to estimate an overall production
function by combining the stage production functions.

Here, descriptive

data of past performance are used as a base point fo r establishing labor
performance standards where they are not ava ilab le .

The fin a l stage

is to synthesize the cost functions by applying facto r prices.
8A1though there have been numerous economic engineering studies
throughout the years, the classic study in the area was reported by
French, Sammet, and Bressler [1 1 ]. The authors thoroughly described
the procedure and theory behind using th is approach and then applied
i t in th e ir e ffic ie n c y study on marketing. The economic engineering
approach was used on a problem of local in te re s t by Benjamin and
Connor [3 ].

One of the main problems with the economic engineering approach
is th at i t is r e la tiv e ly time-consuming, especially where new techniques
are contemplated.

Where expected procedures are s im ila r to existing

procedures, th is approach should not be overly time-consuming because
i t would look at existing costs and how those costs might change in the
new situ a tio n .

Indeed, th is procedure fo r existing technology is almost

exactly lik e the descriptive analysis previously described with the
expectation of a b it more data manipulation.

Where new technologies

are contemplated, however, the costliness in time is apparent.

Here,

operating costs must be estimated by looking a t manufacturers1 s p e c ifi­
cations or at the costs experienced by other companies th at use sim ilar
techniques.

In those instances where the researcher is forced to work

exclusively with manufacturers' sp e cificatio n s, the task o f estimating
input-output relationships becomes especially d i f f i c u l t .

The problem

arises because o f the jo in t objective o f the manufacturer ( i . e . , that
companies not only want to measure the e ffic ie n c y o f th e ir machines
but they also want to s e ll them).

The p ractical conclusion then is

that measurements are made under the most favorable environmental
conditions.

The researcher using th is data is l e f t with the knowledge

that the data needs adjustment, but he does not have the magnitude
(and possibly not the d ire c tio n ) o f th at change.
Other alleged problems with the economic engineering approach
that are d if f ic u l t to refu te in a general manner are th at i t lacks
findings of diseconomies "a ttrib u ted to the use of constant input
co efficien ts (esp ecially fo r labor) and the in a b ility to measure or

39

account fo r coordination problems as plant scale increases" [1 0, p. 73].
Although these are hard to dispute in general in the specific Farm
Bureau case, some doubt as to the extent o f th e ir v a lid ity may be cast.
A main reason behind Farm Bureau's investigation o f a one-warehouse
system is th e ir confident b e lie f th a t coordination w ill be improved.
Their concern is whether other costs w ill o ffs e t these expected co­
ordination benefits.

The other p o in t, lack of d e fin ite pecuniary

economies and diseconomies fo r inputs, can be more d e fin ite ly refuted.
In a case where a research is dealing with one specific firm ,
input suppliers can be a source fo r the kind of price data needed.
In the specific case of labor, estimates can be made by looking at
the experience of other firms a t each proposed location.
Studies th a t use the economic engineering or synthetic firm
approach often do not declare th a t they are assuming perfect comple­
m entarity in th e ir production functions.

The assumption seems operative,

however, from the manner in which they manipulate th e ir data.

They seem

to im p lic itly assume th a t factors o f production must be present in a
certain given proportion in order to achieve given output le v e l.
The decision as to whether or not the complementarity assumption
is a c tu a lly being made is mainly normative.

Some economists, taking a

pragmatic stand, may accept engineering data as approaching a local
optimum output or a minimum cost point.

To in s is t upon the global

optimum or minimum in th e ir eyes would be to push time and d o lla r
budgets over the lim it .
a place to s ta r t.

In other words, engineering estimates give

40

Many other economists would not be s a tis fie d with local optima.
They feel that research based on such unstudied information is mis­
leading.

The former s tartin g point or pragmatic position could be

used to explain the production functions th a t are used.

The fa c t that

i t would be b etter to s ta rt by finding the high p r o fit points on each
production function is not questioned where budgets allow i t .
Black [4 ] has pointed out th a t synthetic builders should be
careful not to omit important aspects o f cost.

In the study of an

individual firm the p o s s ib ility of such an erro r should be lim ite d .
This is especially true fo r two reasons.

F ir s t, the in tric a c ie s of

a m ulti firm study are obviously elim inated.

Second, a close working

relation ship with the firm in question would allow periodic reviews
fo r accuracy.

Such a firm could not afford to base an important

investment decision on research results th at do not include a ll
aspects of cost.
Black also adds th at "the estimates derived from synthesis
are cut a d r ift from the standard measures o f r e lia b ilit y " [4 , p. 275].
This point should be kept in mind whenever the economic engineering
approach is used, as should a ll of the lim ita tio n s mentioned, and a
continuous e ffo r t made to overcome them.

In the case o f v a lid a tio n ,

data should be checked against as many a lte rn a tiv e sources of in fo r­
mation as possible in order to gain confidence in the re s u lts .

41

Systems Simulation
The systems simulations design approach is sim ila r to the
economic engineering technique ju s t discussed.

I t , too, can be used

to model systems that are planned but not ac tu a lly in existence.

The

simulation approach goes fu rth er than the normal economic engineering
approach by exhib itin g the dynamic characteristics o f the system i t
is simulating.

From another point of view, i t is only a subpart of

economic engineering in th at i t is but one method fo r acquiring the
values and parameters needed fo r th at approach.
According to Park and Manetsch [19, pp. 1 -2 ], a system
can be e ffe c tiv e ly simulated i f i t meets the following fiv e c r it e r ia .
1.

The aims or goals of the system are well enough defined so
th at they can be stated mathematically.

2.

The major process involved can be mathematically modeled.

3.

The decision-making process involved in planning and
operating the system is cen tralized .

4.

The planning horizon is long enough so that the planned
process w ill have time to be implemented and operated.

5.

The major processes have s ig n ific a n t

storage or memory effects

and response delays so th at they are dynamic.
This approach might be helpful in th is research because of the
p rio r discussion of time in the form o f rate
tio n , and scheduling.

of output, length of opera

A d d itio n a lly, the presence of ordering intervals

order lead times, and the need fo r parameter estimation d ic ta te the
need fo r a technique that w ill adequately take them into account.

42

The major disadvantages of the systems simulation approach is
its costliness and complexity.

These disadvantages follow from the

fa c t th at the basic algorithm must be b u ilt e n tire ly by the researcher,
requiring a fa m ilia r ity with the system as great or greater than that
required in economic engineering.

This approach should, therefore,

be avoided i f a simpler technique could successfully meet the
objectives set out fo r i t .

CHAPTER I I I

VARIABLE TRANSPORTATION COSTS

Discussions with Farm Bureau Management have revealed th e ir
preference fo r descriptive analyses where accounting data are availab le.
Where Farm Bureau data are not availab le ( i . e . , fo r costing out proposed
investments), other techniques w ill be selected on the basis of th e ir
a p p lic a b ility .

J u s tific a tio n fo r the approaches selected, beyond that

previously discussed, w ill accompany the specific description of that
technique.
The 1972-1973 fis c a l year data were used in th is and the ware­
house cost portion of the research, as i t was the la te s t availab le when
the study was in itia te d .

This fis c a l year was selected as the base year

fo r analysis and not updated because i t had more characteristics repre­
sentative of normal Farm Bureau operations than any of the more recent
data that eventually became av a ilab le .

Since 1972-1973 and u n til

recen tly, shortages in the economy have caused Farm Bureau Warehouse
Management to follow procedures not previously necessary or expected,
at least to such a high degree, in the fu tu re.

Storage space, fo r

example, became exceedingly more valuable because supplies, even at
abnormally high prices, had to be purchased whenever they became
available and stored u n til needed.

For th is reason a ll values

presented in th is dissertation a re, unless otherwise stated, in

T

44

1972-1973 d o lla rs .

Instances when th is procedure might cause biased

results w ill be reviewed in the fin a l chapter.
Variable transportation costs fo r the base year were calculated
to include both the variable costs of assembling product into each of
the two warehouses and o f d is trib u tin g supplies from the warehouses to
a ll dealerships.

The d is tin c tio n between assembly and d is trib u tio n

costs must be made clear as some costs re la tin g to assembling warehouse
supplies are included as part o f what w ill be called "d istinction
co sts."

Because of the advantage in using trucks th a t have delivered

dealer supplies to haul merchandise back to the warehouse rather than
make an empty return t r i p , a model o f the related d is trib u tio n cost
system must, out o f necessity, include some assembly costs.

The 96

dealerships that place the highest demand on the warehouses along with
the 11 most active backhaul points included in th is portion of the study
are 1isted in Appendix A and th e ir d is trib u tio n w ithin Michigan's lower
peninsula is displayed in Figure 8.
Variable D istribu tio n Costs
H istorical Description
A descriptive analysis o f h is to ric a l cost data are essential
as a basis fo r comparison when analyzing a ltern ativ es fo r increasing
the throughput o f the Farm Bureau warehousing system.

I t w ill not only

allow model v e rific a tio n through a comparison of the existing transpor­
ta tio n cost structure and that arrived a t in the computer model, but
w ill also be the primary source of the variable cost figures and other
parameters to be used in th a t model.

45

•
^

Dealerships
Backhaul point locales; number s ig n ifie s backhauls
availab le each week

Figure 8.

Michigan Farm Bureau dealerships and backhaul points.

46

Whenever a reference is made to variable costs, i t immediately
becomes necessary to explain the d e fin itio n used to determine that
c la s s ific a tio n .

Because the d is tin c tio n between fixed and variable

costs depend on the length of time considered, the length of time that
applies in th is case must be examined.

Here, the concern is with a

short-run situ atio n where only route configuration can be changed.
A ll other variables, including plant location and technology
configuration, are fixed .
The major variables that flu ctu ate d ire c tly with number of
miles traveled include d rivers' s a la rie s , truck re p a irs , normal pre­
ventive maintenance, petroleum usage, tire s and tubes.

On the other

hand, items lik e adm inistrative s a la rie s , licenses, and leasing
expenditures (long-term leases with purchase options) are generally
fixed w ithin a lim ited range of the number o f miles traveled.
Table 1 shows the fixed and variable costs taken from actual
accounting data broken down as described above.

With the to ta l yearly

variable costs at $156,150.00, the average weekly variable cost would
be $1,253.25.

With to ta l truck miles fo r the year o f 315,992, the

variable cost per mile is approximately $0.50.

Appendix B shows the

existing routes with th e ir associated demand, m iles, and cost
calculation.
By applying the $0.50 per mile of variable cost to the current
fixed route stru ctu re, the resulting weekly variable cost is $1,606.00
for Jenison and $1,506.50 fo r Zilwaukee or a to ta l weekly variable
d is trib u tio n cost of $3,112.50, $109.61 over the actual variable cost.

47

Table 1.

C la ssificatio n of Yearly Fixed and Variable Transportation
Costs fo r the Michigan Farm Bureau
1972-1973 Total
Transportation Costs
($)

Expenses

Average Costs
(£/m ile)

FIXED COSTS:
Payroll general
Payroll outside labor
FICA
MESC
Unemployment
Blue Cross
Group Insurance
Workmen's Comp.
Retirement & contrib.
Travel dept, head
Travel
Licenses
O ffice supplies
Plant supplies
Telephone & telegraph
Dues & subscriptions
Training
Outstate use tax
Insurance trucks
Truck lease
Tractor rental
Equipment rent
Depreciation trucks
Mi seellaneous
Subtotal

18,068
1,143
4,145
1,743
230
1,855
879
2,086
4,349
734
1,811
5,263
844
1,331
4,042
486
187
420
4,105
14,936
4,736
283
10,649
914
85,239

5.71
0.36
1.31
0.55
0.07
0.59
0.28
0.66
1.38
0.23
0.58
1.67
0.27
0.42
1.28
0.15
0.06
0.13
1.30
4.73
1.50
0.09
3.37
0.29
26.98

76,447
105
34,662
21,164
11,205
1,375
281
9,664
1,247
156,150

24.19
0.03
10.97
6.70
3.55
0.44
0.09
3.06
0.39
49.42

VARIABLE COSTS
Payroll trans.
Repairs & upkeep machinery
Repairs & upkeep trucks
Gas & o il
Tires & tubes
Truck expense
Road service
Normal maintenance
T r a ile r rental
Subtotal
TOTAL

Source:

241,389

"Statement o f Operations and Margins, Transportation,"
June 31, 1973.

48

This derived cost is close to the actual weekly variable cost and
leaves less than 4 percent error to be accounted fo r by deviations
from the specified routes, errors in distances used, and other
measurement errors.
The Model
The objective of th is portion o f the study was to build a model
that would approximate the cost structure of the existing transportation
system by constructing reasonably r e a lis tic routes.

Once the model was

v e rifie d in th is manner, i t was used to construct routes fo r proposed
a lte rn a tiv e one-warehouse systems.

The to ta l variable cost figures fo r

each a lte rn a tiv e were then on a common basis of comparison with the
existing system.
Selecting a model that meets these objectives is not a simple
task, especially because of the previously mentioned problems with
irre g u la r dealer demand, p a rtia l loads, and backhaul points.

The

S tollsteim er, simple transshipment, and mixed integer transshipment
models must be dismissed from consideration because of oversimplifying
assumptions or the high computational costs that res u lt when they are
adapted to include the above troublesome areas.
The Lockset model, however, was modified to force trucks to
fin is h th e ir d eliveries near a backhaul point by simply adding a f i f t h
re s tric tio n to the f e a s ib ilit y check.

With th is change i t not only

forced routes to properly include backhaul points but i t also accounted
fo r irre g u la r dealer demands and p a rtia l loads.

In addition to s a tis fy ­

ing these requirements, i t could be implemented without p ro h ib itive
computational time or cost.

49

The f i f t h re s tric tio n required that any backhaul point included
in a route have at least one leg connected to the o rig in .

The model was

also altered to use dollar-saved coefficien ts so i t not only re fle c ts
the fa c t that savings resu lt by joining dealerships into routes but
also that money is made (costs o ffs e t) by adding backhaul points to
the routes.
The model divides d o lla r demands fo r each of the 16 product
groups by conversion factors (see Appendix C) to a rriv e a t cubic feet
demands fo r each o f the 16 categories by dealer.

Summing the 16 product

group demands give the weekly demand fo r each dealer in cubic fe e t (see
Appendix D).
The individual products were divided into these 16 categories
by grouping items of sim ilar size to the extent possible.

Once th is

was completed, conversion factors were calculated by selecting repre­
sentative products from Farm Bureau's "Wholesale Location Inventory
Status Report," February 11, 1974, fo r each product group according
to three indicators of importance.

A product was considered repre­

sentative of a product group i f i t exhibited e ith e r high inventory
value, large quantities on order, or frequent shipments in the p rio r
12 months.

Conversion factors fo r each representative product were

then calculated by dividing its size in cubic fe e t into the u n it price.
To a rriv e at the required group conversion factors each representative's
conversion facto r was weighted according to its importance w ithin the
group as indicated by d o lla r value.

Demand in cubic feet could then

be acquired from the division of each group's to ta l d o lla r demand by
its weighted conversion factors.

50

I n i t i a l l y , the model assumes one route fo r each dealer as in
the unmodified model.

With th is as a s tartin g point, d o lla r saved

c o efficien ts are calculated that indicate the number of dollars th at
could be saved by combining dealers to reduce the number o f routes.
Any dealer whose demand is greater than the maximum allowed on one
t r a i l e r is lis te d as a round t r i p , one-dealer route.

The residual

demand is then recorded so th at th is dealer can la te r be included in
a m ultip le-d ealer route.

Restrictions applied to the program keep the

to ta l cubic volume carried on one route under some maximum volume and,
of course, force any backhaul component to come a t the end of a route.
Until a backhaul is included, the route is not d ire c tio n a l.

Once one

is included, however, the route is obviously directio n al and must go
in the direction th at would put the backhaul la s t on the route.
This method does not guarantee the "one" minimum cost routing
structure.

I t may, therefo re, be possible to rearrange the ordering

of the dealerships w ithin a route to gain some saving.

The model does,

however, meet the objective o f giving a common basis fo r comparison in
evaluating a lte rn a tiv e s .
Model V e rific a tio n
In order to be va lid i t was necessary to construct the model
so that i t would approximate current average truck capacities as well
as variable costs.

This was important in order to have a model that

re fle c ts the current level o f technology and management.

Using the

demand fig u re s , calculated as previously explained, the current system

51

showed Zilwaukee with average truck capacities of 47 percent and 48
percent and Jenison with 49 percent and 54 percent, respectively, fo r
the f i r s t and second h a lf y e ars.9

With these capacities as startin g

points, the model was adjusted u n til resulting average capacities and
to ta l variable d is trib u tio n costs re fle c te d , as closely as possible,
those ac tu a lly encountered in the warehousing operation.
The results of this comparison process are summarized in Table 2.
Discrepancies between actual and modeled average capacities of up to 7
percent were experienced, although, the average model capacity fo r the
system as a whole f e l l within 3.5 percent o f the a ctu al.

The modeled

average route capacities were obtained by establishing maximum capac­
itie s th a t would force acceptable average capacities.

A 60 percent

maximum fo r the Jenison model and one of 50 percent fo r the Zilwaukee
model yielded the averages reported.

In evaluating the one-warehouse

a lte rn a tiv e , a 54 percent maximum capacity was used.

This fig ure rep­

resents an average of the Jenison and Zilwaukee maximum numbers weighted
by the amount of demand experienced by the two.
Total weekly variable d is trib u tio n costs, when modeled with
the above maximum capacities, f e ll within 4 percent of the derived cost
and were less than .01 percent over the actual accounting cost.

This

close f i t allowed the acceptance of the modified model as a v alid tool
fo r evaluating the d is trib u tio n costs fo r each o f the seven proposed
one-warehouse locations.
9These averages were calculated on the current tr u c k -tr a ile r
capacities o f 2,400 cubic fe e t.

52

Table 2.

Weekly Cost and Capacity Averages: A Comparison fo r
V e rific a tio n with 1972-73 Fiscal Year Data
Average Truck
Capacities

Route Costs
Derived9
($)

Actual9
($)

Modeled
($)

Actual

Modeled

(%)

{%)

49
47

49
42

1,628.50
1,378.50

54
48

47
46

1,624.50
1,377.50

Jenison
Zilwaukee

51.5
47.5

48
44

1,606.00
1,517.50

TOTAL

49.5

46

3,123.50

F irs t H alf Year
Jenison
Zilwaukee
Second H alf Year
Jenison
Zilwaukee
Yearly Averages
1,626.50
1,377.75
3,002.89

3,004.25

The derived costs come from applying $0.50 per m ile to the
existing routes' m iles, whereas the actual costs represent l/52nd of
the actual transportation costs reported fo r the year.

53

Results
Figure 9 illu s tra te s a few of the route configurations that
resulted from the modeling process fo r one o f the single warehouse
a lte rn a tiv e s .

In general, the model appears to be using a logical

approach, although some of the connections selected may be improved
upon s lig h tly .
Table 3 lis ts the 1972-1973 cost results fo r the seven
altern atives considered.10

Examination of Table 3 reveals th a t only

St. Johns, of the alternatives evaluated, had an absolute savings over
the current system with respect to variable d is trib u tio n costs in the
f i r s t h a lf year, while no one-warehouse a lte rn a tiv e was less costly
than the existing system in the second h a lf year.

An averaging of the

two h a lf years1 weekly costs shows an absolute advantage fo r the current
system, ranging from a $22.25 to a $256.75 savings depending on which
one-warehouse a lte rn a tiv e cost is used.

Because o f the possible errors

which can be related to inaccuracies in mileages

used, averaging erro rs,

as well as other observation and measurement erro rs, th is difference
should not be c la s s ifie d as s ig n ific a n t.

In fa c t, such a small d i f ­

fe re n tia l may have occurred as ea sily in the opposite d ire c tio n .

The

conclusion, resulting from the fig u re s , can only be interpreted as
showing e s s e n tia lly no difference.

This is made especially obvious

because the highest cost a lte rn a tiv e is only 8.54 percent above the
weekly costs th at occur in the existing system.
10For a complete lis tin g of the route configurations from which
the costs were calculated, see Appendix E.

54

A

= Proposed Lansing location.

•
(

= Dealerships

J =

Backhaul point locales; number s ig n ifie s backhauls availab le
each week.
Figure 9.

Sample of lockset derived routes.

Table 3.

Modeled Weekly V a ria b le D is trib u tio n Costs f o r 1972-1973

Seven Proposed Locations
Current St. Johns
System

Lansing

Ionia
.............-

Alma

Climax

Jenison

Zilwaukee

$ ...............

F irs t Half Year
Jenison
Zilwaukee
TOTAL

1.628.50
1.378.50
3,077.00

2,983.00

3,101.50

3,099.00

3,127.00

3,273.00

3,250.50

3,258.50

1.624.50
1,377.00
3.001.50

3,062.00

3,072.50

3,147.50

3,079.50

3,225.00

3,254.50

3,263.50

1,626.50
1,377.75
3,004.25

3,022.50

3,087.00

3,123.25

3,103.25

3,249.00

3,252.50

3,261.00

Second Half Year
Jenison
Zilwaukee
TOTAL
Weekly Average
Jenison
Zilwaukee
TOTAL

56

1979-1980 Analysis
Farm Bureau's problem stems from an expected need rather than
a current f e l t need.

I t is , therefore, necessary to evaluate the

a lte rn a tiv e transportation systems with the changes th at are projected.
A major portion of th is change is reflected by the projected demands
presented in Table 4.

They were put together out of the "Farm Supply

Division Five-Year Projections:

July 1, 1974-June 30, 1979" [20] and

a meeting with Farm Bureau Management.

The purpose of the meeting was

to update the projections through June 30, 1980 and to determine the
d iffe re n tia l impact of the projections on the transportation systems,
both actual and proposed.
Given th is information, a two-step task remained before the
desired projections were ready fo r use.

F ir s t, the demand projections

fo r 1979-1980 had to be updated to include petroleum products th at were
not previously included in the projections.
Rather than construct new product groups, petroleum products
were included in previously defined groups displaying characteristics
sim ilar to the new petroleum products.

The second part of the task was

to d eflate the projections which are stated in 1973-1974 dollars back to
1972-1973 d o llars.

For the price indexes used, see Table 4.

Conferences were held with Farm Bureau Management to determine
what possible changes might occur as the re s u lt o f moving to a onewarehouse system.

The l i s t of these changes along with some estimates

of th e ir impact fo llo w s .11

The d o lla r value savings estimates

11 Impact estimates were provided by those people in the Farm
Bureau system who were e ith e r most closely a llie d to the proposed
change or who were most lik e ly to have knowledge about i t .

Table 4.

P rojected 1979-80 Warehouse Demands in Cost o f Sales D o lla rs 9

Product Group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

F e r tiliz e r
Seed
Feed
Medicinal supplies
Chemicals
Roofing
Panels and accessories
Building cosmetics and o il
Posts, poles and lumber
Fence
E lectric fence
Bulkies
Flexibles
Tools
Semi-miscellaneous
Miscellaneous

1972-73 Demands

1979-80 Demands*5

36,803.75
360,133.24
1,228,487.71
529,039.91
1,138,015.06
89,723.89
41,180.09
69,163.51
365,269.72
263,296.00
68,206.88
45,162.83
132,882.74
27,632.56
119,982.19
1,005,234.14

18,438.69
495,082.35
1,044,828.70
979,887.71
4,791,849.80
129,686.91
59,521.70
100,970.08
527,960.84
380,568.40
98,586.22
883,671.53
192,068.71
39,940.10
131,380.49
1,501,135.30

Percent
Change

1973-74
Price Index

49.90
137.47
85.00
185.22
421.07
144.54
144.54
145.99
144.54
144.54
144.54
1,956.63
144.54
144.54
109.50
149.33

125.3
126.4
128.0
115.2
112.6
118.4
118.4
118.4
118.4
118.4
118.4
115.2
115.2
115.2
115.2
115.2

aAll numbers are in terms of 1972-73 dollars.
In the projections the new petroleum items are added as tire s and equipment in "bulkies,"
antifreeze in "chemicals," motor o il and grease in "building cosmetics and o il" and f ilt e r s and
miscellaneous petroleum in "miscellaneous."
cThese indices are in 1972-73 dollars. They were calculated from the "Agricultural
Prices" monthly. They were required to deflate 1979-80 demand projection made in 1973-74 dollars
to 1972-73 dollars.
^The Farm Supply Division expects to sell more f e r t i li z e r in 1979-80 than in 1972-73, but
much more of i t w ill be shipped d ire c tly to the dealers, by-passing the warehouse.

58

presented in th is section are to ta lly the product of Farm Bureau
calculations.

The following two changes dealt d ire c tly with the

transportation system.12
1.

Reduce t r a c t o r -t r a ile r ra tio from two and one-half tractors
per t r a i l e r to two.

This would save $200.00 monthly in lease

charges on three t r a ile r s or $7,200.00 per year.

This is equal

to $5,373.13 in 1972-1973 d o lla r s .13
2.

Eliminate interwarehouse transfers.

Management estimates

a $12,000.00 savings or $8,955.22 savings in 1972-1973 terms.
The to ta l savings o f $14,328.35 results t o t a lly from the elim ination
of costs th a t are unique to the two-warehouse system.
1979-1980 Results
Beyond these extern ally generated estimates, the projected
analysis showed l i t t l e s ig n ific a n t change from the 1972-1973 r e la ­
tionships (see Table 5 ).

Even the s lig h t advantage held by the

two-warehouse system is neutralized by the $14,328.35 of annual
interwarehouse-transfer and t r a il e r savings.
An important discovery was made, however.

Without the trans­

portation model, one might have anticipated an increase in transporta­
tion costs proportional to the increase in d o lla r demand.

The model

12Other projected changes w ill be more appropriately presented
la te r .
13For these two d eflatio n adjustments a d eflatio n facto r of 1.34
with 1972-73 equal to 100 was used. The value was calculated from price
indices in "Economic Indicators," April 1975.

Table 5.

Molded Weekly V a ria b le D is trib u tio n Costs fo r 1979-1980

Seven Proposed Locations
Current System
St. Johns

Lansing

Ionia
..........

Alma

Climax

Jenison

Zilwaukee

$ ...............

F irs t Half Year
Jenison
Zilwaukee
TOTAL

1.756.50
1,585.00
3.341.50

3,491.00

3,618.00

3,624.50

3,532.00

3,802.50

3,897.00

3,643.50

1,758.00
1.575.50
3.333.50

3,508.50

3,707.50

3,609.00

3,677.00

3,948.00

3,946.00

3,710.50

1,757.25
1,580.75
3,338.00

3,499.75

3,662.75

3,616.75

3,604.50

3,975.25

3,921.50

3,677.00

Second Half Year
Jenison
Zilwaukee
TOTAL
Weekly Average
Jenison
Zilwaukee
TOTAL

I
i-

60

demonstrated otherwise.

I t showed an increase in variable d is trib u tio n

costs of s lig h tly over one-third.

Investigation shows th at th is

unexpected outcome results from the relationship between conversion
factors and projected demand increases.

This can be e as ily explained

because products with high d o lla r values per cubic foot are expected
to increase more than those with s im ila rly measured high d o lla r values.
This explanation th at is so obvious expost was very un likely to be
discovered ex ante.

Table 6 shows the comparison between volume and

d o lla r demand increases from 1972-1973 to 1979-1980.
Variable Assembly Costs
Calculating the variable assembly costs fo r each a lte rn a tiv e
was a f a ir l y straightforward process.

The i n i t i a l step was to extract

the quantity values fo r those items with variable inbound fre ig h t rates
(see Table 7) from the Farm Bureau accounting data computer tape.

These

quantities were then converted to th e ir weight equivalents by determin­
ing the weight per u n it fo r each product in a group.

These raw conver­

sion factors were then weighted by the percent o f each product's value
over the to ta l group value to give a group conversion facto r (see
Table 7 fo r the specific numbers).

The remaining calculation was

simply a matter of m ultiplying weight equivalents times rate per
hundred pounds to get the variable assembly costs (see Table 8 ).
Only the product groups lis te d in Table 7 were included because
only they have inbound fre ig h t rates th a t vary with respect to location.

i

, .

61

Table 6.

Predicted Farm Bureau Product Demand Increases in Cubic Feet
from 1972-73 to 1979-80
Demand in Cubic Feet

Product Group

1979-1980

1972-1973

1

F e r t iliz e r

20,446.5

10,243.7

2

Seed

54,565.6

75,012.5

3

Feed

767,804.8

653,017.9

4

Medicinal supplies

50,869.1

94,220.0

5

Chemicals

31,524.0

132,738.2

6

Roofing

4,398.2

6,357.2

7

Panels and accessories

1,855.0

2,681.2

8

Building cosmetics

7,057.5

10,303.1

9

Post poles and lumber

114,146.8

164,987.8

10

Fence

105,318.5

152,227.4

11

E le c tric fence

4,210.3

5,910.0

12

Bulkies

15,054.3

294,507.3

13

Flexibles

9,770.8

12,679.6

14

Tools

8,373.5

11,676.9

15

Semi-miscellaneous

29,264.0

32,044.1

16

Miscellaneous

108,089.7

161,410.3

1,332,748.6

1,820,017.2

TOTAL

D ollar Demand Increase

Volume Demand Increase

W = 2- 064

g

}

I

) J j u )

/ 4o* 0 TX

= I - 366

62

Table 7.

Products with Variable Inbound Freight Rates
Pounds/Unit

Quantity

Product

9.50

129,765 posts

Steel posts
Treated lumber

50,675 boards

53.86

Steel roofing

45,947 sheets

21.60

Fencing

20,615 ro lls

181.20

Dog and cat

73,019 bags

37.00

Mineral

50,407 bags

50.00

Molasses

18,616 bags/barrels

50.00
63.00

150,342 bags

Salt

A ll other products carried in warehouse inventory have a f l a t rate fo r
delivery into Michigan.

The figures presented here w i l l , therefo re, not

r e fle c t to ta l assembly costs but w ill r e fle c t any advantage that one
location might have over another in assembling products from
manufacturers.
In order to calculate projected d iffe r e n tia l assembly costs,
i t was necessary to estimate increased requirements fo r those items
featuring variable inbound fre ig h t rates.

For th is calculation i t was

assumed th at the 1972-1973 to 1979-1980 increase would be proportional
to the demand increase projected fo r the product groups that include
those items.

Once these values were availab le the assembly cost

calculations were repeated fo r the 1979-1980 fis c a l year.

Table 8.

V a ria b le Inbound Michigan F re ig h t Rates

Product

B. Creek

Ionia

Jenison

---------------------------------------------Steel posts
Fence
Steel roofing
Treated lumber
Dog food:
Wells
A1bers
Mineral
Molasses
Soy bean meal
Limestone
Salt:
Marysville
Manistee

Lansing

St. Johns

Zilwaukee

Alma

<£/cwt.---------------------------------------------------

0.47
0.70
0.47
1.07
0.69 excess

0.43
0.47
0.43
1.04
0.67 excess

0.45
0.67
0.45
1.04
0.67 excess

0.49
0.72
0.49
1.05
0.68 excess

0.53
0.78
0.53
1.09
0.69 excess

0.52
0.75
0.52
1.09
0.69 excess

0.65
0.88
0.29
0.27
0.40
0.51

0.66
0.90
0.34
0.29
0.43
0.53

0.66
0.92
0.34
0.32
0.42
0.51

0.67
0.94
0.34
0.27
0.44
0.52

0.67
0.94
0.34
0.32
0.445
0.53

0.67
0.94
0.39
0.38
0.60
0.56

0.67
0.94
0.34
0.27
0.46
0.56

0.39
0.42

0.37
0.33

0.42
0.31

0.32
0.39

0.32
0.38

0.28
0.37

0.37
0.32

0.41
0.46
0.41
1.00
+0.66 excess

aThe original 60,000 pounds costs $1.00 or more per pound but that over 60,000 pounds costs
less than $0.70 per pound.

64

The variable cost calculation results are presented in Tables 9
and 10 along with the yearly d is trib u tio n costs fo r each of the seven
*

alternatives evaluated.

Again, as in the d is trib u tio n cost case, no

p a rtic u la r location has an obvious major advantage.

The 1972-1973

assembly costs show only a possible 6.4 percent savings or 3.8 percent
added cost with respect to the current system, across the range of
alte rn a tiv e s.

The assembly calculations fo r the increases projected

for 1979-1980 show e s s e n tia lly no r e la tiv e difference from the 19721973 comparisons.
Total Variable Transportation Costs
In the fin a l analysis the s lig h t advantage held by the current
system in assembling products turns into a small disadvantage when the
one-warehouse transportation savings (including the variable interware­
house tran sfer savings and the fixed cost savings from the reduced
t r a ile r requirement) are considered.

Across the seven a lte rn a tiv e

warehouse locations the to ta l variab le transportation costs exh ib it
a range of from 3.9 percent savings to a 1.3 percent added cost when
compared to the current system fo r 1972-1973 and 3.2 percent to 0.7
percent fo r the same range in 1979-1980 (see Tables 9 and 10).

It

seems lik e ly that few modeling processes with th is degree of in tric ac y
could claim to be accurate enough to consider as s ig n ific a n t a savings
of less than 4 percent.

Relationships o f th is small magnitude could as

easily be reversed because of measurement erro r alone.

Table 9.

Total Variable Transportation Cost Comparison, 1972-1973
Two-Warehouse System

Item

Actual

Modeled

One-Warehouse System Proposed Locations
St. Johns

Lansing

Ionia

Alma

Climax

Jenison

Zilwaukee

■.... $ —
Total variable distribution.

156,175.00

156,221.00

Distribution saving with
one warehouse (-) = cost
1972-73 total variable
assembly

118,474.00

Assembly savings with
one warehouse
TOTAL VARIABLE
TRANSPORTATION COST

Savings or cost
Less $14,328.35 trailer
and transfer savings

274,721.00

---

157,170.00

160,524.00

162,409.00

161,369.00

168,948.00

169,130.00

169,572.00

-949.00

-4,303.00

-6,188.00

-5,188.00

-12,727.00

-13,429.00

-13,351.00

121,197.00

117,698.00

120,517.00

123,122.00

112,921.00

110,924.00

122,961.00

-2,723.00

776.00

-2,043.00

-4,648.00

5,553.00

7,550.00

-4,487.00

278,367.00

278,222.00

282,922.00

284,491.00

281,869.00

280,574.00

292,533.00

-3,672.00

-3,527.00

-8,227.00

-9,796.00

-7,174.00

-5,879.00

-17,838.00

10,656.35

10,801.35

6,101.35

4,532.35

7,154.35

8,449.35

-3,509.65

Table 10.

Total Variable Transportation Cost Comparison, 1979-1980
Two-Warehouse
System

Item

Modeled

One-Warehouse System Proposed Locations
St. Johns

Lansing

Ionia

Climax

Jenison

Zilwaukee

$ ....... -

1979-1980 Costs
Total variable distribution

Alma

173,550.00

181,987.00

190,463.00

188,071.00

187,434.00

201,513.00

203,918.00

190,684.00

-8,437.00

-16,913.00

-14,521.00

-13,884.00

-27,963.00

-30,368.00

-17,134.00

138,996.49

134,216.54

137,932.22

142,056.29

124,625.31

123,745.50

142,719.61

4,307.32

9,087.27

5,371.59

1,247.52

18,678.00

19,558.31

584.20

320,983.49

324,679.54

326,003.22

329,420.29

326,138.81

327,663.50

333,403.61

Differential cost

-4,129.68

-7,825.73

-9,149.41

-12,636.48

-9,285.00

-10,809,69

-16,549.80

Less $14,328.35 trailer
and transfer savings

10,198.67

6,502.62

5,178.94

1,691.87

5,043.35

3,518.66

-2,221.89

Distribution cost with
one warehouse
1979-80 total variable
assembly

143,303.81

Assembly savings with
one warehouse
TOTAL VARIABLE
TRANSPORTATION COST

316,853.81

67

To th is point, the lack o f apparent advantage fo r any
a lte rn a tiv e only serves to emphasize the importance of three other
a c tiv ity sets.
F ir s t, the importance of factors such as average truck capacity,
number of d eliv e rie s from manufacturers to warehouses, savings from
quantity buying, supplier mix, and the portion of to ta l supplies
available from each supplier are stressed.
Second, the importance of the remaining warehouse engineering
and cost estimation study is emphasized.

I t should play a s ig n ific a n t

role in estimating the impacts of two o f these fa cto rs , namely, inbound
supply runs and quantity buying.
Quantity buying is important because one of the items with a
variable inbound fre ig h t rate could p o te n tia lly experience a change in
its average price per hundred pounds.

Treated lumber has one rate fo r

60,000 pounds or less and a reduced rate fo r th at amount over 60,000
pounds.

In an 80,000 pound load, fo r example, the reduced rate applies

only to 20,000 pounds.

I f the average load size changes with a one-

warehouse system, the costs should be modified to correspond to that
change.

The warehouse cost study w ill give

an indication o f the

likelihood fo r th is kind of change in its comparison of the average
monthly inventories carried in the one- versus two-warehouse system.
A sim ilar indication can also be obtained with respect to the number
of inbound supply runs.

These variables w ill not, of course, e ffe c t

the re la tiv e attractiveness of any one proposed location but w ill have
an impact on the d e s ira b ility of the one-warehouse system.

The other three factors w ill not be quantified but should be
evaluated subjectively i f they deviate from what was assumed about them
in this analysis.
Any substantial change in average truck capacities w ill lik e ly
a ffe c t the d is trib u tio n cost in the opposite direction of that change.
Should th is average increase, more dealers could be included in one
route.

This would lik e ly lead to a decrease in d is trib u tio n costs.

Farm Bureau does not expect th is kind of change, however.

I t is th e ir

experience th at the extra time and expense required to load the trucks
more f u lly is not ju s tifie d by the savings that re s u lt.
fre ig h t rate fo r dog food is a function o f its source.

The inbound
Currently,

90 percent of this product is supplied by a single supplier, and 10
percent by another supplier.
accounted fo r.

Again, any change in this mix should be

Because two s a lt suppliers are now being used, i t was

assumed that each proposed location could acquire a ll the s a lt they
would need from the closest supplier.

Any deviation from this assump­

tion should also be considered.
The la s t a c tiv ity set is the group o f factors not included up
to this point in the study.

Factors such as a v a ila b ility and cost of

land, size of labor fo rce, reaction of current employees, environmental
considerations, and management's personal preferences become r e la tiv e ly
more important.

CHAPTER IV

VARIABLE IN-WAREHOUSE COSTS

In analyzing variable warehouse operating costs i t is
necessary to evaluate the proposed one-warehouse a lte rn a tiv e that
does not have an established cost structure.

For th is reason some

approach designed to predict nonestablished costs is required.

C learly,

the economic engineering technique has the advantage in th is area.
Chapter I I la id out the advantages of using a systems approach
fo r calculating parameters th at display dynamic characteristics lik e
those o f the Farm Bureau warehousing system, when the extra time and
cost can be ju s t ifie d .
The added benefits from the knowledge that would be gained
about factors lik e rate o f output, length of operation, scheduling,
ordering lead times, ordering delays, and storage in the simulation
process is thought to fa r outweigh the added costs.

Even with simu­

la tio n , an awareness must be maintained to avoid assuming independency
where i t does not e x is t.
The Nature of the Simulator
The simulator used in th is research is macro-dynamic in nature.
The dynamism follows from the importance of delays and interdepend­
encies between time periods as was previously discussed.

69

I t is a

70

macro-simulator despite the fa c t that i t studies the individual firm ,
a micro-economic e n tity .

The macro c la s s ific a tio n holds because the

id e n tity o f individual units are lo s t in the process of aggregating
over individuals and product lin e s .

Although, th e o re tic a lly , i t is

possible to model the system on a micro level the costs of engaging
in such a tedious task fa r outweighs the benefits.

This is especially

true when the simpler macro approach is adequate.
Products were aggregated into product groups according to
s im ila ritie s in th e ir three-dimensional measurements to f a c ilit a t e
space requirement calculations.

Therefore, a ll related parameters

are aggregated in the same manner out of necessity.
Worker productivities were aggregated in that the values used
were those o f the work group, not individual workers.
required special attention to work group structure.

This aggregation
Should a two e ig h t-

hour s h ift system be implemented with s p e c ia liza tio n , fo r example, where
the day s h ift unloads and stows and the night s h ift selects and loads,
the average group productivities may increase, other things being equal.
In the simulation portion o f th is research two types of problems,
design and id e n tific a tio n , were faced.
extent, already been discussed.

The design problem has, to some

A design problem is one that requires

simulation o f a system th at does not e x is t.
or b u ilt from scratch.

The system must be designed

The "Economic Engineering" section of Chapter I I

discussed the theory related to that technique as well as how i t could
be extended into a dynamic simulator.

71

The design problem was made easier by f i r s t solving an
id e n tific a tio n problem.

An id e n tific a tio n problem requires the use

of the system's inputs and outputs, together with knowledge of the
system i t s e l f to find equations th a t w ill simulate the system.

By

f i r s t iden tifying the existing two-warehouse system, economic engi­
neering principles can then be applied to make incremental changes
in the model of the existing system so th at i t would r e fle c t the
structure of the proposed one-warehouse system.
A theoretical foundation fo r constructing the id e n tific a tio n
model was obtained through a seven-step approach suggested by Park and
Manetsch [19, pp. 18-12, 18-14].
The steps are presented in the form of seven questions as to
the nature of the id e n tific a tio n problem.

Five of those questions and

the answers th at apply in the case of th is research follow .
1.

What are the variables and how are they modeled?
a.

Controllable input variables include order s iz e , order
frequency, number of laborers, delivery s iz e , delivery
frequency, inventory mix, and the number of dealers
served, among others. The variables can be modeled in
a very straightforward manner using d o lla r amounts, counts,
and time intervals fo r example.

b.

Disturbance variables or noise is very low or nonexistent
so that measured inputs and outputs w ill be very close to
the actual ones.

c.

Inventory le v e l, plant s iz e , and plant costs are three
major output variables fo r th is portion of the model.

d.

Internal state variables include labor p ro d u c tiv itie s ,
portion of variable as opposed to fixed labo r, warehouse
capacity, size and frequency of assembly c a rrie rs , farmerconsumer demand, and prices and wages.

What is known about the system structure?
a.

The system is dynamic because of the inherent importance
of delays and storage to a warehousing system. Also, a
mathematical integration technique w ill be necessary to
determine stocks from flows. Such c la s s ific a tio n s must,
in th is case, come from p rio r knowledge of the system.

b. The system is lin e a r in th is id e n tific a tio n stage. In
the design stage n o n lin ea rities must be watched fo r
because the stages are independent except fo r the flows
between them. In the current system the flows are com­
p a tib le , so a production function fo r the system can be
obtained by aggregating the stage production functions.
In the design stage, however, combining stage production
functions may cause to ta l costs to be greater than the
sum of the stage costs in cases where bottlenecks occur
between stages.
c.

The model has one
well as lags th at
The system's main
bundles so th a t a
indicated.

main delay in the ordering process as
re s u lt when work loads get too large.
inputs and outputs move in discrete
model with discrete components is

d.

This model must r e fle c t more than input/output behavior.
The behavioral structure must be refle cte d fo r the la te r
purpose of changing the structure to simulate the impact
of expected technological and demand change.

W ill the simulation be o n -lin e , connected d ire c tly to the
warehousing operations, constantly receiving data updates?
This procedure w ill not use an on -lin e approach. Instead,
an o f f -lin e approach w ill be used to condense the analysis
of data representing a one-year history of warehousing
operations into a few seconds of computer time.
What c r ite r ia fo r estimation are satisfactory?
To validate th is model the output need only be kept
w ithin an error bound around the actual data.
What are the properties o f the stimator?
The estimator should be corrected fo r any bias ( i . e . , i t
should be unbiased) although a biased estimator would be
s u ffic ie n t i f a constant could be added to make i t track

73

actual outputs. Here, fo r example, the demand
represented by the 96 sample dealers was obviously
less than to ta l demand of the e n tire dealer population.
Knowledge o f the to tal demand allowed the implementation
of the correction procedure mentioned above; a constant
was added to correct the demand input. The variance
need only be acceptable, not best. Sufficiency is a
property th at w ill not be employed except to say that
the estimator w ill have to provide a minimum of in fo r­
mation. The minimum w ill be that amount of information
deemed minimally necessary to make the desired comparison.
Further investigations of model parameters and assumptions can
occur on two le v e ls.

F ir s t, there are those assumptions made when

constructing the mathematical model before computerization.

Second,

at the next highest level of abstraction, more assumptions may be
required as the model is computerized.

Therefore, rather than discuss

the assumptions in two places, they w ill a ll be analyzed within the
computer model presentation.
The Modeling Procedure
Generally, the model as described in the block diagram of
Figure 10 is designed to calculate variable operating costs and give
approximations fo r labor requirements, inventory strategy, and warehouse
size fo r a proposed one-warehouse system.

A d d itio n ally , i t serves to

evaluate the inventory strategy presently being used.
With th is b r ie f, general purpose as a foundation, a more
specific view of how the model works and how i t f i t s into the research
scheme w ill follow .

ORDER
DELAY
DEALER
DEMAND

YES

QUANTITY
ORDERED
NOT YET
RECEIVED

ORDERING
OAY

SPACE
SIZE

YES

WAREHOUSE
SIZE

INVENTORY
DESIRED
INVENTORY
QUANTITY
RECEIVED

INTEREST
RATE

RECEIVING

INVENTORY CARRYING
COST

AND
STOWING
PROCESS

INVENTORY
' STRATEGY
' COST

STOCK
OUTS
PRODUCTIVLABOR

SELECTION

PRODUCTIV

STOCK-OUT
PROFIT LOST

AND

LABOR

HARK

LOADING
PROCESS

LOST
REVENUi

f OFFICE >
' LABOR
iPRODUCTIVSTOCK

SHORT
HANDED

YES

*TY

OUTS

VARIABLE
COST/PER
DEMAND
s. DOLLAR .

MEN
NEEDED

V

WAGE
RATE

f VARIABLE
iCOST/HOUR

WAGE
RATE

PART OF
YEAR
SHORT
HANDED
toGT. LABOR'
PRODUCTIVl ITY j

YES

STOCK
OUTS

WAGE
RATE

FIGURE 10. THE GENERAL WAREHOUSE MODEL

TOTAL
VARIABLE
OPERATING
COST

75

Fundamental Data
This section describes the data that was provided by Farm Bureau
and used to build the warehouse models.

The numbers in question (pre­

sented in Table 11) are called 11I n i t ia l Parameters" because they are
basic to the required calculations.

Where specific warehouse levels

do not appear, the numbers reported are used in a ll three models.
Further comment on some of those values is necessary.
Time between orders. —The ordering-interval not only represents
the time between orders, i t also acts as a proxy fo r order s ize.

In the

course of a year the actual time between orders varies widely fo r each
product.

Some value, however, must be used to simulate the situation

where orders fo r groups of sim ilar products are accumulated and not
made d a ily .

In its basic role th is variable shows th at some products

are ordered more frequently than others.
The variable also acts to approximate order size which is
related but has unique q u a litie s o f its own th at carry considerable
weight.

Order size could be incorporated d ire c tly i f one absolute

order size existed fo r each product group.

As used here, the proxy

variable is required because order size is a re la tiv e concept.

A

large order in a low-demand period might be considered small during
periods of high demand.

I f ordering in tervals were constant in actu al­

i t y , re la tiv e order size could be approximated by a r t i f i c i a l l y varying
ordering-intervals within the simulator.

Because the in tervals are

not constant, they were adjusted s lig h tly and used fo r both
ordering-interval and order-size.

During high demand periods

76

Table 11.

I n i t i a l S im ulator Parameters f o r the 1972-1973, 1979-1980 Farm Bureau Systems'
Models

Product Group

Lead Time
in Days

Ordering
In te rv a ls
in Days

Man Hours to
Unload, Check,
and Stow One
Truck Load
o f Product

Mark Up
as a
Percent
o f Cost

Conversion
Factors in
D o lla rs per
Cubic Foot

1

F e r t iliz e r

2

5

1.40

0.28

1.8

2

Seed

3

20

7.27

0.12

6.6

10

8

7.27

0.19

1.6

7

11

4.34

0.14

10.4

3

Feed

4

M edicinal su pplies

5

Chemicals

7

25

4.34

0.05

36.1

6

Roofing

22

17

0.67

0.30

20.4

7

Panels and
accessories

55

10

16.0

0.30

22.2

8

B u ild in g cosmetics

10

9

8.0

0.30

19.8

9

Post poles & lumber

22

19

1.4

0.30

3.2

Fence

10

23

16.0

0.30

2.5
16.2

10
11

E le c tr ic fence

22

15

16.0

0.30

12

B ulkies

22

7

16.0

0.30

3.0

16.0

0.30

13.6

13

F le x ib le s

130

16

14

Tools

130

14

16.0

0.30

13.3

13

16.0

0.30

4.1

12

16.0

0.30

9.3

15

Semi-miscellaneous

22

16

M iscellaneous

22

Wage ra te s :
Warehousemen

Zilwaukee

Jenison

End-End

3.23

3.23

3.23

O ffic e

2.80

2.80

2.80

Management

6.97

4.74

5.90

Expansion fa c to r —sample to actual

1.154

1.337

1.23

V a ria ble costs re la te d to $ volume fa c to r

0.0094

0.008

0.0087

V a ria ble costs re la te d to la b o r hours
fa c to r

0.335

0.28

0.31

Cost o f c a rry in g in v e n to ry - -9.5% /year
s e le c tin g and loading p r o d u c tiv ity —9.5 man h o u rs /tru c k ; new 4.55 mari hours.

77

long order-intervals force large orders, but as lower demand is
experienced order size becomes smaller.

This reaction is due to

more rapid depletion o f inventories in high demand periods and an
ordering formula that brings inventories to a desired le v e l.
Labor producti v it ie s . --Producti v itie s for warehousemen, including
foremen (see Table 11), were acquired through interviews with the two
warehouse managers.

The in i t i a l productivities only account fo r the

time required to complete each individual task.

From th is startin g

point an in e ffic ie n c y factor of 22 percent was incorporated to account
fo r hours that workers were setting up jobs, cleaning up a fte r a jo b ,
moving between jobs, and taking breaks.

Twenty-two percent was used

to represent a reasonable average fo r Farm Bureau's estimates ranging
from 20 percent to 25 percent.
O ffice worker productivity was calculated s im ila rly .

The

important difference is th at o ffic e worker productivity is set as a
function of to ta l d a ily d o lla r demand rather than the cubic demand of
product groups.
In the case of o ffic e workers, i t is important to recognize
that the estimated productivity parameters r e fle c t the actual e ffic ie n c y
of the workers.

I t does not show th e ir productivity p o te n tia l.

O ffice

workers, fo r example, were thought by management to have the potential
to handle much more volume per man-hour than was measured in the model.
The model was also constructed with the c a p a b ility to predict
management labor requirements.

At th is point in the analysis, however,

the decision was made to set management productivity so th at one

78

manager and one assistant would be assigned to each location despite
the size of the labor force required.

Farm Bureau management feels

that the supervisory requirements fo r any warehouse w ithin a reasonable
demand range could be handled by one manager and his as sita n t.

Manage­

ment labor requirements are, therefore, not determined by the model.
I t does predict the number of clerks and warehousemen, however.
Other i n i t i a l values. —Conversion facto r calculation was neces­
sary to convert demand expressed in dollars to demand expressed in cubic
fe e t.

They also made possible a calculation to approximate warehouse

capacity requirements which w ill be explained la te r .
The i n i t i a l product a rriv a ls and beginning inventories needed
p rio r to model generated a rriv a ls were set at th e ir actual values.

The

"actual" a rriv a l values were calculated from Farm Bureau records using
the formula:
QA = D - BI + El
where:
QA = quantity that arrived ,
D = demand,
BI = beginning inventory, and
El = ending inventory.
A ll other i n i t i a l values were used in the simulator d ire c tly
from Farm Bureau records.

79

General Model Description
Once in it ia liz e d the model proceeds in the following manner:
1.

Actual demands by product group are read into the model

from a s p e c ific a lly selected sample of 96 Farm Bureau dealers.

These

dealers account fo r 81.3 percent o f the to ta l warehouse cost-of-sales
d o lla r demand.

The monthly demands are then divided into d aily demand

groups according to the day they were to be served as determined by the
transportation model (see Appendix B, "Jenison-Zi1waukee F irs t and
Second H alf Year").

For example, monthly demands from dealers normally

receiving supplies on one day of the week ( i . e . , Monday), are grouped
and divided into fourths.

This la s t division is necessary because the

grouping ac tu a lly represents a month of Mondays, and s im ila rly fo r other
days of the week.

Daily demands of sample dealers are then adjusted to

make the sample represent to ta l dealer population (see Table 11 fo r
these values).
2.
group.

Demands are then compared to inventory levels by product

I f there is enough inventory on hand, the to ta l is loaded from

inventory.

I f demand exceeds inventory fo r a p a rtic u la r product, a ll

inventory is loaded, with the remainder coming out of any a rriv a ls
delivered that day.

In instances where inventory plus new a rriv a ls

are not s u ffic ie n t to f i l l demand, the shortage is recorded.
3.

The space required fo r to ta l inventory is calculated each

day and the largest d a ily requirement reported.

This number is an

estimate of the actual space occupied by a ll the products.

I t does

not take room fo r p a lle ts , space between products, etc. into account.

A parameter is then established within the modeling process to convert
space occupied into actual capacity requirements fo r the base year.
4.

Orders are made according to:
t-1
Q0(t) - DINV(t) + Y , CQO(n) - QA( n)]
n=l

where:
Q0(t) = quantity ordered a t time t ,
DINV(t) = desired inventory a t time t ,
IN V (t) = inventory a t time t ,
Q0(n) = quantity ordered p rio r to time t , and
QA(n) = quantity delivered p rio r to time t .
5.

Required man-hours of d ire c t and o ffic e labor are then

calculated a t the d a ily le v e l.

For d ire c t or warehouse labor the

model calculates the minimum number of men required d a ily .

This is

accomplished by dividing the productivity fo r unloading, checking, and
stowing a product into the amount received and the productivity for
selecting and loading products into the amount sent out.

Movement is

converted from dollars to cubic measure and divided by the respective
productivities expressed in man-hours required per cubic foo t.

The

number of men ac tu a lly used is compared to model-calculated estimates.
The simulator actu ally calculates the number of days that the fixed
labor force is inadequate.

These simulator estimates when compared

to actual values provide an in d ire c t validation device fo r the labor
productivities used.

Correct productivity specifications should have

81

forced the number o f short-handed days from the model to f a ll within
the 8-25 range provided by management.

Confidence in the simulator

was reinforced when each of the base-year runs showed a short labor
situation that f e l l within the range provided by Farm Bureau.
6.

Net losses resulting from being out of stock fo r a demanded

product is also calculated.

The normal markups are reduced by expenses

that would have been incurred had the product been on hand.

The

reductions come from the labor costs, hourly-related variable costs,
and volume-related variable costs that would have been experienced.
7.

Inventory carrying-costs are calculated by applying a

d a ily finance charge to ending inventories and summing them over the
year.
8.

A rriv a ls , other than i n it ia l a rr iv a ls , are calculated by

setting them at a point in tim e, t , equal to orders Lt days e a r lie r ,
where Lt is the product specific lead time.

A d d itio n ally, a ll orders

are spread over three days, t + Lt - 1, t + L t, and t + Lt + 1.

This

process was in s ta lle d to substitute fo r management's a b ilit y to spread
receipts of large orders over more than one day when a concentrated
a rriv a l might s train labor capacity.

This allows the model to decrease

labor requirements in the peak periods to more nearly represent r e a lit y .
That i t also has the tendency to underestimate labor requirements in
other than peak periods is o f l i t t l e consequence because a fixed work
force large enough to meet a ll but the very largest peak requirements
w ill be more than s u ffic ie n t to meet lower level requirements.

Fixing

the labor force a t th is level would seemingly cause id le time.

I t is

82

important to recognize, however, that a ll work required in the warehouse
is not computed by the simulator.

Work that is necessary but not

sequential (not required at any one point in time but rather within
some longer period of time) th at can be done when unloading and loading
is completed, such as cleaning s p ills and rearranging storage, acts to
f i l l the time not accounted fo r in the model.
9.

F in a lly , yearly to ta ls including labor costs, work-related

variable costs, and volume-related variable costs are calculated.
Table 12 shows the items included in each of these categories.

In

addition to labor costs, the lis te d variable costs were c la s s ifie d
according to whether they were thought to be a function of hours worked
or business volume.
Analysis Process
Once the general model was formulated, data specific to each
of the two existing warehouses was fed into i t .

The product-specific

monthly-desired inventories were manipulated u n til model endinginventories reflected actual inventories.

In most cases the size of

the monthly-desired inventories only estimates the inventory levels
desired fo r the period in question.

With longer lead times or delays

between orders and a rr iv a ls , the variable must include expectation of
future demand.

I f , fo r example, two products A and B, have six month

lead times, are equal in the following four categories:

(1) July

inventories, (2) desired inventories fo r January, (3) expected
deliveries between July and January, and (4) expected demand up

83
Table 12.

Warehouse Operating Cost C la s s ific a tio n s fo r Farm Bureau's 1972-1973 System
Zilwaukee

Operating Expenses

Fixed

V a ria ble

Jenison
Fixed

Total

V ariable

Fixed

V ariable

$

P a yroll General:
Supervisory
Management & assistance
O ffi ce
P a yroll P la n t:
Foreman & warehousemen
LABOR
P a yroll o u tsid e lab or
FICA
MESC
Federal unemployment
Blue Cross
Group insurance
Workmen's Compensation
Salary c o n tin u a tio n
Retirement c o n trib u tio n
T ra in in g
Repairs/upkeep l i f t tru c k
Gas and o il
T ire s and tubes
L i f t tru c k expense
Normal maintenance
WORK RELATED
Travel
Demurrage
Rubbish disposal
Repairs/upkeep machinery equipment
Damaged merchandise
O ffic e supplies
M ail and messenger se rvice
Heat, l i g h t , and power
Plant and warehouse supplies
Telephone and telegraph
Postage
Insurance in ve n to ry
Equipment re n t
VOLUME RELATED
Repairs/upkeep grounds
A d v e rtis in g
Dues and su b s c rip tio n s
Donations
Miscellaneous
Taxes— p ro pe rty
Insurance—b u ild in g
Insurance—miscel laneous
P rin tin g
Rent
D epre ciatio n —b u ild in g
D ep re ciatio n —machinery & equipment
D ep re ciatio n — l i f t tru c k s
D ep re ciatio n —o ffic e equipment
Car lease
Board expense
Remaining Fixed Costs
TOTAL
Plus D e s c rip tiv e Account:
T ra c to r & Truck re n ta l

GRAND TOTAL
Source:

1,751

—

29,000
11,648

—
—

—

1,751
—
—
—
- —
—
—
- —

40,310
80,958
4,234
4,130
1,946
268
2,112
798
4,075
105
2,214

- -

—

1,522
—

—

1,522
—
- —
- —
- - —
- —

3,821
1,167
69
362
1,848
27,149

—

- -

1,804
80

—

- -

- -

- -

- —
—
—
—
—
_ _

—

1,820
1,586
2,802

—

—

- —

—

3,848
3,966
4,475
320
6,480

—

—

—
—
—
—

27,181

—

1,955
35

—
—

—

- —
—
- —

—
—
- —
—
—
—

5,912
1,253
4,881

- —
—

—

—

1,626

—

—

—

43,082
44,833

—

135,288

—

—

41,427
72,775
1,459
3,888
1,879
253
2,178
692
3,094
71
2,938
202
2,139
127
129
21
1,020
20,090

- -

2,308
385
15
28
102
855

- -

9

_ _

- —

1,811
3,538
4,005
224
7,585
179

—
—
—
- —
—

21,044

- -

5,264
—

—

120

—

125
113
25,247
1,799
54
82

3,273

—

19,700
11,648

- -

- —

—

1,832
13,725
1,223
104

—
—
- —

- -

—

120
4,987
342
886
48

—
- —
—
—
—

—

190
28,841
30,363

—

113,909

1,219

180 J21

"Statement o f Operations and M argins," June 30, 1973.

145 ,491

—

- -

48,700
23,296

—
- -

—

3,273
- - - —
—
—
- —
—
- - —
—

—
- -

81,737
153,733
5,693
8,018
3,825
521
4,290
1,490
7,169
176
5,152
202
5,960
1,294
198
383
2,868
47,239
4,112
465
15
1,848
1,688
3,657

_ _
- —
- —
—

9

- -

5,659
7,504
8,480
544
14,065
179
48,225

—
—
—
—
—
—
- -

7,219
35
120
125
1,945
38,972
3,022
158
82
120
10,899
1,595
5,767
48
1,626
190
71,923
75,196

—
—
—
- —
- - —
—
—
—
- —
—
—
—
- -

249,197

1,219
325 ,612

- -

84

to January, but have d iffe re n t expected demands fo r January, the
desired inventories used fo r ordering would have to include expected
future demand.
Product A

(IT

1.

July ending inventory

2.

Product B

(IT

1,000

1,000

July through December receipts

20,000

20,000

3.

July through December demands

-19,000

-19,000

4.

January beginning inventory

2,000

2,000

5.

January demand

-4,000

-1,500

6.

Net amount needed ( - ) or
remaining (+)

-2,000

500

7.

Desired January ending inventory

1,500

1,500

8.

Necessary size of July order to
a rriv e in January

3,500

1,000

Necessary July desired inventory

4,500

2,000

9.

With the situ atio n described, product A requires that January
receipts equal $3,500, therefore a July desired inventory of $4,500
would be required as the amount ordered is essen tia lly desired inven­
tory less inventory on hand, $4,500 - $1 ,000 = $3,500.
The two main purposes o f the desired inventory estimations are
(1) to force the model to track r e a lit y , and (2) to investigate other
desired inventory levels in order to find where to ta l inventory carrying
cost and net p r o fit lo st from stock-outs were lowest.
Next, the two warehouse flows were combined in an End-to-End
model and treated as i f they were one, while a ll other parameters were

85

l e f t unchanged.

By making only th is one change i t was possible to

evaluate the s o lita ry e ffe c t of inventory consolidation.
With this step accomplished the base period (1972-1973 fis c a l
year) analysis was complete.
quately track r e a lity .

A model was available that could ade­

The move to the projected impact analysis

was then in itia te d by updating the End-to-End simulator so that i t
would represent a warehouse in the proposed one-warehouse system.
I t was updated by increasing labor productivities to r e fle c t tech­
nological improvements.

O ffice worker productivities were also

changed in a ll three warehouse models.

They were increased over

the values measured in the base period to re fle c t the previously
discussed higher potential p ro d u ctivities.

O ffice productivities

were increased again because of a finding from the transportation
analysis with regard to projected demands.

There i t was found that

although d o lla r demand more than doubled by 1980, demand in volume
terms increased only a l i t t l e over one-third.

The reason fo r this

apparent contradiction comes from larg er projected increases fo r high
dollar-to-volum e items and smaller projections fo r low d o lla r-to volume products (see Table 3 in Chapter I I I ) .

The use of unchanged

productivities would have overstated labor requirements.

For this

reason o ffic e prod uctivities were changed so that they would be more
closely related to transaction volume rather than d o lla r volume.
Once the indicated changes were made, demands were updated
to r e fle c t projected demand changes.

I t was then possible to calculate

the costs that would occur in 1979-1980 with and without changing to a
one-warehouse system.

86

The one-warehouse model provides cost comparisons as well as
the factors from which the projected costs are calculated.

I t provides,

fo r example, capacity and labor requirements fo r the one-warehouse
system.
The analysis process used can now be summarized according to
the four major steps required.
1.

2.

3.

4.

The model of the two existing warehouses w ill:
a.

demonstrate that the model can track r e a lity within
small e rro r boundaries.

b.

give some feelin g fo r the magnitude and s e n s itiv ity
of design parameters lik e the facto r used to change
space occupied to space required.

c.

give inventory-strategy cost-functions with mathematically
minimum cost-points.

d.

demonstrate how the current system would perform under
expected future conditions.

The End-to-End Model w ill:
a.

give design parameters fo r the proposed one-warehouse
system.

b.

calculate savings from flow consolidation.

The new one-warehouse model w ill:
a.

give an estimation of capacity requirements.

b.

give variable cost estimates.

c.

calculate an inventory strategy cost-function.

Together the models w ill:
a.

demonstrate how a one-warehouse system would have compared
to the 1972-1973 warehouse system.

b.

demonstrate how the one-warehouse system would compare to
the two-warehouse system in 1979-1980.

87

Model V e rific a tio n
Table 13 shows the closeness of f i t with respect to month-ending
inventories between the modeled and actual data.
however, used in the model's construction.

These to ta ls were not,

Adjustments were made in the

model to establish a close correspondence between actual and modeled
month-ending inventories on a product basis.

Once each product group

adequately traced the actual situ atio n the sixteen groups were totaled
to a rriv e at the comparisons presented in Table 13.
Table 14 shows the representative desired inventory levels fo r
the Jenison Warehouse that caused the model to approximate actual
inventory le v e ls .

Desired inventory levels were also calculated fo r

the Zilwaukee and End-to-End models but are not shown.

The Jenison

figures should be s u ffic ie n t fo r an understanding of the process used.
The costs experienced by the Farm Bureau Warehousing System in
1972-1973 which were discussed e a r lie r are presented in Table 12.

With

these values plus the i n i t i a l parameters also presented e a r lie r a com­
parison between actual and modeled costs was made (see Table 15).

The

comparison seemed to support the argument that the models constructed
to trace r e a lity in 1972-1973 could be ju s t ifia b ly used to evaluate
performance in 1979-1980.

A more elaborate scheme may have been

necessary i f the anticipated technological or policy changes under
e ith e r a lte rn a tiv e were more d ras tic.

Table 13.

Monthly In ventory L e v e ls , 1972-1973

Zilwaukee
Year and
Month

Actual
-

Modeled

Jenison
Actual

End-to-End

Modeled

Actual

Modeled

$

-

1972:
June

917,050

908,234

778,935

776,003

1 ,695,985

1,686,023

July

893,834

875,234

734,964

707,413

1,628,798

1 ,588,175

August

902,329

879,045

742,320

727,144

1,644,649

1,620,965

September

862,554

818,711

747,905

719,702

1,610,459

1,568,331

October

872,447

851,270

710,917

691,103

1,583,364

1,535,280

November

850,854

850,816

705,824

717,271

1 ,556,678

1 ,587,415

December

858,501

856,610

731,233

740,467

1,589,734

1,586,302

January

1,015,018

888,646

852,043

763,213

1 ,867,061

1,763,233

February

1,231,688

1,213,504

1,019,370

1,051,645

2,251 ,058

2,273,234

March

1,013,852

1,033,256

968,555

968,550

1,976,402

2,028,664

Apri 1

947,574

962,215

922,516

932,003

1 ,870,090

1,870,032

May

745,526

813,414

831,540

796,126

1,577,066

1,507,773

June

603,724

622,498

660,322

652,622

1,264,046

1 ,271 ,274

1973:

Source:

Gross margin worksheets and model.

Desired Inventory Levels fo r the Jenison Warehouse, 1972-1973
1

2

3

5

N
r—

<0

"O
a>

T3

V)

e *1—
U f—
*a a.

•r- Q_

t/j
<o
u
'i

OJ
CO

at
at
u.

954

35,620

85,287

61,882

203,031

August

954

53,430

85,287

61,882

203.031

September

954

53,430

102,344

61,882

203,031

October

954

53,430

102,344

61,882

203,031

0)

Month

u_

J u ly

6

7

8

ut

Sai

S_

4

Q) =3
£ OO

0)
.c
o

9
ts, Poles,
Lumber

Table 14.

10

11

12

13

14

15
XA

3
O
at
£

16
XA

3

o

o

T3 a>
E i<0 so
XA XA
r— (fl
a> oj
c o
>0 u
a. c

•*— CO
3 O
CQ O

nca

nc

11,419

nc

41,862

21,439

nc

11,419

82,813

41,862

12,251

9,709

nc

nc

27,432

348,805

21,439

14,088

11,419

82,813

41,862

12,251

9,709

nc

nc

27,432

300,892

21,439

14,088

11,419

82,813

41,862

12,251

9,709

nc

nc

27,432

216,566

nc

27,432

191,651

Ol
e

•r—
4O
ce.

CO
cn u
C 'r•i- +J
*a a)
i— £

U1 TJ
O £
a . ra

IV
u

£
at
u.

o
*1—
s_
4-> at
CJ u

QJ £
r - <L
ixi Li­

ne

XA

10

at
XA

at
•r—
r—
3
m

nc

xi
■r—
X
a>
Li­

ne

nc

XA

t—

1 'flj

1- o

o

o
1—

E XA
0) •!xsx s :

nc

nc

at
£
■a
'at
XJ
XA

*r—
z:

nc

November

954

53,430

85,287

61,882

203,031

21,439

14,088

11,419

82,813

41,862

12,251

9,709

December

954

53,430

85,287

100,868

203,031

21,439

14,088

11,419

82,813

41,862

12,251

9,709

nc

nc

27,432

191,651

39,378

9,626

27,432

191,651

January

954

53,430

85,287

100,868

446,668

21,439

14,088

11,419

99,376

41,862

12,251

9,709

February

954

81,926

68,230

100,868

578,638

21,439

14,088

11,419

99,376

41,862

12,251

9,709

39,378

9,626

27,432

214,649

6,650

39,378

9,626

27,432

191,651

6,650

39,378

15,113

27,432

172,486

15,113

19,202

222,315

15,113

19,202

176,319

March

5,726

81,926

102,344

100,868

594,881

16,079

8,453

11,419

99,376

41,862

12,251

A p ril

954

81,926

85,287

100,868

446,668

16,079

8,453

11,419

69,066

41,862

15,926

May

954

53,074

110,873

100,868

402,001

16,079

11,270

11,419

69,066

41,862

12,251

6,650

39,378

June

954

53,074

106,609

0

203,031

16,079

11,270

11,419

69,066

41,862

12,251

6,650

39,378

aWhere no values appear, desired in v e n to rie s were not req uired because model generated a rr iv a ls were not ca lc u la te d .
f o r those months were s e t a t t h e ir actual values.

The a rr iv a ls

Table 15.

Annual Variable Cost Comparison, 1972-1973 Data
Jenison

Variable Costs

Actual

Modeled

Zilwaukee
Actual
■.....................

End-to -End

Modeled

Actual

Modeled

$

Labor

72.775.00

71,676.80

80.958.00

80.953.60

153.733.00

153,004.08

Hour related

20.090.00

20,069.50

27.149.00

26.567.61

47.239.00

47,431.49

Volume related

21.044.00

21,806.08

27.181.00

27,119.45

48.225.00

48,025.87

113,909.00

113,522.38

135,288.00

134,640.66

249.197.00

248,461.45

TOTAL

91

Results
Inventory Strategy Costs
The f i r s t set o f outputs from the simulation process allows
analysis of current inventory strateg ies.

Table 16 and Figures 11

through 13 show the results of the analysis.

The actual cost incurred

is estimated by the model a t 100 percent o f the desired inventory
required to make the model track r e a lit y .

By reducing the desired

inventory levels and, therefo re, the inventory c arrie d , inventory
carrying costs are decreased.
The model indicates that the Zilwaukee location could cut its
inventory level to 80 percent before incurring even the slig h te st level
of stock-outs.
cent.

S im ila rly , Jenison could reduce its inventory by 10 per

I f i t were possible to consolidate inventories to one location,

inventories could then be decreased to 73 percent before lik e levels
o f stock-outs would occur.

The lik e ly reason fo r th is lower inventory

requirement is th at the high fluctuations in demand from two locations
cancel out when inventories are consolidated.111
Here i t is essential to c la r if y the variable used to represent
demand and the zero stock-out level th at results from its use. The
zero level of stock-outs reported from the simulator has a small error
associated with i t .
Indeed, stock-outs did occur in 1972-1973, but
those were considered by Farm Bureau to be o f l i t t l e significance.
One could not expect stock-outs to re s u lt when cost of sales figures
are used as a proxy fo r demand. This is apparent because cost o f sales
figures represent sales made and not u n fille d requests. A small adjust
ment of less than .01 percent of sales was introduced through the
adjustment factors but no inventory outs were predicted by the
simulator.

92

Table 16.

Inventory Strategy Cost Comparison, 1972-1973
Zilwaukee

Item

100%a
Stock-outs
Inventory carrying cost
TOTAL
90%
Stock-outs
Inventory carrying cost
TOTAL
80%
Stock-outs
Inventory carrying cost
TOTAL
73%
Stock-outs
Inventory carrying cost
TOTAL

Jenison

End-to-End

— - ...........$ -------------------0
0
84,828.88 + 75,111.84= 160,002.09
84,828.88
75,111.84

0
161,109.98
161,109.98

836.03
65,465.16
66,301.19

NA

2,496.93
56,000.00
58,496.93

0
119,760.76
119,760.76

NA

95.94
67,076.26
67,172.20

NA

NA

1 ,486.23
105,293.76
106,779.99

70%
Stockouts
Inventory carrying cost
TOTAL

563.45
55,620.56
56,184.01

4,298.71
46,083.19
50,381.90

2,462.75
101,000.00
103,462.75

60%
Stock-outs
Inventory carrying cost
TOTAL

2,035.05
46,000.00
48,035.05

7,444.12
36,000.00
43,444.12

7,358.40
82,000.00
89,358.00

50%
Stock-outs
Inventory carrying cost
TOTAL

17,830.14
37,000.00
54,830.14

27,468.81
25,000.00
52,468.81

19,727.32
61,845.71
81 ,573.03

40%
Stock-outs
Inventory carrying cost
TOTAL

NA

NA

83,922.37
42,000.00
125,922.37

a

Reflects percent o f desired inventory level that was required to
make the simulator track r e a lity .
bNA = No analysis was run because other results would provide
l i t t l e i f any additional information.

Thousands of Dollars

93

Total
Inventory
Strategy
Cost
50--

40-Inventory
Carrying
Cost

30--

Stock-Outs
Net P ro fit
Lost

10- -

100
90
80
70
60
50
Percent of Possible Inventory Levels Desired by Farm Bureau Management

Figure 11.

Zilwaukee s tra te g y costs f o r 1972-1973.

94

Total
Inventory
Strategy
Cost

Stock-Outs
Net P ro fit
Lost

20

--

10

-

100

Inventory
Carrying
Cost

90

80

70

60

50
Percent of Possible Inventory Levels Desired by Farm Bureau Management

Figure 12.

Jenison s tra te g y costs f o r 1972-1973.

95

160--

140 - -

Thousands of Dollars

Total Inventory
Strategy Cost
120

- -

100

-

Stock-Outs
Net P ro fit Lost

80 -•

60 -■

Inventory
Carrying
Cost \

40

20

- ■

100
90
80
70
60
50
40
Percent o f Possible Inventory Levels Desired by Farm Bureau Management

Figure 13.

End-to-end s tra te g y costs f o r 1972-1973.

96

By reducing inventory le v e ls , to a point where trace stock-out
levels are experienced, some savings re s u lt.

By going to a centralized

inventory, savings would be $26,693.40 in 1972-1973 (see Table 16 for
Zilwaukee a t 80 percent, Jenison at 90 percent, and End-to-End at 73
percent of desired inventory le v e l).

By moving to the minimum inventory

strategy-cost levels (60 percent fo r both Zilwaukee and Jenison) a
saving of around $9,906.14 res u lts .

I t seems safe to conclude that

a savings of 6 to 16 percent over current inventory carrying costs is
meaningful, despite the p o s s ib ility o f sortie modest e rro r w ithin the
model.
Estimated Parameters
By modeling the two-warehouse system as i f the inventories are
consolidated at one location i t is possible to estimate two parameters
necessary fo r the construction o f the new one-warehouse simulator.
These parameters are the desired inventory levels and the capacity
requirement parameters.
The One-Warehouse System
Previously i t has been reported th at conferences with Farm
Bureau management resulted in predictions of transportation savings
should a one-warehouse system be implemented.

These same conferences

were the source o f additional predictions fo r one-warehouse related
savings over the two-warehouse system.

The savings estimates described

below are t o ta lly Farm Bureau calculations.

The savings calculated by

97

the simulator are not presented here, they w ill follow in a la te r
section.
1.

Include one manager, one assistant manager, and two foremen.
This was included in the simulator and w ill be reported la te r .

2.

Decrease the number of yard trucks from fiv e to two.

This w ill

lengthen the useful l i f e of the fiv e tractors on hand.

The

data fo r these trucks are presented below.
Yard Trucks Owned:

Purchase
Date

Description

Book
Value

Zilwaukee

1967

A llis Chalmers

$ 1,636

Zilwaukee

1971

John Deere

7,486

Jenison

1973

IT80

13,335

Yard Trucks Leased:
Zilwaukee

1974

50 months

Baker

$336.70/month

(The lease charge declines with the book
value—book value ranges from $10,853 to
$200 over 50 months.)
Jenison

1974

50 months

Clark

$307.08/month

(The lease charge declines with the book
value—book value ranges from $10,978 to
$224 over 50 months.)
The values fo r the leased trucks average $325.00 per month,
ranging from $350.00 fo r the f i r s t month to $300.00 fo r the
50th month.

Cutting to two tractors with one warehouse would

save $11,700.00 annually or $325.00 per truck per month.

In

1972-1973 d o lla rs , th is would represent a $8,730.34 savings.15
15 For the remaining d eflatio n adjustments a d eflatio n facto r of
1.34 with 1972-1973 equal to 100 was used. The value was calculated
from price indices in "Economic Ind icato rs," April 1975.

98

3.

Packing dealer orders in shrink packs should:
a.

Reduce damage to merchandise.

Farm Bureau's estimate

of savings from the damage reduction is $2,000 annually.
b.

Decrease p a lle t requirements.

Farm Bureau Management

estimates a $700 per year savings here.
This $2,700.00 in 1975 dollars from 3a and 3b repre­
sents a $2,014.93 savings in 1972-1973 d o llars.
c.

Save four man-hours in the loading o f each truck for
peddle runs.

The d o lla r savings is estimated fo r this

portion o f the change by the simulator.

The results

w ill be reported la te r .
4.

Use a s lo t system fo r storage.

In th is system each product has

a specific designated storage location.

Farm Bureau estimates

th at loading time would be decreased by 10 percent (9.5 hours
times 0.1 equals 0.95 hours) due to ease in finding the products
to be loaded.

Again, th is estimate is included as one of the

updated parameters in the new warehouse simulator.
5.

Cut to one switching tra c to r from two.

The Zilwaukee tra c to r

was purchased in March of 1973 fo r $7,352.90 and is depreciated
a t the rate o f $306.40 per year.

There is no book value

recorded fo r the Jenison switching tra c to r.

These machines

were once road tractors converted fo r use in switching railro ad
cars.

Given the 1973 purchase date, the savings in 1972-1973

dollars is the actual amount depreciated or $306.40.

99

Two other savings were considered but dismissed.
to do with l i f t trucks.

The f i r s t had

Management feels th at fiv e f o r k lif t s could do

the work required in a one-warehouse f a c i l i t y .

As six f o r k lif t s are

now assigned to the two warehouses, an apparent savings was forecast.
This is not an actual savings, however, as Farm Bureau Management la te r
decided that fiv e tractors would also be adequate in the current system
because of the id le time now being recorded by the six f o r k lif t s .
Farm Bureau Management also expected savings from quantity
discounts in the purchase of chemicals and medicinal supplies.
Table 17, however, shows that the average chemical order size would
not increase sub stan tially in a one-warehouse system.

In fa c t, less

than 600 additional cubic fe e t of c a rrie r space per load is indicated.
This seems to indicate that no s ig n ific a n t savings would res u lt from
quantity discounts.
The savings from a one-warehouse system predicted by Farm
Bureau Management are summarized below:
Annual One-Warehouse Savings Predicted by
Farm Bureau Management in 1972-1973 D o lla rs:
Three less yard trucks
Shrink pack p a lle t and damage reduction
One less switching tra c to r

$ 8,730.34
2,014.93
306.40
$11,051.67

100

Table 17.

Chemical Order Size Comparison Between a One- and TwoWarehouse System Using 1972-1973 Data
Order Size in Cost o f Sales Dollars

Day
Ordered

Jenison

Zilwaukee

End-to-End
3,104.08

1

1 ,775.19

1,328.89

25

2,928.24

3,061.62

50

3,876.96

4,382.04

4,065.99

75

4,308.89

2,106.93

7,129.71

100

4,527.42

240.03

4,409.85

125

1,360.41

17,382.69

268,790.16

150

245,490.63

327,938.58

357,646.38

175

160,711.92

64,422.60

205,895.34

200

58,599.54

67,546.23

136,413.45

225

51,760.95

37,469.97

85,754.19

0

250

Average order
size

0

18,503.79

0

536,340.15

544,383.37

1,073,209.15

53,634.00

49,489.40

119,245.45

I f one load is divided between two warehouses:
average order size = 98,247.59

$199,245.45 - $98,247.59 =

= 581.7 more cu. f t .

101

Changes such as removing the ordering functions from the

*

warehouses or elim inating at-warehouse dealer pickups were not included
in th is analysis as they are expected to occur regardless of which
warehouse a lte rn a tiv e is selected.

The purpose of th is action was to

emphasize the impacts from differences between the two a ltern a tive s;
i t is assumed that s im ila r changes would have sim ilar e ffe c ts .
The 1979-1980 Simulator
To review, two changes were found to be necessary in a ll models
to prepare them fo r the projected analysis.

F ir s t, managers' produc­

t iv i t i e s were changed to r e fle c t Farm Bureau's opinion th at only two
managers are needed per warehouse.

Second, o ffic e productivity was

increased to show a higher potential than the model measured and again
to r e fle c t the smaller increase in transactions as opposed to d o lla r
demand.

The one-warehouse model also was changed to r e fle c t the new

s lo t system and shrink pack technologies by reducing loading time from
9.5 to 4.55 man-hours per truck.

Although th is man-hour savings seemed

larg e, Farm Bureau management stood s o lid ly behind th e ir estimate.
I t should be mentioned th at most of the labor requirement stems
from the unloading function where product flows flu ctu ate widely and
not from the loading function where i t is regular from day to day.
Therefore, the loading productivity can have sizable errors and not
g reatly a ffe c t the fin a l labor requirements.
In th is portion of the study i t was also necessary to update
the numbers used fo r the past year's demand.

When desired inventory

102

is a function of demand one year e a r lie r , i t becomes necessary
to update the previous year's demand fo r each new year evaluated.
S im ila rly , the values fo r beginning inventories and i n i t i a l a rriv a ls
required updating.

A ll altera tio n s were achieved by applying to the

values in question the percentage changes used fo r projecting demands
(see Table 4 in Chapter I I I ) .
With these changes included in the model, the next step was
to compare performances between the two altern atives a t the 1979-1980
demand levels.
Simulator Results With Projected Demands
The results from the simulator with respect to projected demands
and improved technology are surrenarized in Table 18 and Figures 14
through 16.

I f the same re la tiv e levels of desired inventories are

used that resulted in minor levels of stock-outs with 1972-1973 data,
both components of the two-warehouse system would be over th e ir capacity
by 1980.
At the same safety stock level used in 1972-1973 Jenison would
require 173,648 cubic fe et more space than is availab le and Zilwaukee
85,153 cubic feet more.

With the current storage capacity, Zilwaukee's

net loss from stock-outs would be $1,379.45 with an inventory carrying
cost o f $117,496.92.

The sim ilar amounts fo r Jenison would be

$10,432.95 and $97,149.19 (see Table 19).

103

Table 18.

Inventory Strategy Costs by Capacity and Percent o f Desired Inventory le v e l Projected
1979-1980
Zilwaukee

Item

cubic fe e t

d o lla rs

100%a
Size
Stock-outs
Inventory carrying cost
TOTAL

NAb

90%
Size
Stock-outs
Inventory carrying cost
TOTAL

NA

80%
Size
Stock-outs
Inventory carrying cost
TOTAL

65%
Size
Stock-outs
Inventory carrying cost
TOTAL
60%
Size
Stock-outs
Inventory carrying cost
TOTAL

40%
Size
Stock-outs
Inventory carrying cost
TOTAL

d o lla rs

cubic feet

d o lla rs

NA

0
398.136.76
398.136.76

433,648
1,212.11
167,763.61
168,975.72

345,153

374,194

NA

686,498

118,35
156,104.19
156,222.55

3,592.99
144,070.00
147,662.99

0
299.961.44
299.961.44
610,535

NA

NA

2,154.76
265,600.82
267,755.58

292,469
775.12
130,346.49
131,121.61

NA

1,379.45
117,496.92
118,876.37

NA

NA

523,721

266,127

239,785

6,523.15
226,493.96
233,017.11
478,225

257,586
10,432.95
97,149.19
107,582.14

2,593.01
104.678.65
107.271.66

53%
Size
Stock-outs
Inventory carrying cost
TOTAL
50%
Size
Stock-outs
Inventory carrying cost
TOTAL

cubic fe e t

New

903,533

73%
Size
Stock-outs
Inventory carrying cost
TOTAL
70%
Size
Stock-outs
Inventory carrying cost
TOTAL

Jenison

10,538.88
202,132.69
212,671.57
422,432

NA

NA

18,187.74
168,430.67
186,618.41
398.521

213,231

188,351

38,623.77
75,018.36
113,642.13

24,417.72
79,663.91
104,081.63

26,446.70
154,172.14
180,618.84
317,436

NA

NA

111,737.68
108,901.97
220,639.66

aR eflects percent o f desired inventory leve l th a t was required to make the sim ulator track
r e a lity .
bNA = No analysis was run because other re s u lts would provide l i t t l e
inform ation.

i f any additional

(Inventory

Carrying

Cost Plus Net Profit Lost
Strategy Cost Dollars

From Stock-Outs)

104

Thousands
170-fMaximum
Capacity
160- -

150- -

140

130- •

110 -

-

100

430

400

370

340

310

280

250

220

190

160

130

Capacity Required in Thousands o f Cubic Feet

Figure 14.

Zilwaukee s tra te g y costs and c a p a c ity requirem ents f o r 1980.

(Inventory

Carrying

Thousands
170 ••
Maximum
Capacity

160 - -

1 40-

Cost

Dollars

150 "

Strategy

Cost

Plus Net

Profit

Lost

From Stock-Outs)

105

130 *

120-

110 - .

100 - -

430

400

370

340

310

280

250

220

190

160

130

Capacity Required in Thousands o f Cubic Feet

Figure 15.

Jenison s tra te g y costs and c a p a city requirem ents f o r 1980.

106

From Stock-Outs)

Thousands
390

Carrying

Cost Plus Net Profit Lost
Strategy Cost Dollars

360

330 -•

300 -■

270

240 ■■

(Inventory

210

- -

180--

900

850

780

720

660

600

540

480

420

360

Capacity Required in Thousands o f Cubic Feet

Figure 16.

The one-warehouse system's s tra te g y costs and c a p a c ity
requirem ents f o r 1980.

300

107

Table 19.

Annual Warehouse Cost Comparisons Between a One- and TwoWarehouse System at Approximately Equivalent Performance
Levels or Stock-Out Rates
Number o f Warehouses in the System
Two

Item

Zilwaukee

One

Jenison

Total
-

Net p ro fit
loss

Cost

D iffe re n tia l

$

1,379.45

10,432.95

11,812.40

10,538.88

1 ,273.52

Inventory
carrying
cost

117,496.92

97,149.19

214,646.11

202,132.69

12,513.42

Labor cost

107,827.20

85,113.60

192,940.80

148,616.00

44,324.80

Variable Costs Related to:
Labor

36,122.11

23,831.81

59,953.92

46,070.96

13,882.96

Dollar
volume

55,608.47

43,806.80

99,415.27

98,927.54

487.73

318,434.15

260,334.35

578,768.50

506,286.07

72,482.43

TOTAL

Other savings related to one-warehouse
GRAND TOTAL

11,051.67
83,534.10

108

The new one-warehouse system would give approximately the
same performance while using 45,488 less cubic fe et o f storage space
or a saving o f $12,513.42 in inventory carrying costs.

Shrink pack

and s lo t system productivity improvements provide furth er savings in
labor and labo r-related variable costs.

At th is performance le v e l,

the two-warehouse system would require 18 warehousemen (two foremen,
and 16 workers), four clerks, two assistant managers, and two managers.
The new one-warehouse system would need three less warehousemen
(two foremen and 13 workers) , four c lerks, one manager, and one assis­
tant manager.

The difference here is $44,324.80 more savings fo r the

new warehouse in 1979-1980.

There are also other variable cost savings

related to labor costs and business volume that amount to $13,883.96
and $487.73, respectively.

These model estimates plus the $11,051.67

of plant cost savings previously estimated by Farm Bureau gives the
one-warehouse system an advantage of $83,534.10 in 1980.
The most apparent im plication of the resu lt is , however, that
the current system could not, without major policy and technological
changes, continue much, i f any, beyond the projected demand level fo r
the 1979-1980 fis c a l year.
The simulator has shown that by 1980 the Zilwaukee warehouse
would lose $1,379.45 worth o f p r o fits , $4,733.73 cost o f sales d o lla rs ,
and be near the mathematically minimum inventory-strategy cost point
(see Figure 14).

A review of that fig ure does not, in i t s e l f , substan­

t ia t e the position th at the current system could not continue beyond
1980.

There are, however, two related considerations th at emphasize

the r e a lity o f th at position.

109

The f i r s t o f these considerations has to do with the shape of
the inventory-strategy cost curve.

The inventory-strategy cost function

(net p r o fit lo s t plus inventory carrying cost) decreases gradually to
a minimum and then increases sharply.

Because the model cannot be 100

percent accurate, i t is important to know the repercussions of making
various errors.

For example, the cost of adopting a 50 percent strategy

when the 60 percent level is the actual minimum is much higher than when
a 50 percent strategy is implemented and the 40 percent level is the
true minimum (see Figure 17).
The second consideration is consumer i l l - w i l l .

Because i l l - w i l l

wasn't q u an tified , the prob ability of underestimating net losses in ­
creases at the lower desired inventory levels.

This is true because

the tendency to change suppliers would seemingly increase with the
increase in out-of-stock replies to dealer requests.
I t is , therefore, not only quite probable that i t is more costly
to be on the lower side o f the "true" minimum cost point, but i t is also
lik e ly that this costliness is underestimated in this analysis.

With

the above data in mind, i t would be very d if f ic u lt to recommend staying
with the unmodified Zilwaukee warehouse much beyond 1980.
The importance of 1980 and possibly pre-1980 as the deadline
fo r change is reemphasized upon analyzing the other h a lf o f the current
system.

The results show that the Jenison warehouse w ill have already

been forced to its mathematically minimum inventory-strategy cost by
1980.

The kind o f safety margin enjoyed by the 1980 Zilwaukee warehouse

w ill not be available to the Jenison location.

As a re s u lt, policy and

technological changes by 1980 seem in evitable for the current system.

110

Thousands o f V a ria b le
Cost D o lla rs

140"

—

—

Modeled function

--

Assumed actual minimum to the l e f t o f modeled

—

Assumed actual minimum to the rig h t of modeled

/

I
120

9

/

/
110

/

\

\

\

\

\

#

/

/

/

/

/

/

A

/

/

/

* *

/

/

/

/

80
*
**

Costs w ill be much higher than predicted i f true minimum is
a t a higher percent of desired inventory than estimated.
Costs w ill be s lig h tly higher than predicted i f true minimum
is at a lower percent of desired inventory than estimated.

70%

40
Percent of Desired Inventory

Figure 17.

New warehouse inventory strategy costs:
versus true values.

predicted costs

30

Ill

Warehouse S ize A lte rn a tiv e s

I t has been shown that the current system may not be able to
handle a ll that is required o f i t by 1980.

Further evaluation of the

one-warehouse system's a b ilit y to meet those requirements would, there­
fo re , seem desirable.
A ll capacities greater than 478,000 cubic fe e t, where the onewarehouse system duplicates the current system's low 1980 performance
le v e ls, and those capacities less than 900,000 cubic fe e t, where the
high 1972-1973 performance is duplicated w ill be considered.

The

$83,500 savings at the smallest of these capacities has already been
reported.
This savings should, however, be weighed against stock-outs
and potentials fo r expansion.

F ir s t, i t should be decided whether

$10,538.88 of net p r o fit lo st (approximately $36,000 cost of sales
do llars) is an acceptable level of performance.

Second, without room

fo r expansion an expectation o f higher future demands w ill force even
higher levels of stock-outs.

I f higher demand is expected, would Farm

Bureau be w illin g to cut the safety margin fo r error and poor customer
relations even1 fin e r (see Figure 16)?
C learly, there are reasons fo r examining larger capacities.
Moving from the 478,000 cubic fe e t size toward the 900,000 cubic feet
of capacity (see Figure 1 8 ), the new system's $83,534.10 is being eroded
away by ever-increasing inventory carrying costs.

This erosion con­

tinues u n t il, at the 900,000 cubic foot le v e l, the annual variable cost

$1,000

$1,000
Savings o r Cost o f One Warehouse Over Two in 1980 w ith :
•■10.5

$^\$2,200 Stock-Out Loss Inventory Strategy

0 Stock-Out Loss Inventory Strategy
15.0

^ \ i 0 Stock-Out Loss Inventory
'£x\.

Strategy

\

-113.2

'

600

700

800

Capacity in Thousands of Cubic Feet

Figure 18.

New warehouse capacity selection.

900

113

is $113.2 thousand more fo r the one-warehouse system than the current
system.

This is very deceptive, however, because the two alternatives

are no longer comparable.
The $113,200 would be paying fo r a zero level of stock-outs,
safety stocks equivalent to the 1972-1973 s itu a tio n , plus room fo r
expansion.

This amount would move Farm Bureau to the situation

described from the one with $83,534.10 o f savings but also with
$11,800 o f net p r o fit lo s t, no safety stocks, and no room fo r
expansion.
The change from $83.5 thousand of savings to $113.2 thousand
of cost over the range o f capacities considered arise from the
sim p listic assumption th at fo r each size considered, the relevant
inventory-strategy would be one th at u tiliz e s the warehouse's f u ll
capacity.
assumption.

The "variable strategy" lin e in Figure 18 shows this naive
The other three lines in Figure 18 attempt to circumvent

this problem by showing the 1980 savings following from three d iffe re n t
fixed inventory strateg ies.

Once fix e d , the strategy is changed only

when forced to do so by capacity re s tric tio n s .

This highlights the

benefit of building a larg er warehouse; th at is , the a b ilit y to handle
expanded demand without being forced into an undesired inventory
strategy.
Strategies other than the three presented in Figure 18 can be
evaluated by selecting an acceptable stock-out level and constructing
a lin e a t th at point p a ra lle l to the horizontal axis.

114

At th is point in the analysis, the size selection for the
one-warehouse system revolves around expected demand increases and
desired warehouse l i f e .

A fourteen year l i f e and two extreme demand

increase expectations w ill be used fo r illu s t r a t iv e purposes only.
Here a fourteen year l i f e is measured from the base period, which
implies a search fo r the warehouse capacity that would allow the
desired inventory strategy to continue through 1987.
By 1980, expectations are that capacity requirements w ill
have increased by 402,802 cubic fe e t from 500,731 cubic fe e t (from
the 1972-1973 End-to-End Model at 100 percent o f desired inventory)
to 903,533 cubic fe e t (from the 1979-1980 New Model a t 100 percent of
desired inventory).

I f the same increase occurs in the following seven

years, required capacity would be 1,306,335 cubic fe e t, i f zero stock­
outs and the same level of safety stocks th at were available in 19721973 is desired.

This is a very optim istic expectation, but i t was

used to establish the upper end o f the range of desired capacities.
I f , however, demand stays at the 1980 le v e l, a 903,533 cubic fe e t
capacity w ill be adequate.
Given an inventory strategy that accepts $2,154.76 of losses
from stock-outs, a warehouse of 1,013,337 cubic fe e t would be ade­
quate.

On the other hand, i f demand is expected to plateau a fte r

1980, i t could be accommodated by a warehouse of 610,535 cubic fe e t
(see Table 20).

115

Table 20.

One-Warehouse Capacity Requirements fo r Performance To Be
Acceptable U ntil 1987 fo r Two Performance Levels and Two
Demand Projections
Capacity Requirement
Inventory Strategy

Expected 1980-1987
demand increase

Same as that used
in 1972-1973

An acceptable net
p r o fit loss of less
than $2,000.00

Same as that experienced
from 1973-1980

1,306,335 cubic
feet

1,013,337 cubic
feet

No increase a fte r 1980

903,533 cubic feet

610,535 cubic fe et

Construction Timing
Another decision that would arise should a one-warehouse system
be selected has to do with selecting the correct time to build.

The

answer is not obvious because data are only available fo r two time
in te rv a ls , 1972-1973 and 1979-1980.
Again, as in the capacity decision, the desired inventory
strategy is central to the issue.
should aid in th is decision.

Table 21 shows calculations that

The inventory strategy of accepting trace

levels of net p ro fits lo s t is one that might be preferred by Farm Bureau.
For any other performance le v e l, calculations sim ilar to those that
follow can be made.

116

With th is inventory strategy, the Jenison location would
e ffe c tiv e ly use 182,913 cubic fe e t in 1972-1973 and expect an increase
in space required of approximately 36,000 cubic fe e t per year.

At this

ra te , Jenison's capacity would be reached in the la tt e r part o f 1975.
Zilwaukee, however, could continue u n til mid-1975 before
reaching capacity with the 20,000 cubic fe e t per year increase.
The inventory strategies required to allow the current system
to run u n til mid-1980 without modification has already been presented.
I t was shown that Jenison and Zilwaukee would reach capacity by the
end of the 1979-1980 fis c a l year i f stock-out levels o f $10,432.45
net p ro fits lo s t were accepted, respectively.
A word of caution is essential a t this point.

The v ita l

assumption in this analysis is that the 1980 projections were treated
as i f they would be achieved in equal yearly increments.

Should more

o f the increase occur in the e a r lie r years, capacities would be reached
e a r lie r , and conversely.

117

Table 21.

Construction Timing fo r the Proposed One-Warehouse System
Capacity Required

Location
Inventory Strategy

Zilwaukee
80% of Di nva

Jenison
90% of Dinv

----------------- cubic f e e t ----------------Fiscal Year:
1972-1973

207,230

182,913

1979-1980

345,153

433,648

137,923

250,735

19,703

35,819

1973-1974

226,933

218,732

1974-1975

246,636

254,551

1975-1976

266,339

290,270

mid 1976

mid 1975

Increase
Yearly increase
Capacity required by end
of:

Over warehouse capacity by:

aDinv is the desired inventory level used in the warehousing
system in 1972-1973.

CHAPTER V

INVESTMENT ANALYSIS

In the evaluation of the one-warehouse system, the discussion
has been in terms of absolute d o lla r savings fo r the 1979-1980 fis c a l
year.

In order to evaluate the attractiveness of this proposal i t is

necessary to analyze the nature of the cash flows in the years before
and a fte r 1980, including investment requirements and residual values
not yet considered.
The warehouse savings presented previously were generated from
a comparison of the current system and a one-warehouse structure that
would e x h ib it equivalent performance.

Chapter IV indicated th at a

larg er building would be required to improve upon that 1980 performance.
I t is , th erefo re, important to know what size building Farm Bureau would
select i f they decide to proceed with construction of a one-warehouse
system.

With th is knowledge the magnitude of the required investment

can be determined.
Farm Bureau management currently feels that a 610,535 cubic
fe e t capacity would be s u ffic ie n t.

They have also determined th at the

new system could be in operation by the end of the 1975-1976 fis c a l year.
I t was suggested in the previous chapter that the current system
could not continue beyond 1976 a t acceptable levels of performance.

118

119

Here, however, the comparison w ill be made as i f the choice is between
investing in the new one-warehouse system and continuing with the
unmodified existing f a c il it ie s .

The warehousing system would, of

course, experience ever decreasing levels o f performance i f the la t t e r
a lte rn a tiv e were selected.
lost calculations.

I l l - w i l l was not included in the net p r o fit

As the current system's stock-outs increase, the

importance of i l l - w i l l w ill be magnified and the accuracy of the func­
tion th at excluded i t decreased.

A second method fo r continuing the

current system would be to carry only high p r io r ity inventories while
dropping others to take advantage of lim ited f a c i l i t y capacity.

This

change, a policy change, would lik e ly generate another kind o f i l l w ill.

I 11-w i11 would res u lt because dealers would be forced to choose

from a smaller varie ty and might have to acquire supplies d ire c tly from
manufacturers.
Cash Flows
A comparison of the variable costs fo r a 610,535 cubic fe e t
warehouse (see Table 22) and those fo r the existing system indicates
that only net p ro fits lo st and inventory carrying costs d if f e r from
those of the smaller warehouse previously examined (see Table 19,
Chapter IV ).

As expected, the larger warehouse has greater inventory

carrying costs but lower net p ro fits lo st because i t is capable of
carrying larger inventories.

Even though the inventory cost is higher

in th is warehouse than those in the current system, the other savings
allow i t to show a net savings fo r 1979-1980.

Table 22.

Warehouse Cost Comparisons Between the Current and Proposed Warehouse Systems as Predicted fo r 1979-1980

Two-Warehouse

One-Warehouse System

Svstem

_ _

Jenison

Total
Variable Cost

1,379.45

10,432.95

11,812.40

Inventory carrying
cost

117,496.92

97,149.19

Labor cost

107,827.20

Zilwaukee

Net profit lost

u iT T e r e n tia i savings

Total
Variable Cost

or Cost (-)

In 1972-73 Dollars

In 1975 Dollars

2,154.76

9,657.64

13,192.34

214,646.11

265,600.82

-50,954.71

-69,604.13

85,113.60

192,940.86

148,616.00

44,324.80

51,416.77

36,122.11
55,608.47

23,831.81
43,806.80

59,953.92
99,415.27

46,070.96
98,927.54

13,882.96
487.73

18,964.12
666.24

318,434.15

260,334.35

578,768.50

561,370.08

17,398.42

14,635.34

11,051.67

14,809.24

28,450.09

28,292.28

Variable costs
related to:
Labor
Dollar volume
Subtotal
Other one-warehouse
savings3
Total

NAb
318,434.15

NA
260,334.35

NA
578,768.50

NA

561,370.08

aYard truck, switching engine, damage, pallet, and slot system savings.
bNot applicable.

121

A ll annual net savings are expected to be a t the values given
fo r 1979-1980 from the time the warehouse begins operation except fo r
net p r o fit lo s t and inventory carrying cost.

The labor savings and

other advantages (in yard truck, switching engines, damage, p a lle t,
and s lo t system savings) related to a one-warehouse operation w ill not
change.

Inventory carrying cost and net p r o fit lo s t values w ill change,

however, because the demand volume is not as high in the e a r lie r years.
The d iffe re n tia ls fo r these values w ill increase over the years u n til
they reach those 1isted fo r 1979-1980.
Chapter IV disclosed a lin e a r relationship between the amount
of inventory carried and the cost of carrying inventory.

I f the one-

warehouse structure had been in operation in 1972-1973, the amount of
inventory carried in the two systems would have been equivalent.

In

subsequent years the two-warehouse system would be forced to stay at
the 1975-1976 inventory le v e l, despite increased demand, while the
proposed warehouse could increase its inventory level a fte r 1975-1976.
As a re s u lt the expectation is that the d iffe re n tia l in inventory
carrying costs would expand in a lin e a r manner from zero in 1972-1973
through the $50,954.51 of added costs predicted fo r 1979-1980.

With

th is basic assumption, the additional inventory costs expected fo r
the one-warehouse system in other years were calculated; see Figure 19
and Table 23.
Savings from decreased net p r o fit losses were calculated in
a s im ila r manner; see Figure 20 and Table 24.

The lin e a r ity condition

that exists with respect to inventory carrying costs does not, however,

D o lla rs

100,000

80,000

60,000

40,000

20,000

0
1972-73

Figure 19.

1979-80

1985-86

Estimated additions to cost from higher inventory
carrying costs in a one-warehouse system.

123

Table 23.

Estimated Additions to Cost from Higher Inventory Carrying
Costs in a One-Warehouse System

Year

In 1972-73 Dollars

In 1975 Dollars

1976-1977

29,116.98

39,773.79

1977-1978

36,196.94

49,445.02

1978-1979

43,675.47

59,660.69

1979-1980

50,954.71

69,604.13

1980-1981

58,233.95

79,547.58

1981-1982

65,513.19

89,410.02

1982-1983

72,972.44

99,680.35

1983-1984

80,071.68

109,377.91

1984-1985

87,350.93

119,321.37

1985-1986

94,630.17

129,264.81

Table 24.

Estimated Savings from Lower Net P ro fits Lost in a OneWarehouse System

Year

In 1972-73 Dollars

In 1975 Dollars

1976-1977

5,518.65

7,538.48

1977-1978

6,898.31

9,423.09

1978-1979

8,277.98

11 ,307.72

1979-1980

9,657.64

13,657.64

1980-1981

11,037.30

15,076.95

1981-1982

12,416.96

16,961.57

1982-1983

13,796.57

18,846.11

1983-1984

15,176.29

20,176.29

1984-1985

16,555.95

22,615.43

1985-1986

17,935.62

24.500.06

D o lla rs

20 , 000”

15,000 -

10, 000'

5,000..

1972-73

Figure 20.

1979-80

1985-86

Estimated savings from lower net p ro fits lo s t in a
one-warehouse system.

125

s t r ic t ly hold fo r stock-out losses.

Figures 14 through 16 in

Chapter IV show th at as the inventory-to-demand ra tio decreases
(demand is held constant while inventory is reduced), the net p ro fits
lost from stock-outs increase slowly up to a point but then increase
sharply.

By 1979-1980 the current system is expected to be beyond

that point.

The proposed system w ill be experiencing some stock-out

losses but only a t low lev els.

In fa c t, considerable demand increases

could occur before stock-out losses increase fa s te r than the carrying
cost savings, unlike the current system (see Figure 21).
The possible shape of the true function derived from expected
d iffe re n tia ls lik e those in Figure 21 is presented in Figure 20 with
the contrasting lin e a r approximation.

That fig ure demonstrates that

the lin e a r approximation overestimates savings in the early years and
underestimates them a fte r 1979-1980.
The cash flow estimates to th is point in the evaluation have
been expressed in 1972-1973 d o lla rs .

Because the cost estimates

that

w ill follow are in 1975 terms, i t is necessary to adjust a ll cash flows
to one common basis or year.

Analyses using 1972-1973 dollars have

been appropriate because the concern was with absolute performance
comparisons in a year representing normal Farm Bureau operations.
Investment-cash flow analyses should, however, include re la tiv e changes
in savings and costs resulting from d iffe r e n tia l in fla tio n rates.

The

impact on cash flows from these d iffe r e n tia l in fla tio n rates w ill be
evaluated both o b jectively and su b jectively.

The objective evaluation

w ill be accomplished by expressing the savings and costs previously

F
Dollars
40,000

30,000 •-

20,000

- ■

10,000

- -

-Two-Warehouse System

$9,657.64
One-Warehouse
System

1979-80

1972-73

Figure 21.

Net p ro fits lo s t.

1985-86

127

calculated fo r 1972-1973 in 1975 d o lla rs .

Once rates o f return are

calculated from values expressed in 1975 terms the possible effects
of subsequent in fla tio n can be investigated subjectively.
Tables 22, 23, and 24 include the 1975 values fo r the 19721973 estimates.

These estimates were in fla te d using an index o f 136.6

fo r a g ric u ltu ra l inputs from the "Agricultural Prices" monthly and
116.0 fo r labor from the "Michigan State Economic Record."

The index

used fo r s ite -re la te d savings not already in 1975 terms is 134, o rig ­
in a lly used to convert them from 1975 to 1973 dollars (see page 97 of
Chapter IV ).
In addition to warehouse cost savings, some possible trans­
portation savings associated with one warehouse were indicated in
Chapter I I I .

Calculations there revealed a d iffe r e n tia l of between

$10,198.67 savings and $2,221.89 added cost depending on which one
of the seven proposed location costs are used.

Because a location

has not been selected, the Climax transportation savings of $5,043.35
w ill be used.

The Climax number is used because i t is the median point

fo r the seven values calculated and is , th erefo re, with the information
availab le to this point, the most representative.
$5,043.35 becomes $6,152.88.

In 1975 dollars the

An index of 122 fo r transportation equip­

ment from the "Wholesale Prices and Price Index" was used as a proxy
index fo r transportation services.
I f the one-warehouse system is implemented, required investments
would include costs fo r the building i t s e l f , shrink pack equipment,

128

other new equipment,16 transportation and in s ta lla tio n of transferred
equipment, and construction o f a railro a d siding.

Because a s ite has

not been selected, a f a ir l y exact estimate o f these la s t three costs
is not a v a ila b le .

The investment estimate w i l l , however, be increased

and a range of values used that w ill lik e ly contain any reasonable
value that might re s u lt fo r these s ite -re la te d costs.
According to Farm Bureau management and contractor estimates
a suitable building w ill cost $259,400.00.

The shrink pack technology

w ill be $15,000.00 while the twenty acres of land desired is expected
to cost $5,000 per acre or $100,000.00.

The to ta l investment without

costs fo r equipment tra n s fe r, new equipment, and railro ad siding is
$374,400.00
Farm Bureau expects the ra ilro a d siding to cost $20 per foot.
With th is price an additional investment of between $13,200.00 and
$26,400.00 w ill be used fo r a range of between one-eighth and onefourth of a mile of railro a d siding.

I t is also expected that costs

fo r the remaining tran sfer and equipment variables w ill f a ll within a
range of $10,000.00 to $20,000.00.

In t o t a l, the new warehouse system

is expected to cost between $397,600.00 and $420,800.00.
Two other cash flows are important in addition to those already
discussed.

I f the new system is implemented, Farm Bureau Services

expects to s e ll one o f th e ir warehouses fo r $100,000.00 and tran sfer
16The plan would be to tra n sfer a ll required equipment from the
two-warehouse system; however, some small investment may be necessary
i f existin g equipment is not compatible with the new building.

129

the other w ithin Farm Bureau to another division at its book value—
$189,147.42.

These transactions would add to cash inflows once the

new warehouse is operating.

The $100,000.00 building has a zero book

value and has been owned by Farm Bureau fo r enough years to c la ss ify
its sale as a capital gain.

This c la s s ific a tio n exempts $25,000.00

of the sales price so the a fte r tax return from the two warehouses w ill
be $270,397.42 with th e ir 25 percent e ffe c tiv e tax ra te .
The remaining cash flow of importance is
of the new building at the end of the evaluation

the residual value
time period.

Farm

Bureau uses stra ig h t lin e depreciation so the residual w ill be x/30
of the i n i t i a l value where x equals the years of l i f e remaining in
the warehouse.
Evaluation Interval
Selecting the number of years over which to evaluate the
proposed investment, 3 0 - x, is an important yet f a ir l y a rb itra ry
decision.

Because Farm Bureau depreciates th e ir warehouses over

a th irty -y e a r expected l i f e , a th irty -y e a r period might be considered.
There is , however, a problem with th is long interval stemming
from the assumption th at Farm Bureau w ill e ith e r construct the new
warehouse or continue with the current system unchanged.

Over such

a long period i t seems lik e ly that a lte rn a tiv e warehouse system
investments could not be avoided.

Because estimates fo r a lte rn a tiv e

investments have not been included in th is research, the value o f this
longer evaluation period is questionable.

130

On the other hand, a very short analysis tim e, say to 1980,
could also be misleading because the residual value of the new ware­
house in 1980 would dominate the analysis (only four years, 4/30 of
the warehouse l i f e would be depreciated away).17

I t is necessary,

therefore, to select a length of time th at w ill make the residual value
less important without co n flic tin g with the investment-no investment
assumption.

By evaluating the cash flows fo r one-third o f the new

warehouse's expected useful l i f e , through 1985-1986, the distortion
from both shortcomings should be m inim al.18

I t also seems more lik e ly

that Farm Bureau could, with d if f ic u lt y , continue the current system
without major investments over an eleven-year in te rv a l.
With this eleven-year interval (ten years of warehouse
l i f e used) the residual value fo r the new warehouse w ill range from
$181,733.33 to $190,533.33 fo r i n i t i a l investments of $397,600.00
and $420,800.00, respectively.

These residuals are expected fo r

the building and the railro a d siding.

The equipment investment of

$10,000.00 to $20,000.00 w ill be to ta lly depreciated over the ten
years of th is evaluation.
17 For those fa m ilia r with discounting procedure, the present
value of one d o lla r expected at the end of fiv e years is $0.49718,
nearly h a lf of its current value when discounted at a rate of
15 percent.
18With discounting procedures the present value fo r one d o llar
at the end of eleven years is only $0.21494 a t 15 percent and s t i l l
under one-half $0.47509 a t the low discount rate of 7 percent.

131

Return on Investment

A single rate of return w ill not s u ffic ie n tly evaluate the
proposed one-warehouse a lte rn a tiv e .

A proper analysis should survey

a range th a t includes the most lik e ly cash flows.

A range fo r the

i n i t i a l investment has previously been discussed with respect to the
s ite -re la te d variables:
siding.

new equipment, equipment tran sfers, and r a il

Other s im ila r r e a lis tic p o s s ib ilitie s should also be evaluated

Unfavorable results from any one contingency might d isq u alify or
devalue an otherwise p ro fitab le investment.
One contingency has to do with the expectation fo r demand
beyond 1980.

Farm Bureau's selection of the 610,535 cubic foot

warehouse suggests, according to the capacity recommendation in
Chapter IV , th at they expect demand to plateau a t the 1980 le v e l.
The a fte r tax cash flows in Table 25 must therefore be adjusted to
account fo r th is p o s s ib ility .

The adjustment requires that the savings

from 1980-1981 through 1985-1986 be the same as the value fo r 1980-1981
The savings were, however, calculated to decrease fo r that period
because of the higher inventory carrying costs required to meet demands
increasing at a rate equivalent to that p rio r to 1980-1981.

The flows

in Table 25 were calculated with an i n i t i a l investment of $397,600.00:
$259,400.00 fo r the building, $13,200.00 the low end of the expected
range of costs fo r the railro ad siding, $15,000.00 fo r shrink pack
equipment, $10,000.00 fo r the lower expected costs of tran sferring
old and buying new equipment, and $100,000.00 fo r land.

Table 25.

Year

Annual Cash Flows A fte r Taxes fo r a $397,600.00 I n it ia l Investment Through 1985-1986
Column 1

Column 2

Column 3

Column 4

Column 5

Column 6

Before Income
Tax Cash Flows
for a OneWarehouse System
at Year Enda

Taxable Cash Flows
(1 - Additional
Depreciation of h
$5,234.67 per Year)0

Incane Tax.
(3 x 0.25)

After Tax
Cash Flows
(1 - 4)

After Tax
Warehouse
Residual Value

Total After Tax
Cash Flows
(4 + 5)

270,396.42

270,396.42

$
1975-1976

0

0

0

0

1976-1966

53,621.06

48,386.39

12,0%. 60

41,524.46

0

41,524.46

1977-1978

45,834.44

40,599.77

10,149.94

35.684.50

0

35.684.50

1978-1979

37,503.40

32,268.73

8,067.18

29,436.22

0

35.684.50

1979-1980

29,909.88

24,675.21

6,168.80

23,741.08

0

23,741.08

1980-1981

21,385.74

16,151.07

4,037.77

17,347.97

0

17,347.97

1981-1982

13,407.92

8,173.25

2,043.31

11,364.61

0

11,364.61

1982-1983

5,022.13

-212.54

-53.14

5,075.27

0

5,025.27

1983-1984

-3,345.25

-8,579.92

-2,144.98

-1.200.27

0

-1,200.27

1984-1985

-10,849.57

-16,084.24

-4,021.06

-6.828.51

0

-6,828.51

1985-1986

-18,908.38

-24,143.05

-6,035.76

-12,872.62

281,733.00

268,860.71

aIncludes $85,856.37 of constant yearly flows from labor, labor and volume related variable costs, damage, pallet,
yard truck, switching engine and slot system savings plus the inventory carrying cost and slot system flows of Tables 23
and 24.
^Includes $9,080.67 per year of added depreciation for the building and its rail siding plus $1,000 for equipment
less $4,154.00 of old depreciation. Negative values represent losses to reduce taxable income.
cNegative values represent tax credits, a source of cash.
dThe $397,600.00 investment would also be an outflow in the beginning of the 1975-1976 fiscal year.

133

These flows when adjusted fo r demand le v e lin g -o ff a t the
1980 level resulted in a 16.23 percent rate o f return a fte r taxes.
This and the remaining returns were calculated according to the
formula:
n
£

A,

t= o

(l+ r )*

J

= 0

where:
At = cash flow fo r period t ,
n = the la s t (eleventh) period, and
r = the internal rate of return.
This return includes three yearly net p r o fit lo s t savings
values th at were s lig h tly overestimated as previously explained.
Because o f the r e la tiv e ly low magnitude of those savings the internal
rate o f return should not be grossly overstated.
The evaluation of the remaining contingencies w ill include
estimates o f residual value s e n s itiv ity , a point o f e a r lie r concern.
In the situ atio n described above the warehouse residual value could
decrease 63.3 percent before the return would drop below 14 percent
(see Table 26).

Table 26.

In te rn a l Rate o f Return and S e n s itiv ity C alculations Through 1985-1986 fo r a One-Warehouse System

Demand Expectations
from 1979-80
Through 1985-86

Depreciable
Investment3

Continue to
Increase at
the 1972-73
to 1979-80
Rate

Plateau at
the 1979-80
Level

($)

Residual Value Sensitivity
Internal
Rate of
Return on
Investment
(IRR)

Residual Value
of the New
Warehouse by
the End of
1985-86

Dollar Amount
that Residual
Could Decrease
Without Greatly
Changing IRR

Percent
Decrease
in
Residual

Resultant
IRR

(%)

($)

($)

(%)

(%)

297,600.00

No

Yes

16.23

181,733.33

115,071.88

63.3

14

320,800.00

No

Yes

14.63

190,533.33

32,769.80

17.2

14

297,600.00

Yes

No

14.12

181,733.33

4,987.15

2.7

14

320,800.00

Yes

No

12.63

190,533.33

100,506.89

52.8

10

450,500.00

No

Yes

8.98

277,000.00

55,061.02

19.9

8

450,500.00

Yes

No

7.19

277,000.00

55,936.92

20.2

6

aThe depreciable investment includes the warehouse and siding value depreciated over th irty years and
equipment over ten, but does not include the $100,000.00 for land.

135

S e n s itiv ity Analysis
Table 26 shows fiv e additional contingency rate of return
calculations.

The second row of th at tab le indicates th at a 14.63

percent return would re s u lt i f the previous analysis was only modified
to include the higher costs fo r s ite -re la te d variables.
The th ird row of the same table reports a 14.12 percent return
should demand not plateau at the 1979-1980 le v e l.

The 2 percent

decrease resulted solely from including the flow estimates from
Table 25 fo r 1980-1981 through 1985-1986 rather than holding them
at the 1980-1981 levels as in the i n i t i a l c alcu latio n .

This retu rn ,

however, is not overestimated as was suggested in the f i r s t case.
Here the three overestimated values fo r 1976-1977 through 1978-1979
should be more than o ffs e t by the six underestimated values fo r 19801981 through 1985-1986, depending on the magnitude of the o ffs e ttin g
errors.
The fin a l three intern al rate o f return calculations represent
d iffe rin g mixes of i n i t i a l investments and one or the other of the two
previous demand expectations.

The $450,500.00 i n i t i a l outflow is made

up of a building cost 50 percent higher than the one previously used
as well as the higher s ite -re la te d estimates.

This calculation also

gives an indication of returns th at would be expected from a building
with 50 percent more flo o r space at the lower price level i n i t i a l l y
used.

136

There is a t least one other area o f concern that is d if f ic u lt
to quantify that can be adequately handled subjectively.

By stating

the 1972-1973 savings calculations in 1975 d o lla rs , d iffe re n tia l
in fla tio n rates fo r labor, transportation, and agricu ltu ral inputs
have been accounted fo r through 1975.

The returns as presented,

however, have included zero in fla tio n fo r the post 1975 estimates.
In the most general sense, in fla tio n would cause the cash
flows fo r 1976-1977 through 1985-1986 reported in Table 25 to increase,
resulting in higher rates of return fo r each of the contingencies
previously evaluated.

In fla tio n could also, with lim ited subjective

in te rp re ta tio n , demonstrate the opposite e ffe c t.
In Table 22 the 1979-1980 savings were lower when expressed
in 1972-1973 terms.

In th a t analysis additional inventory carrying

costs fo r the proposed warehouse were o ffs e t by savings from numerous
other sources, including a r e la tiv e ly large savings from labor.

The

in fla tio n index fo r labor showed a 16 percent increase fo r those years
while a ll other values, inventory carrying costs among them, increased
at a fa s te r ra te .

In 1975 terms, th e refo re , there was r e la tiv e ly less

labor savings to help o ffs e t inventory carrying costs than in 1972-1973.
Should the same re la tiv e rates of in fla tio n continue through 1985-1986,
the flows reported in Table 25 would have to be decreased and the
internal rates of retu rn , as presently calculated, would be
overestimated.
I t is important to note, however, th a t th is alleged over­
estimation is a s t r ic t conceptual extrapolation of the mathematical

137

estimates used in these calculations.

What the mathematics cannot

re fle c t is the fa c t th at the warehousing alte rn a tive s under evaluation
are not operating at equivalent performance lev els.

I f the current

system were to continue by deleting product lines of lesser importance,
the resulting loss in revenue from those products would add greatly to
the savings as currently expressed fo r the one-warehouse system.
The previous analysis has evaluated Farm Bureau's lik e ly
short-run strategy fo r continuing th e ir current system:
higher stock-outs as demand increases.

accepting

In the longer run, c r itic a l

inventory shortages may force Farm Bureau into another strategy fo r
maintaining th e ir unmodified current f a c i lit ie s .

Should they decide

to delete e n tire product lin e s , the internal rates of return from the
comparison with the larger one-warehouse system w ill increase sub­
s ta n tia lly .

An internal rate o f return of over 70 percent ensues

from the following assumptions:
1.

Once the current system reaches capacity a t some desired
performance le v e l, product lines w ill be deleted to
maintain that performance le v e l.

2.

Continued products w ill ex h ib it average dollar-to-volum e
ratios lik e those in the current system.

Given the above assumptions, stock-out p r o fit lo s t values that were
previously used are replaced by the much larger d iffe re n tia ls from
sales plateauing at the 1975-1976 level fo r the existing system but
continuing to grow with demand fo r the one-warehouse system.

138

This la s t analysis provides objective input as a basis fo r
subjective analysis of the product-deletion approach.

To claim more

fo r the objective analysis might be misleading because of the narrowness
of assumption number two.

I t seems equally as lik e ly that continued

product lines could ex h ib it dollar-to-volum e ratios unlike those of
the current system.

Higher r a tio s , fo r example, would lead to higher

sales and higher inventory carrying costs than those used in the
objective analysis.
I f , on the other hand, the current system continued with a ll
product lin e s , accepting higher and higher losses from being out of
stock, i t is lik e ly that both warehouses would be past the c r itic a l
point on th e ir net p r o fit loss functions.

This situation would create

savings fo r the one-warehouse system th at would tend to o ffs e t the
increased inventory carrying costs.
In essence, th is la s t argument stems from knowledge of the
costs th at e x is t when the one and two-warehouse altern atives are
compared at equivalent performance levels (see Table 19, Chapter IV ).
When the two altern atives are performing equivalently the one-warehouse
system demonstrates an advantage in each cost area.

With this in mind,

the only possible e ffe c t of in fla tio n , whether or not they are d if f e r ­
e n tia l ra te s , would be to increase the yearly savings flows and the
related internal rates of return.

CHAPTER VI

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Summary
Increasing demand fo r ag ricu ltu ral products has forced an ever
decreasing farm population to provide more output from fewer acres.
Farmers in Michigan are no exception.

They too are attempting to

remain competitive in a ll ag ricu ltu ral enterprises by increasing
th e ir productivity.
The Michigan Farm Bureau, in its role as input supplier, plays
a v ita l part in th is attempt to increase productivity.

To remain com­

p e titiv e , Farm Bureau must also continually s triv e to keep its costs
low.

They are concerned, however, th at th e ir warehousing f a c ilit ie s

are not adequate to meet the expected increase in demand fo r
a g ricu ltu ral inputs.
The purpose of this research was to determine whether the
existing warehouse system is s u ffic ie n t to f u l f i l l expected needs.
In addition, Farm Bureau requires that the current system's c a p a b ilitie s
be weighed against those of a c e n tra lly located one-warehouse system.
The objective was to compare projected future assembly, d is trib u tio n ,
and warehouse cost structures fo r the current f a c ilit ie s to those fo r
each of seven proposed one-warehouse locations.

139

140

A modified lockset model was selected fo r use in analyzing
d is trib u tio n costs.

The method can account fo r irre g u la r dealer

demands, p a rtia l load delivery requirements, and backhaul supply
points without excessive computational costs, where other methods
cannot.

The many and varied product lines carried in the Farm Bureau

warehousing system were aggregated into sixteen representative product
groups.

This aggregation process fa c ilita te d the calculation of d o lla r

to cubic fe e t conversion factors necessary to the modeled reconstruction
of h is to ric capacity and cost experiences.

The d is trib u tio n portion of

the transportation analysis proceeded by constructing modeled routes
that exhibited average capacities and variable costs sim ilar to those
experienced in actual practice.

Once the lockset model adequately

duplicated existing behavioral structures, its v a lid ity was established
fo r calculating the proposed one-warehouse location's d istrib u tio n costs.
Assembly costs fo r suppliers not included as backhaul elements
in the d is trib u tio n study were analyzed d e scrip tively.

Variable in ­

bound fre ig h t rates were applied to the quantity of products received
or expected a t the two-warehouse system and at each of the seven pro­
posed one-warehouse locations.

The m ajority of the products assembled

into Farm Bureau warehouses have standard costs fo r delivery anwhere
in Michigan.

The assembly cost calculatio ns, therefo re, included only

those few product lines with fre ig h t rates that vary with distance and
therefore location.
The findings from the transportation analysis exhibited no
substantial advantage fo r any of the seven one-warehouse locations

141

proposed.

S im ila rly , no advantage was found fo r a one-warehouse system

over the current two f a c ilit ie s with respect to transportation costs.
This lack of advantage holds even though Farm Bureau predicted a
$14,328.35 savings beyond that calculated in the model fo r elim inating
interwarehouse transfers and reducing t r a ile r requirements.
Without the lockset model an increase in transportation costs
proportional to projected increases in d o lla r demand might have been
expected.

The model, instead, calculated cost increases only one-third

the size of the projected d o lla r demand increase.

What is obvious with

lockset is that the demand increases in cubic measure are not as great
as th a t indicated by the d o lla r amount.

Further investigation into the

cause of th is res u lt showed that predictions fo r demand increases fo r
high dollar-to-volum e products were larger than those with low d o lla rto-volume ra tio s .
With the transportation study completed, only the study of
in-warehouse operations remained.

Warehouse operating costs were

analyzed using a combined economic-engineering systems-simulation
approach.

An economic engineering technique was required in order

to determine cost structures fo r a system not yet in existence, the
proposed one-warehouse system.

Knowledge with respect to important

dynamic factors such as rate of output, length of operation, scheduling,
ordering lead times, ordering delays, and storage was extended beyond
what could be gained from a basic economic engineering study by using
a systems simulator.

142

The operations simulator fo r the two existing warehouses
demonstrated that i t could track r e a lity within small e rro r bounds.
I t also performed three other functions in addition to model v e r i f i ­
cation.

F ir s t, i t provided indicators of magnitude and s e n s itiv ity

fo r design parameters necessary in constructing the one-warehouse model.
Second, the current systems model generated inventory strategy cost
functions showing the tra d e -o ff between costs of inventories carried
and p ro fits lo st fo r being out of items requested.

Third, the simu­

la to r's most important function was to demonstrate how the current
system would perform under expected future demand conditions.
The End-to-End Model b u ilt to react as i f the current system
could have consolidated inventories, gave design parameters fo r the
proposed one-warehouse system in addition to calculating savings that
would be made possible through inventory consolidation.

I t was the

End-to-End Model that was modified according to Farm Bureau and man­
ufacturer specification in developing a model fo r the proposed onewarehouse system.
The c a p a b ilitie s of the new-warehouse simulator allowed i t to
generate capacity requirements and inventory strategy cost functions
to compare with those calculated fo r the current system.

I t was also

the source of variable cost estimates required in comparing the two
systems' performances fo r the 1979-1980 fis c a l year.
The essence of the findings from th is portion o f the research
can be expressed in terms of inventory strategy costs, capacity
re s tric tio n s , and variable cost comparisons.

A s t r ic t mathematical

143

interp retatio n of the quantified variables would indicate that the
current system could minimize inventory-related costs by reducing
stock levels 40 percent i f one ignores i l l - w i l l created by higher
stock-out rates.

On the other hand, the results imply that the

existing system could not continue u n til 1980 with current performance
levels because o f capacity re s tric tio n s .

Lastly, the two-warehouse

system would cost Farm Bureau a to ta l of $83,534.10 more in 1979-1980
at the forced lower performance level than would a one-warehouse system
providing a sim ilar service.
Warehousing and transportation enterprises have been analyzed
separately.

An investment analysis was performed to t ie the two

together and to include cost estimates and cash flows not previously
evaluated.

The cash flow estimates fo r 1985-1986 were made possible

through lin e a r approximations and extrapolations fo r inventory carrying
cost and net p r o fit lo st d iffe r e n tia ls .

In addition, internal rate of

return calculations were made fo r several d iffe re n t investment con­
tingencies to better account fo r costs th at could not be predicted
with s u ffic ie n t accuracy.
The a fte r tax rates of return ranged from 7.19 percent to
16.23 percent over the e n tire set o f contingencies evaluated.

The

two lowest returns were calculated fo r a warehouse costing 50 percent
more than the estimates made by Farm Bureau and th e ir building con­
tra c to r.

The remaining rates that s ta rt at 12.63 percent and increase

up to the 16.23 percent figure include Farm Bureau cost estimates fo r
building, land, and shrink-pack machinery plus d iffe rin g combinations

144

of possible costs fo r the railro ad siding, new equipment, and equipment
tra n sfe r.

The contingencies also include two extreme demand predictions

and s e n s itiv ity analyses th at measure the importance of warehouse
residual values.
Conclusions
1.

The 1972-1973 and 1979-1980 d istrib u tio n costs fo r each

proposed one-warehouse location would not be substantially higher than
those in the current two-warehouse system.

I t therefore follows that

l i t t l e substantial difference exists between the one-warehouse
alte rn a tiv e s.
2.

The one-warehouse locations would have s lig h tly lower

assembly costs than those exhibited by the present system.
3.

For a ll intensive purposes the assembly savings from the

one-warehouse locations cancel the existing system's d is trib u tio n
savings.

Therefore, a ll alternatives are e ss en tially equivalent with

respect to transportation costs.
4.

Should Farm Bureau decide to select a s ite fo r a one-

warehouse system, the importance of variables other than those o vertly
included in the analysis is emphasized.

Factors such as a v a ila b ility

and cost of land, size of local labor force, and management's personal
preferences become r e la tiv e ly more important than they would have been
i f any one location had exhibited superior cost savings.
5.

Quantity discounts w ill not be a source o f savings fo r the

one-warehouse system.

The warehouse simulator indicated no substantial

difference in the size of supply receipts between the two systems.

145

6.

Other things equal, lower inventory levels w ill gain more

savings from inventory carrying costs than losses from stock-outs in
e ith e r system.
7.

The 1979-1980 variable costs fo r the unmodified two-

warehouse system would be sub stan tially higher than those fo r a
one-warehouse system th at provides equivalent service.
8.

Equivalent service could be provided with less capacity

requirement in the one-warehouse f a c ili t y .
9.

Major modifications w ill be required in the current

warehousing system by 1979-1980 unless management accepts substantially
higher stock-outs than they have in the past, or unless they modify
th e ir service policy by deleting product lines o f lesser importance.
10.

Internal rate of return estimates were made conservative

by basing them upon an assumption th at the existing f a c ilit ie s could
continue, without m odification, through the 1985-1986 fis c a l year.
Expenditures fo r improving that system would increase the calculated
return values to some degree depending upon the magnitude o f the
investments that would be required.
Recommendations
Most of the recommendations to be drawn from th is research
come d ire c tly from the conclusions made in the previous section.

A

review of that section w ill lik e ly suggest some appropriate actions
so those recommendations w ill not be lis te d in th is section.

Recom­

mendations that do not follow d ire c tly from the conclusions are
presented below.

146

1.

I f a decision is made to invest in the one-warehouse

system and no other modifications are made in the current system,
the new warehouse should be operating by mid-1976.

This assumes a

maximum acceptable net p r o fit lo st in the $1,300.00 neighborhood.
Higher minimum acceptable levels would, of course, extend this
deadline.
2.

With the same maximum stock-out level ($1,3 00 .00 ), the

new building should have between 610,535 cubic fe e t and 1,013,337
cubic fe e t of capacity in order to be adequate u n til 1987.

The

smaller value would be adequate i f demand levels o ff at the 19791980 le v e l.

The larger value assumes an increase in demand between

1980 and 1987 equal to the 1973 to 1980 increase.

Lower acceptable

stock-out levels or longer desired warehouse l i f e times would increase
these requirements.
3.

Scheduling has been mentioned as a method fo r keeping the

to ta l rate of output constant in the face o f highly seasonal or flu c ­
tuating demand.

Because management was assumed constant in th is study,

the scheduling function should be investigated as a potential source of
improved output.

A less immediately important nonsequential task may

be rescheduled, fo r example, to keep i t from hindering those that are
sequential.
4.

Demand predictions may not include proportional increases

in d o lla r and volume terms, therefore future planning should include
estimates fo r both values.

147

5.

Reductions in inventories to take advantage o f the

potential savings demonstrated in th is study should not be taken
to the minimum points calculated.

This is true because consumer

i l l - w i l l was not included in the inventory strategy cost functions
and because i t is more costly to be below the true minimum cost
inventory level than i t is to be above i t .
6.

The internal rate of returns fo r the one-warehouse

investment should be weighed against Farm Bureau's cost of capital
and evaluated in context of the conditions w ithin which the calculations
were made.

I f any of the returns are outside Farm Bureau's range of

ac c e p ta b ility , the decision to accept or re je c t the investment should
include p ro b ab ility estimates fo r those contingencies th at caused the
unfavorable values.
7.

The decision to accept or re je c t the one-warehouse system

should also include subjective impact estimates fo r important nonqu antifiab le factors such as reactions of the current employees,
th e ir union, and the local community.
8.

Farm Bureau might also want to re-evaluate other

alternatives to th e ir current system that were previously thought less
desirable than the one-warehouse option.

In lig h t of th is research

they may, but would not necessarily, decide to investigate some of
these options more thoroughly.
9.

Farm Bureau might also capture a greater return from th e ir

investment in this research i f they could integrate these analyses

techniques into th e ir decision processes.

The modified lockset model,

for example, could be easily adapted to aid in the route structuring
process.

The warehouse simulators might be used fo r e ith e r of the two

a lte rn a tiv e warehousing systems to assist in ordering and inventory
strategy, as well as labor force planning.

I t , however, would be

more d if f ic u l t to incorporate into Farm Bureau's computer system.
10.

F in a lly , Farm Bureau Services and other agribusiness

firms should continue to take advantage of studies th at use university
resources.

Increased university-industry intimacy should provide

advantages to both participants by improving theory's a p p lic a b ility
while seeking sound solutions to actual agribusiness problems.
Taken as a whole, the research demonstrates some re la tiv e
economic advantages fo r a one-warehouse system but no real preference
fo r any one of the seven proposed locations.

I f the new warehouse is

not operationalized, some other a lte rn a tiv e w ill be needed to keep
service from deteriorating with the unmodified two-warehouse system.
In a l l , the study confirms the Michigan Farm Bureau's suspicion that
th e ir warehousing system may not be adequate to s u ffic ie n tly
accommodate expected future demand increases.

APPENDIX A
DEALERSHIPS AND BACKHAUL POINTS

APPENDIX A

DEALERSHIPS AND BACKHAUL POINTS

Reference
Code
1

2

3
4
5
6

7
8
9
10

11
12

13
14
15
16
17
18
19
20
21

22
23
24
25
26
27
28
29
30

Dealer Name

Reference
Code

Dealer Name
Hart
S c o ttv ille

Cadillac
Evart
Reed City
Traverse City
B attle Creek, Climax
Coldwater, Union City
H ills d a le
Allegan
Buchanan
Eau C laire

31
32
33,
34J
35,
36J
37
38,
39
40

Holland
Three Oaks
W atervliet
Kalamazoo
Marcell us
Mendon
Schoolcraft
Albion
Charlotte
Hastings

41
42
43
44
45
46
47
48
49
50

Bay C ity*
Brooklyn
Chelsea
Dexter
South Lyon
Ypsilanti
Caro
Crosswell
M arlette
Mt. Clemens

Lake Odessa
Leslie
Marshal 1
Nashville
Portland
Big Rapids
Fremont
Kent C ity
Stanwood
Coopersvilie

51
52
53
54
55
56
57
58
59
60

New Haven
Richmond
Snover
Yale
Elkton
Harbor Beach
Kinde
Minden City
Pigeon
Ruth

149

Chicago, J o lie t, Calumet*
B attle Creek, H ills d a le
and surrounding area*
Manistee
Lima, Kenton*
Saginaw, Midland, Bay C ity *

150

Reference
Code

Dealer Name

67
68
69
70

Sebewaing
Ubly
Adrian
B lis s fie ld
D eerfield
Highland
Ida
Maybee
Tecumseh
W illis

71
72
73
74
75
7b
77
78
79
80

Gladwin
Pinconning
Sterling
West Branch
C laire
Falmouth
Marion
McBain
M e rritt
Breckenridge

81
82
83
84
85
86
87
88
89
90

Hemlock
Mt. Pleasant
Remus
Vestaburg
Chesaning
Durand
Lennon
Middleton
Mt. Morris
Ovid

61
62
63
64
65
66

♦Backhaul supply points.

Reference
Code
91
92
93
94
95
96
97
98
99
100
101
102

103
104
105
106
107

Dealer Name
Owosso
St. Johns
Almont
Armada
Capac
Lapeer
Oxford
Washington
Fow lerville
Holt
Howel1
Lansing
Mason
Webberville
Williamston
B attle Creek, H illsd ale
B lis s fie ld *
Midland, Bay C ity ,
St. Johns*

APPENDIX B
EXISTING ROUTE STRUCTURES

APPENDIX B

EXISTING ROUTE STRUCTURES

Jenison
Total Variable D istribu tio n Cost $1,600.00
Weekly Demand in Cubic
Feet per H alf YeaF
Reference
Number
3
2
1
4

7
6

5
35

11
8

13
10
9
12
34

Miles

Route Component
Jenison t o :
Reed City
Evart
Cadillac
Traverse C ity
Manistee
Return

F irs t
H alf Year

Second
H alf Year

76
19
42
52
65
128
382

3
212
18
777
1,010

1
253
7
964
1,225

Jenison to:
H ills d a le
Coldwater-Union City
Climax
B attle Creek
Return

121
24
39
0
261

162
499
416
1 ,077

171
574
392
1 ,137

Jension t o :
Holland
Allegan
W atervliet
Eau C laire
Buchanan
Three Oaks
Chicago
Return

26
118
209
27
296
345
36
54
56
18
23
22
19
170
181
22__________ ___ 65_____ ___20
80
726
833
414

151

152

Meekly Demand in Cubic
Feet per H alf Year
teference
Number
15
16
17
14
41

Miles

F irs t
H a lf Year

74
33
29
15
143

246
380
44
605
1,275

-

Route Component
Jenison to:
Marcell us
Mendon
Schoolcraft
Kalamazoo
Bay City
Return

Second
H alf Yeai
320
376
66

928
1,690

121

415
25
21
20

24
19
22

18
23
36

28
27
29
26
40

Jenison to:
Portland
Lake Odessa
Hastings
Nashville
Charlotte
Leslie
Albion
Marshall
B attle Creek
Return
Jenison to:
Kent C ity
Freemont
Stanwood
Big Rapids
Bay City
Return

41
17
22

39
24
24
34
12

14
77
304
32
42
34
17
98

249
292

34
39
563
19
299
284

102

88

7
32
632
11

4
1,329

5
1,331

533
467
385
52
1,437

521
359
374
76
1,330

643
341
366
1,350

394
584
468
1,446

121

344
30
31
32
38

Jenison to:
Coopersville
Hart
S c o tts v ille
Manistee
Return

33

Chicago round t r ip backhaul

39

Lima-Kenton round t r ip backhaul

29
66

28
27
128
278

153

Zilwaukee
Total Variable D istribution Cost $1,506.50
Weekly Demand in Cubic
Feet per H alf Year
Reference
Number
45
46
44
43
42

Route Component
Zilwaukee to :
South Lyon
Ypsilanti
Dexter
Chelsea
Brooklyn
Return

Miles
82
32
18
14
34

F irs t
H alf Year

Second
H alf Year

15
171
44
133
126
474

174
94
179
34
502

30
35
25
39
28
17
69

259
17
235
391
24

468
31
165
410
26

8

3
939

121

21

301
47
49
53
54
48
52
51
50

61
59
55
57
56
60
58
62

Zilwaukee t o :
Caro
M arlette
Snover
Yale
Croswel1
Ri chmond
New Haven
Mt. Clemens
Return
Zilwaukee t o :
Sebewaing
Pigeon
Elkton
Kinde
Harbor Beach
Ruth
Minden City
Ubly
Return

93
344
50
16
0

35
35
56
28
28
91
339

2

12

8

69
4
1,185

72
294
230
39
91
586
15
38
1,365

104
221

216
63
77
433
13
39
1,166

154

Weekly Demand in Cubic
Feet per H alf Year
Reference
Number

68

70
65
67
64
63
66

69

Route Component
Zilwaukee t o :
Maybee
W illis
Deerfield
Ida
B lis s fie ld
Adri an
Highland
Tecumseh
Return

72
73
74
71

Zilwaukee t o :
Pinconning
Sterling
West Branch
Gladwin
Return

75
77
78
76
79

Zilwaukee t o :
Clare
Marion
McBain
Falmouth
M e rritt
Return

81
80
82
83
84

Zilwaukee t o :
Hemlock
Breckenridge
Mt. Pleasant
Remus
Vestaburg
Return

Miles

F irs t
H alf Year

120

64

0

12

Second
Half Year

26
26
26
14
59
48
120
439

17
173
41
82
388
163
940

73
16
18
133
114
136
307
100
897

34
17
36
34
14
191

478
361
808
265
1,912

505
366
527
195
1.593

61
34
19
23
0
102
239

42
64
263
218
96
683

12
181
261
261
162
877

18
30
22
21
80
146

271
4
505
266
91
1,137

231
56
272
224
95
878

317

155

Weekly Demand in Cubic
Feet per H alf VeaF
Reference
Number
97
93
96
98
95
94

Route Component
Zilwaukee to:
Oxford
~
Almont
Lapeer
Washington
Capac
Armada
Return

85
88
92
90
91
86
87
89

Zilwaukee t o :
Chesaning
Middleton
St. Johns
Ovid
Owosso
Durand
Lennon
Mt. Morris
Return

101
99
104
105
106

Zilwaukee t o :
Howel1
Fow lervilie
Webberville
Williamston
B attle Creek
Return

Miles

F irs t
H alf Vear

Second
H alf Year

40
41
27
100
332

122

795

59
91
396
83
33
28
690

30
29
18
9
13
17
23
27
32
198

318
10
275
24
91
198
25
132
1,073

523
17
338
24
70
269
29
167
1,437

72
12
0
15
130
106
335

205
519

336
238
8
152
734

76
27
21

66

56
551

2
86

812

APPENDIX C
PRODUCTS BY PRODUCT GROUP

APPENDIX C

PRODUCTS BY PRODUCT GROUP
Conversion
Factors

1.8

01 FERTILIZER:
470000-4799993

6.6

02 SEED:
440000 THROUGH 446999

1.6

03 FEED:
450000
453215
453247
435255

THROUGH
THROUGH
THROUGH
THROUGH

453213
453236
453253
456999
10.4

04 MEDICINAL SUPPLIES:
45321400-45321499
458000-458999t
}
459000-459999J
482200 THROUGH 48299999
483000 THROUGH 48349999

HORSE CARE
ANIMAL HEALTH
ORTHO
MISC. CHEM.
36.1

05 CHEMICALS:
480000 THROUGH 48119999
447000 THROUGH 44709999

HERB., INSECT., FUNG.
SEED TREATMENT & INOCULANTS
20.4

06 ROOFING:
460000-460499
460500-460599

STEEL ROOFING
ALUMINUM ROOFING

a

Farm Bureau product lin e id e n tific a tio n code.

156

157

Conversion
Factors

22.2

07 PANELS AND ACCESSORIES:
461000-661299
461300-4613599
461600-461699

FIBERGLASS PANELS
POLE BARN NAILS
NAILS & STAPLES
9.8

08 BUILDING COSMETICS:
462000-462199
462200-462599
462600-462699
462700-462799
462800-462899
462900-462999

ASPHALT ROOFING
PAINT
TURPENTINE
PAINT BRUSHES & ROLLERS
BROOMS & BRUSHES
POLYETHYLENE
3.2

09 POST, POLES, AND LUMBER:
463000-463199
463200-463399
463400-463499
463500-463599
463600-463699
463700-463799
463800-463899
463900-463999

ROUND POSTS
ROUND POLES
SQUARE POLES
PRESSURE TREATED LUMBER
TREATED LUMBER & GLUE
DIMENSIONAL LUMBER
STEEL POSTS
GATES
2.5

10 FENCE:
464000-464099
464100-464299
464300-464399
464400-464599
464600-464999

DOMESTIC FARM FENCE
IMPORTED FARM FENCE
WIRE
WELDED WIRE FABRIC
MISCELLANEOUS FENCE
16.2

11 ELECTRIC FENCE:
465000-465099
465100-465199

ELECTRIC FENCE ACCESSORIES
ELECTRIC FENCE
3.0

12 BULKY CONTAINERS:
465200-465299
465300-465499
465500-465899
465900-465999

TANKS
FOUNTAIN, TROUGHS & HEATERS
FEEDERS
TRASH BURNERS & LAUNDRY TUBS

158

Conversion
Factors

13.6

13 FLEXIBLES:
466000-466199
466200-466299
466300-466399
466400-466499
466500-466599
466600-466799
466800-466899

TWINE
CHAIN
ROPE
PLASTIC PIPE
WORTHINGTON PRODUCTS
LADDERS
TARPS
3.3

14 TOOLS:
467000-467299
467300-467599
467600-467799

LAWN MOWERS & ACCESSORIES
POWER TOOLS
HAND TOOLS

15 SEMI-MISCELLANEOUS:
468000-468099
468100-468299
468300-468399
468400-468499
468500-468599
468600-468699
468700-468899
16 MISCELLANEOUS:
469000-469999

4.1
BARN DOORS & ACCESSORIES
BARN EQUIPMENT
FEED BINS, AUGERS & CRIBS
GALVANIZED WARES
SPRAYERS, DUSTERS & FOGGERS
SEEDERS, WHEEL BARROWS, &
CEMENT MIXERS
CALF, POULTRY EQUIPMENT, &
ELECTRIC SUPPLIES
9.3

APPENDIX D

WEEKLY AVERAGE SEMIANNUAL DEALER DEMAND IN CUBIC FEET

APPENDIX D

WEEKLY AVERAGE SEMIANNUAL DEALER DEMAND IN CUBIC FEET

Dealer9
Code

0

1

2

18
118
32
341

212

23
632
643
0

0

3
1,786

8

2

72
265
271
91
205

563
394

7
209
39
584

0

0

9

4
1,633
16
56
24

10

0

69
104
195
231
70
336

3

4

5

6

7

8

9

3
54
4

777
605

499
380
52

162
44
467

296

170
249
385

F irs t h a lf y ear:
0
1
2

3
4
5
6

7

12

8

4
24

9

0

10

11

416
246
7

0

0

0

0

0

0

0

38
478
505
275

133
235
82
361
266
46

44
391
41
808
91

15
230
17
42
318

259
39
173
64
25

24
15
64
263

0

0

171
91
388
218
198
551

66

122

17
294
163
96
132
519

0

0

2

86

0

253

1

392
320
34

574
376
76

345

56
5

964
928
19

171

20

66

88

359

521

0

0

0

0

0

0

0

94
410
114
527
95
28

21

174
77
307
261
269
396

468
63
133
181
29
59

26
13
73
261
17
83

31

39
505
272
338

179
165
136
366
224
91

0

0

8

0

0

65
292
366
126

102

533

10

Second h a lf year:
0
1
2

3
4
5
6

7
8

22

284
468
34
12

216
18
12

523
33
152

181
299
374

221
100

162
167
238

Dealer codes along the v e rtic a l portion of the table represent
the f i r s t sub-part o f the e n tire dealer code while the horizontal
portion represents the second h a lf. In the f i r s t h alf-y ea r dealer 67,
fo r example, had demand fo r products requiring 173 cubic fe e t o f truck
space.
159

APPENDIX E

GENERATED ROUTE CONFIGURATIONS FOR SEVEN
PROPOSED ONE-WAREHOUSE LOCATIONS

APPENDIX E

GENERATED ROUTE CONFIGURATIONS FOR SEVEN
PROPOSED ONE-WAREHOUSE LOCATIONS

Jenison-Zilwaukee F irs t H alf Year
Jenison--Variable D istribution Cost $1,628.50
Route Demand
in Cubic Feet

ROUTE NUMBER AND COMPONENTS
1—W,
2—W,
3—W,
4—W,
5—W,
6 —W,
7—W,

20,
22,
26,
27,
30,
11,
28,

25, 19, 5, 24, 40, W
23, 18, 7, 6 , 16,36, W
3, 2, 4, 1 , 37, W
32, 31 ,
38, W
8 , 34, W
13, 10, 9, 12, 15, 17, 14, 35, W
29, 41 , W

9- W* 39*

1,347
1,439
1,062
1,174
939
1,325
918

Round Trip Backhauls

Zilwaukee—Variable D istribution Cost $1,378.50
ROUTE NUMBER AND COMPONENTS
1- -w,
2- -w,
3- -w,
4- -w,
5- -w,
6- -W,
7- -W,
8- - w,
9- - w,
10- -W,
11- -w,

43,
55,
59,
74,
75,
82,
85,
93,
99,
72,
60,

42 ,
53,
61,
71,
77,
80,
81,
95,
105
73,

68, 69 , 65, 6 3 , 6 4 , 70 , 66 , 6 7 , 106, W
47, W
56, 58, 62, 57, 6 0 , 52 , 48 , 4 9 , W

W
79, 78, 76, 8 4 , 8 3 , W
88, 92, 90, 91, 8 6 , W

W
54, 94, 51, 50, 98, 97 , 96 , w
, 104, 101, 45 , 46 , 44, 8 7 , 8 9 , W
107 , w

W

Total V a ria b le D is trib u tio n Cost $ 3 ,0 0 7 .0 0
Total M ile s :

6,014

160

1,199
724
1,178
1,073
1,0 40
1,107
589
1,197
1,199
839
1, 200

161

J e n ison-Zilw aukee Second H a lf Year

Jenison—Variable D istribution Cost $1 ,625.00
ROUTE NUMBER AND COMPONENTS
1—W,
2—W,
3—W,
4
u
5—w!
6 —W,
7—W,
8 —W,
9—-W,

21 , 22,
19, 5, 24, 36, W
26, 3, 2, 4, 1 , 37, W
27, 32,
31 , 38, W
14
34 w
I l l 8 , *13, 10, 9, 12, 15, 35, W
20, 39,
W
17, 16,
6 , 7, 18, 23, 25, 40, W
30, 28,
29, 41 , W
33, W Round Trip Backhaul

Route Demand
in Cubic Feet
1,033
1,301
1,411
928
1,153
563
1,314
1,289

Zilwaukee--Variable D istribution Cost $1,377.00
ROUTE NUMBER AND COMPONENTS
1 -W ,
2--W,
3--W,
4 - W,
5--W,
6 -W ,
7 - W,
8 -W ,
9 - W,
10—W,

59, 61 ,
56, 58, 62, 57, 60, 52, 48, 49, 53, W
1,184
72, 55,
47, W
1,189
75, 77, 79, 78, 76, 84, 83, W
1,196
82, 80, 8 8 , 92, 90, 91, 8 6 , W
1,046
85, 81,
W
754
93, 95,
54, 94, 51, 50, 98,97, 96, W
1,173
104, 43, 42, 6 8 , 69, 65, 63, 64, 70, 6 6 , 67, 45, 87, W 1,168
89, 44, 46, 101 , 99, 105, 106, W
1,161
71 , 74, 73, 107, W
1,088
60, W
1,200

Total Variable D istribu tio n Cost $3,001.50
Total M iles:

6,003

162

S t. Johns F i r s t H a lf Year
Route Demand
in Cubic Feet

ROUTE NUMBER AND COMPONENTS

1—W,
2—W,
3—W,
4—W,
5—W,
6 —W,
7—W,
8 —w,
9—W,
10—W,
11—W,
12—W,
13—W,
14—W,
15—W,
16—W,

18, 16, 14, 36, W
22, 19, 25, 20, 21 , 33, W
26, 3, 32, 31 , 27, 38, W
28, 30, 11 , 34, W
80, 73, 9, 12, 10, 13, 15,17, 8
5, 23, 6 , 7, 42, 39, W
87, 89, 49, 48, 52, 60, 57, 62,
43, 44, 46, 67, 65, 70, 6 6 , 6 8 ,
72, 55, 53, 47, 41 , W
75, 79, 4, 1, 78, 77, 37, W
76, 74, 71 , 107, W
83, 2, 29, 84, 8 8 , 92, W
85, 81 , 82, W
90, 96, 93, 95, 54, 50, 94, 51 ,
105, 104, 101 , 99, 8 6 , 91 , W
60, W

, 24, 35, W
58, 56,
64, 69,

61 , 59,40, W
63, 106, W

98, 97,

45, W

1,083
1,212
1,229
1,294
1,274
1,207
1,239
1,288
1,202
1,260
1,291
1,239
1,094
1,236
1,101
1,296

Total Variable D istribu tio n Cost $2,983.00
Total Miles:

5,966
St. Johns Second H alf Year

1—W,
2—W,
3—W,
4—W,
5—W,
6 —W,
7—W,
8 —W,
9—W,
10—W,
11—W,
12—W,
13—W,
14—W,
15—W,
16—W,
17—W,

4, 1 , 78, 107, W
1,232
19, 24, 14, 21, W
1,285
22, 5, 39, W
676
26, 3, 32, 31 , 38, W
1,129
25, 20,
8 , 11 , 34, W
1,151
71 , 73, 9, 12, 10, 13, 15,17, 23, 35, W
1,231
18, 7, 6 , 16, 36, W
1,209
84, 29, 27, 30, 37, W
1,222
87, 89, 53, 49, 48, 52, 60, 57, 62, 58, 56, 61 , 59, 40, W
1,284
45, 44,
46, 67, 65, 70, 6 6 ,6 8 ,64, 69,63, 42, 106, W 1,220
75, 77,
79, 74, 76, 8 8 , W
1,160
80, 72,
55, 47, 41 , W
1,245
82, 83, 2, 28, 33, W
1,270
85, 81 ,
90, 92, W
1,116
96, 93,
95, 54, 50, 94, 51 ,98,97, 91 , W
1,243
105, 104, 101, 43, 99, 8 6 , W
1,182
60, W
1,296

To tal V a ria b le D is tr ib u tio n Cost $ 3 ,0 6 2 .0 0
Total M ile s :

6,124

163

Lansing F i r s t H a lf Year
Route Demand

ROUTE NUMBER AND COMPONENTS
CO

1- -w,
2- -w,
3- -w,
4- -w,
5- -w,
6- -w,
7- -w,
8- -w,
9- -w,
10- -W,
11- -w,
12- -W,
13- -w,
14- -w,
15- -w,
16- -w,

in Cubic Feet

1,0 98
16, 14, 24, 35, W
1,281
26
,
3
,
;
2
,
77,
38
28
,
29,
21,
, W
1,102
22, 105 , 101 , 99, W
W
1,275
30, 20, 36,
1,046
92, 82 , 83 , 33, W
1,265
19, 17, 15, 9, 12, 10, 13, 8 , 1 1 , 34, W
1,272
25, 8 4 , 31, 32, 27, 37, W
1,207
5, ;2 3, 6 , 7, 4 2 , 39 , w
1, 269
80, 73, 74, 79, 40, W
1, 263
45, 98, 50, 51, 94, 54, 53, 55, 4 7 , 4 1 , W
1,2 88
W
43, 4 4 , 46 , 67, 65, 70, 66, 68, 64, 69, 6 3 , 106,
1, 224
86, 96, 8 9 , 87 , 8 5 , W
1,286
88, 76, 4 , 1 , 78, 107, W
90, 59, 61 , 56, 58, 62!, 57, 60, 52, 48 , 4 9 , 9 5 , 93, 9 7 , 104, W 1, 230
1,147
91, 8 1 , 72 , 71 , 75, W
1, 296
60, W

Total Variable D istribution Cost $3,101.50
Total M iles:

6,203
Lansing Second H alf Year

1-

-w,

2 - -w,

3- -w,
4- -W,
5- -w,
6 - -W,
7- -w,
8 - -w,
9- -w,
1 0 - -W,
1 1 - -W,
1 2 - -W,
13- -W,
14- -w,
15- -w,
16- -W,
17- -w,

, 77, 76, 83, 82, W
19, 24, 14, 35, W
2 1 , 1 1 , 8 , 13, 10, 12, 9, 15, 17 , 22 1, 39, W
25, 30, 2 0 , W
5, 33, W
18, 7, 6 , 16, 36, W
78, 1 , 4, 37, W
48, 52, 60, 57, 52, 58, 56, 61, 59, 53, 55, 41 , w
50, 94, 51, 98, 97, 93, 95, 54, 49, 47, 40, W
80, 84, 26, 3, 32, 31, 38, W
85, 81, 72, 87, W
8 6 , 96, 89, 91, 90, 92, W
8 8 , 28, 29, 27, 34, W
104 , 45., 44, 46, 67, 65, 70, 6 6 , 6 8 , 64, 69, 63, 42, 106, W
105 , 99 , 101 , 43, 22, W
75, 71, 73, 74, 79, 107, W
60, W
2

Total V a ria b le D is tr ib u tio n Cost $ 3 ,0 7 2 .5 0
Total M ile s :

6,145

,191
,246
1 ,263
991
392
1 ,209
1 ,232
1 ,273
1 ,276
1 ,280
1 ,288
1 ,264
1 ,271
1 ,228
1 ,189
1 ,262
1
1

164

Io n ia F ir s t H a lf Year
ROUTE NUMBER AND COMPONENTS

1-W ,
2 -W ,
3—W,
4—W,
5 -W ,
6 —W,
7—W,
8 —W,
9—W,
1 0 —W,
11-W ,
1 2 —W,
13—W,
14—W,
15—W,
16—W,

Route Demand
in Cubic Feet

, 78, 4, 38, W
2 0 , 5, 36, W
2 1 , 19, 105, 104, 101, 99, 8 6 , W
24, 14, 17, 15, 16, 35, W
26, 1, 79, 74, 76, 77, W
84, 27, 31, 32, 3, 37, W
80, 72, 73, 9, 12, 10, 13, 11, 33, W
2 2 , 6 , 7, 42, 18, 23, 39, W
45, 97, 98, 51, 94, 50, 54, 95, 93, 96 , 40, W
83, 29, 28, W
90, 59, 61 , 56, 58, 62, 57, 60, 52, 48, 49, 89, 87, 41 , W
91, 85, 81, 82, W
92, 30, 8 , 34, W
25, 63, 69, 64, 6 8 , 6 6 , 70, 65, 67, 46, 44, 43, 106, W
8 8 , 47, 53, 55, 71, 75, 107, W
60, W
2

1,252
1,048
1,291
1,286
1,256
1,268
1,273
1,185
1,212

1,184
1,263
1,185
1,214
1,295
1,041
1,296

Total Variable D istribution Cost $3,099.00
Total Miles:

6,198
Ionia Second H alf Year

1- -w,
2- -w,
3- -w,
4- -w,
5- -w,
6- -w,

7- -W,
8- -W,

9- -W,
10- -w,
11- -w,
12- -w,
13- -w,
14- -W,
15- -W,
16- -w,
17- -W,

2 1 , 23, 18. , 7, 6, 5, 36, W
22, 19, 20. , w
2 9 , 27, 30., 39, W
11, 14, 2 4 ;, 34, W
8 , 13, 15, 17, 16, 35, W
8 4 , 26, 3, 32, 31, 37, W
97, 98, 51. , 94, 50 , 54, 95, 93 , 96, 40 , W
8 7 , 89, 53, 4 9 , 4 8 , 52, 6 0 , 57 ,6 2 , 5 8 , 56, 61 , 59 , 41 , W
4 5 , 4 4 , 46,, 67, 65 , 70, 66, 68 , 64 , 6 9 , 6 3 , 4 2 , 2 5 , W
75, 76, 4 , 38, W
80 , 72, 55,, 47, 88 , w
83 , 28, 33,, w
92, 91, 85,, 81, 90 , w
8 6 , 99, 43,, 101 , 104, 105, W
1, 79, 74, 73, 9, 12, 10, 106, W
2, 77, 78, 71, 82 , 107, W
60 , W

Total V a ria b le D is tr ib u tio n Cost $ 3 ,1 4 7 .5 0
Total M ile s :

6,295

1,2 69
1 ,1 46
1, 127
1 ,1 56
1,163
1,2 24
1,1 73
1,2 84
1 ,2 54
1, 237
1,262
745
1, 186
1,182
1 ,2 85
1, 162
1, 296

165

Alma F i r s t H a lf Year
Route Demand

ROUTE NUMBER AND COMPONENTS
1 -W ,
2--W,
3—W,
4—W,
5--W,
6 --W,
7--W,
8 —W,
9—W,
1 0 —W,
1 1 —W,
1 2 —W,
13—W,
14—W,
15—W,
16—W,

19, 24, 14, 5, 106, W
42, 7, 6 , 23, 18, 36, W
84, 27, 31, 32, 3, 38, W
28, 30, 11, 34, W
71, 76, 2, 26, 29, 33, W
44, 46, 63, 64, 6 8 , 6 6 , 70, 65, 67, 69, 43, 35, W
87, 96, 97, 98, 50, 51, 94, 54, 95, 93, 39, W
47, 53, 55, 72, 41, W
59, 61, 56, 58, 62, 57, 60, 52, 48, 49, 89, W
75, 79, 4, 1, 78, 77, 37, W
80, 74, 73, 40, W
82, 85, 81, W
8 8 , 105 , 104, 101 , 45, 99, 8 6 , 91 , 90, W
92, 25, 20, 21, 83, W
8 , 13, 10, 9, 12, 15, 17, 16, 107, W
60, W
22,

in Cubic Feet
1,281
1,185
1,268
1,294
1,132
1,288
1,222
1,202

1,214
1,260
1,173
1,094
1,150
1,212

1,278
1,296

Total Variable D istribution Cost $3,127.00
Total Miles:

6,354
Alma Second H alf Year

1-W ,
2 —W,
3—W,
4—W,
5—W,
6 -W ,
7-W ,
8 —W,
9—W,
10-W ,
1 1 —W,
1 2 —W,
13—W,
14—W,
15—W,
16—W,
17-W ,

25,
28,
83,
45,
11,
78,
84,
21,
89,
75,
80,
88,
92,
93,
18,
60,
82,

20, 5, 22, 106, W
30, 27, 34, W
76, 77, 2, 29, 33, W
44, 46, 63, 64, 6 8 , 6 6 , 70, 65, 67, 69, 42, 35, W
8 , 13, 10, 9, 12, 15, 17, 23, 36, W
1, 4, 37, W
26, 3, 32, 31, 38, W
14, 24, 19, 39, W
53, 49, 48, 52, 60, 57, 62, 58, 56, 61, 59, 41, W
79, 74, 73, 71, W
72, 55, 47, 40, W
105, 104, 101, 43, 99, 8 6 , 91, 90, W
85, 81, W
95, 54, 94, 51, 50, 98, 97, 96, 87, W
7, 6 , 16, 107, W
W
W

Total V a ria b le D is trib u tio n Cost $ 3 ,0 7 9 .5 0
Total M ile s :

6,159

1,273
1,274
1,293
1,2 2 0

1,224
1,232
1,224
1,285
1,255
1,262
1,245
1,293
1,092
1,2 0 2

1,209
1,296
272

Climax F irs t H alf Year
ROUTE NUMBER AND COMPONENTS
1—W,
2—W,
3—W,
4—-W,
5—W,
6 —W,
7—W,
8 —W,
9—W,
10—W,
11—W,
12—W,
13—W,
14—W,
15—W,
16—W,
17—W,

Route Demand
in Cubic Feet

1 , 79, 74, 73, 80, 107, W
1,287
5, 16, 6 , 34, W
1,295
11 ,
30, 27, 24, W
1,239
20,
19, 39, W
881
25,
84, 29, 26, 3, 32,31 , 37, W
1,245
17,
15, 9, 12, 10, 13, 8 , 33, W
898
23,
18, 7, 42, 22, 99, 35, W
1,205
86,
96, 97, 101 , 105, 36, W
1,106
93, 9 5 , 49, 48, 52, 60, 57, 62, 58, 56, 61 , 59, 89, 87, 40, W 1,295
104, 45, 98, 50, 51 , 94, 54,53, 55, 47, 41 , W
1,265
78,
76, 4, 38, W
1,258
83,
82, 81, 91 , 90, W
1,157
88,
72, 71 , 75, 77, 2, W
1,071
92,
85, 28, 21, W
1,158
43,
44, 46, 63, 64, 6 8 , 6 6 , 70, 65, 67, 69, 106, W
1,288
60, W
1,296
14, W
605

Total Variable D istribution Cost $3,273.00
Total Miles:

6,546
Climax Second Half Year

1—W,
2—W,
3—W,
4—W,
5—W,
6 —W,
7—W,
8 —W,
9—W,
10—W,
11—W,
12—W,
13—W,
14—W,
15—W,
16—W,
17—W,

1 , 79, 74, 73, 71 , 107, W
21 ,
84, 26,
3, 84, 32, 31 , 37, W
23,
18, 22,
19, 20, W
24,
30, 11 ,
8 , 33, W
25,
28, 29,
27, W
5, 17, 15, 9, 12, 10, 13, 34, W
16, 6 , 7, 39, W
44, 45, 93, 49, 48, 52, 60, 57, 62, 58, 56, 61 , 59, 53, 40, W
43,
46, 69,
67, 65, 70,6 6 ,6 8 ,64, 63, 42, 106, W
80,
72, 55,
47, 41 , W
83, 82, 2, 78, 77, W
87,
89, 96,
95, 54, 94,51 ,50,98, 97, 35, W
88,
75, 76,
4, 38, W
90,
85, 81,
91 , 8 6 , W
92, 105, 104, 101 , 99, 36, W
60, W
14, W

Total Variable D istribution Cost $3,225.00
Total M ile s :

6,450

1,257
1,263
1,239
967
1,288
1,057
1,121
1,294
1,284
1,245
1,191
1,278
1,254
1,117
1,072
1,296
605

167

Jenison F ir s t H a lf Year
ROUTE NUMBER AND COMPONENTS

1 -W ,
2 -W ,
3—W,
4—W,
5—W,
6 —W,
7 -W ,
8 —W,
9 -W ,
10-W ,
1 1 —W,
1 2 —W,
13—W,
14—W,
15-W ,
16—W,
17--W,

, 75, 71, 76, 78, 77, 3, W
14, 17, 15, 12, 9, 10, 13, 34, W
2 1 , 22, 19, 5, 24, 8 , 33, W
25, 43, 44, 46, 67, 65, 70, 6 6 , 6 8 , 64, 69, 6 3 ,1 0 6 ,W
26, 4, 83, W
84, 27, 32, 31, 38, W
29, 28, W
30, 11, W
16, 6 , 7, 42, 18, 23, 36., W
80, 73, 74, 79, 1, 37, W
92, 8 6 , 99, 101, 105, 39, W
91, 97, 93, 49, 48, 52, 60, 57, 62, 58, 56, 61, 59, 40, W
47, 53, 55, 72, 41, W
8 8 , 85, 81, 82, 107, W
ii
90, 87, 89, 96, 95, 54, 94, 51 , 50, 98, 45, *i1 A il , 0o r-3 , to
60, W
20, W
2

Route Demand
in Cubic Feet

1,067
1,207
1,296
1,295
1,095
1,265
918
761
1,293
1,287
1,283
1,295
1,202

1,104

t

A*7 A
1 , CIO

1,296
632

Total Variable D istribution Cost $3,250.50
Total Miles:

6,501
Jenison Second H alf Year

1- -w,
2- -w,
3- -w,
4- -w,
5- -w,
6- -W,
7- -W,
8 - -w,
9- -W,
10- -w,
11- -w,
12- -w,
13- -W,
14- -w,
15- -W,
16- -W,
17- -w,

2,
3,
14,
24,
26,
28,
20,
25,
17,
87,
80 ,
84,
90,
91,
92,
83,
60,

77,
75,
n ,
5,
4,
29,
30,
42 ,
16,
89,
72,
32,
86,
96,
22,
82,

79, 78, 76, 1, w
1 ,125
71, 74, 73, 9 , 3 4 , W
1 ,282
W
1 ,137
15, 12, 10, 13, 8 , 33, W
1 ,174
38, W
1 ,040
27, , w
1 ,254
W
957
63,, 69 , 64 , 6 8 , 6 6 , 70, 65, 67, 46, 44 , 35, W
,233
1
1 ,280
6 , 7 , 18, 23, 36, W
53,, 4 9 , 48, 52 , 6 0 , 57, 62.» 58, 56, 61, 5 9 , 4 1 , W
1 ,284
55, , 47, 40 , w
1 ,245
31,, 37, W
1 ,147
99,, 101 , 4 3 , 105, 39, W
1 ,198
97, , 93, 95 , 54, 9 4 , 51 , 50, 98, 45, 104, 106, W 1 ,272
19,, 21, W
960
88
8
5
,
,
107,
W
,267
1
81,,
W
1 ,296

Total V a ria b le D is tr ib u tio n Cost $ 3 ,2 5 4 .5 0
Total M ile s :

6,509

Zilwaukee F i r s t H a lf Year
ROUTE NUMBER AND COMPONENTS

1 -W ,
2--W,
3 - W,
4--W,
5--W,
6 - W,
7 -W ,
8 -W ,

9 - W,
10— W,

11— W,
12— W,

13—W,
14—W,
15—W,
16—W,
17—W,

Route Demand
in Cubic Feet

76, 83, 2, 26, 29, 34, W
45, 67, 6 6 , 70, 64, 63, 65, 69, 6 8 , 42, 43, 44, 36, W
75, 77, 78, 1 , 4 , 79, 37, W
84, 3, 32, 31, 27, 38, W
90, 92, 21, 20, 25, 22, 39, W
5, 23, 6 , 7, 18, 105, 40, W
87, 96, 97, 98, 50, 51, 94, 54, 95, 93, 41, W
55, 53, 47, W
59, 61’, 56* 58, 62, 57, 60, 52, 48, 49, 89, W
73, 72,
W
74, 71,
W
80, 30,
28,
35,
W
85, 82,
81,
W
8 6 , 104, 101, 99, 91, 33, W
88,
11 ,
8 , 13, 10,12,9, 15, 17, 46, 106, W
19, 24,
14,
16,
107,W
60, W

1,133
1,258
1,260
1,268
1,262
1,269
1, 222

724
1,214
839
1,073
1,180
1,094
1,015
1,197
1,245
1,296

Total Variable D istribution Cost $3,258.50
Total Miles:

6,517
Zilwaukee Second H alf Year

1- -w,
2- -w,
3- -w,
4- -w,
5- -w,
6- -w,
7- -w,
8- -w,
9- -w,
10- -w,
11- -w,
12- -w,
13- -w,
14- -w,
15- -w,
16- -w,
17- -w,

3, 31, 32, 2 6 , 84 , 34, W
11, 8 , 13, 10, 12, 9 , 15, 17, 23, 36, W
21, 24, 14, 19, 39, W
28, 30, 27, 37, W
87, 96, 97, 98, 50, 51, 94, 54 , 95, 93, 41, W
4 5 , 4 6 , 6 8 , 6 9 , 65 , 6 3 , 64 , 70, 66 , 67 , 4 3 , 104, 4 0 , W
59, 61, 56, 58, 6 2 , 5 7 , 6 0 , 52 , 4 8 , 49, 53, 8 9 , W
72, 55, 4 7 , W
73, 74, 71, W
75, 4 , 1 , 78, 38, W
79, 77, 76, 8 3 , 29, 8 0 , W
81, 8 2 , 2, 33, W
86, 8 5 , W
8 8 , 25, 20, 5, 22, 35, W
91, 92, 90, 105, 99 , 101, 44 , 106, W
4 2 , 18, 7 , 6 , 16, 107, W
60, W

Total Variable D istribution Cost $3,263.50
Total M ile s :

6,527

1, 224
1,224
1, 285
1, 274
1,202
1 ,2 79
1, 255
1 ,1 89
1,088
1, 244
1,258
756
792
1,290
1, 252
1,243
1 ,2 96

BIBLIOGRAPHY

BIBLIOGRAPHY

1.

Beckmann, M artin.
In c ., 1968.

2.

Bellmore, M ., and G. L. Neuhnumer. "The Traveling Salesman
Problem: A Survey." Operations Research 16 (May-June
1968): 538-558.

3.

Benjamin, Gary L . , and Larry J. Connor. Economies of Size of
Machinery Systems on Southern Michigan Cash-Grain Farms.
Agricultural Economics Report No. 112. Department of
A gricultural Economics, Michigan State U n iversity,
East Lansing, September 1968.

4.

Black, Guy. "Synthetic Method of Cost Analysis in A gricultural
Marketing Firms." Journal of Farm Economics 37 (May 1955):
270-279.

5.

Boutwell, Wallace K ., and Richard L. Simmons. "Estimating Route
Assembly Costs." Journal of Farm Economics 46 (November
1964): 841-848.

6

.

7.

Location Theory.

New York:

Bressler, R. G ., J r. City M ilk D is trib u tio n .
University Press, 1952.

Random House

Cambridge:

Harvard

Carley, D. H. Transporting Packaged Fluid M ilk to Distant Markets,
Costs and Systems in Georgia. Georgia A gricultural Experiment
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Chern, Wen-Shyong, and Leo Polopolus. "Discontinuous Plant Cost
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