~—' . - _ MANUFACTURING SYSTEM SIMULATION UTILIZING A DIGITAL COMPUT ER Thesis for “19 Degree of M. S. MICHIGAN STATE UNIVERSITY Jasvantrai C. Shah 1962 0-169 This is to certify that the thesis entitled MANUFACTURING SYSTEM SIMULATION UTILIZING A DIGITAL C(MPUTER presented by Jasvantrai C. Shah has been accepted towards fulfillment of the requirements for M.S. degree in Mechanical Engineering I I i A A fl Date February I __-___e 1m: .0"th ’ ‘ mr‘m'hah MANUFACTURING SYSTEM SIMULATION UTILIZING A DIGITAL COMPUTER BY JASVANTRAI C. SHAH A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1962 ABSTRACT An attempt was made to study the transient behavior of a manufacturing system. A Signal Flow Chart with a feed— back network was prepared for a logical operation of the manufacturing system. Customer demand was created assuming a statistical distribution. Dynamics was imparted to the system by introducing an element of randomness in demand, product and part productions, as well as raw material delivery time. This was also achieved by the presence of lead times. Each part was produced on its own production line; operating for either one, two, or three shifts, or sometimes completely shut down. In order to experiment with the model a digital com- puter simulator was designed. For initial study three runs, each simulating a period of four years of the system operation, were made at three demand levels, on a typical system. From the results the response of the system was examined in terms of various patterns of inventories and man-machine utilization. In general it was observed that for the specific design configuration, the system did not seem to attain a steady state. It was concluded that, although only initial study was made here, this approach and technique should provide a Jasvantrai C. Shah powerful tool for testing and improving design of a manufacturing organization. ACKNOWLEDGEMENT The author wishes to express his most sincere thanks to Dr. Wayland P. Smith for his help in setting up the initial parts of the project, his excellent guidance and suggestions throughout this investigation, and a great amount of understanding and encouragement shown as a major professor. Appreciation is extended to Dr. G. P. weeg, Dr. M.CL Keeney, and staff of the MISTIC Computer Laboratory for their valuable assistance and cooperation in computer- assisted phase of the project. ii iii CONTENTS Chapter Page I. INTRODUCTION . . . . . . . . . . . . . . . . 1 Summary 1 An Outline of the Problem 2 The Simulation Approach 3 II. REVIEW OF THE LITERATURE . . . . . . . . . . 5 III. THE DESIGN OF A MANUFACTURING SYSTEM . . . . 9 General Discussion 9 Customer Demand 12 Mode of Operation and Control 13 The Signal Flow Chart 25 IV. THE SIMULATOR . . . . . . . . . . . . . . . 31 Some Characteristics 31 The Master Routine 34 807: A Sub-routine To Convert Standard Normal Distribution into a Specific NOrmal Distribution 41 The MISTIC Computer Library Routines Used 42 General Operating Procedure 44 V. A HYPOTHETICAL SYSTEM AND THE INITIAL RUNS . 46 Description of the Product 46 Design of the Factory 46 The Initial Runs 53 Results and Analysis 56 VI. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK . . . . . . . . . . . . . . . 75 Conclusions 75 Recommendations for Further Work 76 LIST OF REFERENCES . . . . . . . . . . . . . . . . 78 Table l. 2. 3. LIST OF TABLES The Product Data . . . . . The Parts Data . . . . . . The Raw Materials Data . . . iv Page 48 54 55 10. ll. 12. 13. 14. 15. l6. 17. 18. LIST OF ILLUSTRATIONS Block Diagram of Simplified Overall Operation . Pattern of Raw Material Inventory Level . . Pattern of Finished Part Inventory Level Pattern of Product Inventory Level . . . . . The Signal Flow Chart . . . . . . . . . . . . Flow Diagram of the Master Routine . . . . . The Output Format . . . . . . . . . . . . . Truncated Normal Distribution . . . . . . . . Assembled Drill Press Vise . . . . . . . . Exploded View of Drill Press Vise . . . . . . Equivalent Lead Time for One Shift . . . . . Equivalent Lead Time for Two Shifts . . . . . Equivalent Lead Time for Three Shifts . . . . Illustration of Inside Area and Outside Area Cumulative Average of Total Actual Inventory per Designed Cycle for Part No. l . . . . . . Cumulative Averages of Actual Inside, Outside and Total Inventories per Designed Cycle for Part No. 2 . . . . . . . . . . . . . . . . . Cumulative Average of Total Actual Inventory per Designed Cycle for Product . . . . . . Pattern of Inventory Level for Part No. l Page 11 15 18 22 26 36 41 42 47 47 52 52 52 58 6O 61 63 64 Figure 19. 20. 21. 22. 23. 24. 25. 26. vi Page Pattern of Inventory Level for Part No. 2 . . . 65 Pattern of Inventory Level for Product at d. = 200 . . . . . . . . . . . . . . . . . . . 67 1 Pattern of Inventory Level for Product at d. = 120 . . . . . . . . . . . . . . . . . . . 68 1 Pattern of Raw Material Inventory Level for Part No. l . . . . . . . . . . . . . . . . . . 69 Pattern of Raw Material Inventory Level for Part No. 2 . . . . . . . . . . . . . . . . . . 70 Patterns of Operating Shifts and Idle Shifts for Part No. l . . . . . . . . . . . . . . . . 71 Patterns of Operating Shifts and Idle Shifts for Part No. 2 . . . . . . . . . . . . . . . . 72 Patterns of Operating Shifts and Idle Shifts for Product . . . . . . . . . . . . . . . . . . 74 CHAPTER I INTRODUCTION Summary Within the last decade, with the advent of high speed electronic computers, investigators have utilized a power— ful approach to study complex man-machine systems--that is, the simulation approach. Their contributions have helped manufacturing organizations gain better and more efficient operation, sometimes resulting in large economic gains. New methods and techniques are being developed to help management executives in making adequate short, as well as long-range decisions. Even though many operations re- searchers have experimented with the problems of job shop scheduling, inventory control, advertizing and distributing networks, etc., much work remains to be done in the areas of overall problems of manufacturing systems. Conway (7) and Rowe (18, 19), among many others, have investigated the job shop scheduling and dispatching problems; while work of Forrester (9, 10) is in the areas of industrial dynamics. It is conceivable that the simulation approach could be employed more profitably if, in the first place, an effective configuration of a manufacturing system were designed and selected by adequate manufacturing system synthesis technique, as for example one developed by Smith (22). The problem area of concern in this thesis is the application of simulation approach to overall opera- tions of manufacturing systems. An Outline of the Problem The purpose of this thesis was to experiment with a manufacturing system and analyze its simulated behavior. The manufacturing organization that is studied here was a simplified version of its more complicated real world counterpart. The system was composed of the following phases: the raw materials inventory, the parts production and their inventories, the assembly operation and product inventory, and finally, shipment of the product to cus— tomers. Even in the simplification, an attempt was made to approach real world situations by creating random demand, by allowing variations in production outputs and raw mater- ials delivery, and by providing production lags or lead times as they are often times called. Even a controlled backlog of unfulfilled customer orders was considered pos- sible in the specific design. The model was restricted to producing parts on a production line basis and assembling them into a single product. The study was aimed at selecting a configuration of the system and simulating its behavior by changing values of various system parameters, which hopefully would lead to the selection of a "most effective" design that would make the system operation ”near optimal." How- ever,this investigation allowed simulation of the system only at three different demand levels with four years of operation in each case. The very size and nature of the problem warranted use of a digital computer. A simulator, that can simulate an organization manufacturing at the most 100 parts, was pro— grammed for the MISTIC computer. The flexibility of the simulator would allow many variations of the system parame- ters to design and test manufacturing organizations of various size for effective operations. The Simulation Approach The simulation approach has found a great deal of application in the areas of industrial and other research programs. When used with a digital computer, this tech- nique can provide months or even years of simulated system-operation within a matter of minutes. It reduces the necessity of actual physical set up to test a design, amd can thus avoid many mistakes and expenses. This technique can be used either to test a configuration or to compare various alternatives. However, to simulate manufacturing system operations, it is necessary to have a model which provides a formal statement of the system. The success of this procedure will then depend upon the degree with which the chosen system parametersanxivariables correspond to their real world counterparts. Finally, the technique of simulation has promising application in train- ing personnel and in enhancing the learning process. CHAPTER II REVIEW OF THE LITERATURE Among all the literature that has been written so far on manufacturing sub-systems and systems, much of the simu- lation work that is related to the problem area of concern of this study has been done within recent years only. A considerable amount of literature is available in the areas of optimal inventory and inventory control. However, most of the investigators have developed single-stage inven- tory models. A cost minimization approach has generally been adopted in such models. The books concerned with pro- duction and inventory control have also taken a qualitative approach to comparisons between intermittent and continuous manufacturing systems. Arrow (1), Churchman (6), Magee (15), and Vazsonyi (23) have all discussed various inventory models with deterministic as well as probabilistic approach. Most of the work in this area is listed in the extensive bibliography prepared by Whitin (24). Smith (22) has studied multi-stage networks of inventories that exist within the manufacturing systems and has developed a methodology of optimizing and selecting ”near best” configuration from static-system considerations. Many powerful tools have been developed within recent years to help management in decision—making process. Linear programming discussed by Gass (11) and dynamic programming discussed by Bellman (2) are two major developments that could be cited. Application of queueing theory to the ser- vicing problems of job shop has been made. Satty (21) has discussed various types of queue-dhxfirdines and their appli- cation, and has prepared an extensive bibliography related to that area. Another area of investigation which has provided insight with respect to the complex problems of manufacturing systems is that of servomechanism and process control theory as discussed by Campbell (4), and edited by Grabbe (12), and many others. Another powerful approach made by many investigators to various stages of the overall manufacturing systems is simulation. Since analytical solution of large scale sys- tems problems becomes very cumbersome, and experimenting with a physical set up would—-in many cases-—be impractical, the technique of simulation has great appeal. Many opera— tions research investigators have experimented with prob— lems of job shop scheduling and routing using digital com- puters. Rowe (18, 19) has developed mathematical models and simulated job shop production system with different priority rules for scheduling. WOrk of Conway (7) is similar to that of Rowe, but he has compared job shop operation using more numbers of priority rules for scheduling. Jackson's (14) work is conceptually similar to the investigations in job shop system. He has investigated customer service time and waiting time in a queue using priority rules based on customer arrival time and urgency number generated using a fixed distribution. Forrester (10) has done interesting work in the areas of system management. He has investigated effects of advertising and resulting sales patterns. Another area of experimentation by Forrester (9) is simulation of multi—stage production—distribution network composed of retailers, distributors, factory warehouse, and factory. Brown (3) and Robinson (17) both have experimented with multi-product inventories. Considerable amount of simu— lation work has been done in the areas of military operation and traffic control. Conway (8) has clearly described the advantages and limitations with particular emphasis on manufacturing simulation utilizing a digital computer; while Canning (5) has brought forth the requirements in the way of computer equipment and methods for such operations. Though the study under consideration in this thesis has no direct bearing on any other simulation work, the literature available on simulation application in various fields has been very helpful conceptually. The study presented here is concerned with simulation of a manufacturing system com- posed of multi-stage inventory network with parallel inven— tories within some stages with an emphasis on production- line manufacturing. CHAPTER III THE DESIGN OF A MANUFACTURING SYSTEM General Discussion One major task in designing a manufacturing system was to introduce the dynamic element in the system. This was accomplished by introducing randomness, controlled by a probability distribution, for the various elements of the system dynamic in nature. These distributions were then truncated to keep the operation of the system practically feasible. Another source of dynamics in the system was the inclusion of lead times. The lead times were designed on arbitrary assumptions bearing on practical considera- tions, and use was made of feed-back loops to implement the lead times in the system. Normal distributions with different parameters (u,o) were selected to satisfy the variability that occurs many places in such systems. The justification for such a decision is that many real world situations tend to be normally distributed. Moreover, other distributions such as Poisson, Binomial or rectangular could be approximated by normal distribution in many cases. 10 Though it was understood that some parts could more economically be produced in optimal lot quantities utili- zing the equipment provided for other parts, this model allowed parts to be produced only on separate production line(s) basis and assembling into a single product. The machines in each line were tightly COupled with no inprocess inventory. The control of the system was very much simplified by this arrangement. For the system operation four states were considered: not opera- ting (i.e. 0 shift) or operating for one, two, or three shifts. A sub-ordering or a day-to-day overtime practice was excluded from the present model. However, a limited overtime was allowed in some marginal cases.* A simplified overall operation of the manufacturing organization is presented in the block diagram of Fig. (l), where flow of material and flow of information are indi- cated. It can be seen that the customer demand was the driving force for the system. * An adequate precaution was taken to limit the inven- tory levels for parts and raw materials to non-negative values. However, a negative part inventory indicated that the product assemblies were made without the part and it was assembled during overtime on a later date when it was available. Similar logic was applied to a negative raw material inventory. 11, mumwaamsm Hmfiumuma 3m» F. IIIII nympho Hm Huouma awn IIIL HmwumuMB amp aouumuoao Humuo>o emuuuuasum no smummua sooum "H .wum Spouso>sw m” sofiumuomo soHuo=poun QUHQQ QUHNQ ) _ Pu llllll .L muopuo sowuoswoumnmuuma 30.3 sowumauomfi kill 30.: Hmwuouma lull QHUUHO HQEOUUSU .4 uuuuuuu 1“ manammmm , muoEoumsu . <fi run.l. IIIII L nympho hflaammmm 12 Customer Demand In an existing industrial organization, the future pattern of demand for a particular product can usually be forecast from the past records of sales. In absence of such data, or even otherwise, various forecasting tech- niques could be employed to determine the general nature of such patterns. In the system modelled overall demand was conceived in two parts: 1) estimates of annual demand, D 2) estimates of daily demand, di 1) Assumptions about annual demand, D: No seasonal trend for annual sales was considered; but a variation in sales from year to year was possible presumably due to major design changes in the product, changes in overall economic atmosphere, business competition, etc. The distribution of annual sales was broken down into relatively small groups reasonably representative of the overall distribution. The histogram thus obtained was approximated by a normal distri- bution with parameters: expected annual demand (5) and standard deviation of annual demand (GD). 2) Assumptions about daily demand, di: The histogram for daily demand was also approximated to a truncated normal 13 distribution. The parameters, expected daily demand (di) and standard deviation of daily demand (0 i) were derived d from their annual counter parts as shown in eq. (3.1) and ' eq. (3.2) assuming 250 working days per year. - 5 di — 250 (3.1) o D odi—- 250 (3.2) The customer orders were shipped on the day requested if items were available. However, the unfulfilled orders were registered as a backltxg. The shipping capacity was in excess of the maximum assembly production such that any quantity produced could be shipped without any delay. Mode of Operation and Control (a) Raw materials: A theoretical pattern of raw materials inventory level was assumed as shown in Fig. (2). The level of each raw material inventory was checked every day after the amount of raw material needed by part production was withdrawn. Whenever this level fell below a lower control limit an order was entered for an optimal quantity of raw material according to eq. (3.4). However this decision was not implemented when a previous order was pending. Thus duplication of orders was avoided. An attempt was made to 14 approach reality by providing a random arrival of raw materials. Here again, a normal distribution with expected delivery time (T) and a standard deviation of delivery time (CT) was assumed. The lower control limit (LCL), also referred to as a reordering point, was set by con— sidering expected values of daily demand and delivery time according to eq. (3.5). However, a little modification in the design of LCL was found necessary to safeguard against unanticipated failure of the system in special cases. A special case could be this: suppose the lower control limit is less than the minimum requirement quantity of the raw material. Now, by a chance, the raw material inventory level happens to be less than the minimum requirement quantity for part production, but greater than the reordering level. In a situation like this, if the system is decoupled, no raw material will be ordered and no further part production will ever come. The result will be the failure of the system. Such a stalemate was resolved by providing the lower con- trol limit a little higher (at least by one unit) than the minimum requirement quantity of raw material. 15 H . E g - \\\. \\\\\ - r - d.t C 3 1 \\ 3 >. \ m u r . E 8 \‘m.\ \ 5 5 \- LCL a: a TCSWF- -__.-.-...-.._.-_,...-.;_.-. ~~ "-1 , O I “NJ \.\‘ ffv~ time t, days Fig. (2): Pattern of Raw Material Inventory Level Let cr = total variable cost per unit of raw material for a part r = the optimal quantity of raw material for a part di = expected daily demand S = an order placing cost h = raw material holding cost per unit-day T = expected delivery time LCL = lower control limit Then . . S order plaCing cost per unit =‘; And . r average inventory level = 3 time at which maximum r inventory level occurs 5— 16 :3" r 25. 1 holding cost per unit = Combining the above expressions for cost yields the total variable cost per unit as a function of quantity of raw material per order c _§+.T_1.1;_ r ’ r 2d, (3.3) 1 dcr Setting a;—'= O and solving for the minimum cost value yields _ 2d,S r = 1 (3 4) h . The lower control limit can be computed as LCL = 551 (3.5) (b) Part production: Even though every line was prac- tically balanced, the production rate for each line was dominated by the limiting operation in it. Even when the line was ”under statistical control" a considerable varia- tion was to be expected in the daily production output of each line. The major items causing variations were the downtime on the machines caused by failure of machine com- ponents, tool wear etc. and the inherent variations due to operators' efforts and attitudes. With the line closely coupled; the larger the number of men and machines in the 17 production unit, the larger would be the variance of the output. The number of parallel production lines for each part was selected on the basis of meeting average annual demand at average output, and this number was considered fixed over the entire life of the product. However, the provi— sion of at least 25% slack was considered essential for each line. All the production lines for a part were con- sidered as being alike in production output, distribution, and operation. Finally, the equivalent expected output and the equivalent standard deviation of output per shift were computed statistically. i5 = M5) (3.6) and GP =~JR (Up) (3.7) where P = expected output of a part per shift P expected output of a part per production line k number of parallel production lines for a part. The part production for each shift was generated using the above parameters, and then added together to arrive at the daily part production (Pi)° Similarly, the ex— pected daily output rate was 18 Ei = F (number of shifts specified by design) (3.7a) and this was used to specify the pattern of finished part inventory level of Fig. (3). Each production unit was put in one of the four operating states: not operating (i.e. 0 shift) or operating for one, two,or three shifts. The logic of changing an operating state is discussed at length while describing The Signal Flow Chart (page 29). The finished goods were moved to the finished part storage at the end of each day, and used for assembly on the next day. The upper and lower controllimits (UCL & LCL) of a finished part inventory were computed on the basis of the pattern shown in Fig. (3). I. /\ /\ UCL — Finished Part Inventory Level H m I Dal ”- LCL—— 0 *1‘2,‘ Time t, days Fig.(3): Pattern of Finished Part Inventory Level 19 Let c. = total variable cost per unit of a part Pi = average daily output rate of a part di = expected daily demand IP = optimal inventory of a part L = maximum overage level of a part S = a production run setting up cost h = finished part holding cost per unit-day T1 = production stop lead time T2 = production start lead time UCL = upper control limit LCL = lower control limit Then , S set up cost per unit = IP And . . . . IP time at which maXimum inventory occurs = P— i . . . . IP time at which inventory is depleted to zero level = 3—- i (§.—d.) IP average inventory = £‘= l l 2 2Pi h(P.— di) IP 1 213.61. 1 l holding cost per unit Combining the expressions for set up cost and holding cost yields the total variable cost per unit as a function of 20 maximum inventory per production run h(P.-d.)IP = §_ + i i cj IP 2§.a. (3.8) i 1 dc. Setting HIP = O and solving for the minimum cost value yields, . W/ 235i Ei IP = h (57:73?) (3.9) i i W/ 255i fii- 51 L = 11 (-—ii;- (3.10) The upper and lower control limits can be computed as UCL L - T (§.- 5.) (3.11) 1 i i LCL = T a, (3.12) 2 i (c) Assembly production: As stated before, a single pro— duct was the final result when all the finished parts were assembled together. The number of assembly stations was selected on the basis of meeting average annual demand at the average daily output of assembly production, and this number was considered fixed over the entire life of the product. Slack of at least 25 percent was again provided at each assembly station. 21 Here also, the output rate of assembly production was assumed to vary normally. The average output rate per shift (5) and its standard deviation (0a) were specified. Then knowing the number of operating shifts determined by a specific design, the equivalent daily output of assem- blies (5i) could be computed statistically as ai = 5 (number of shifts specified by design) (3.13) If number of assembly stations is more than one, an equivalent average output per shift and equivalent standard deviation per shift can be computed from the respective individual values using statisticalformulas of equations (3.14) and (3.15). These equivalent values will then be used as parameters of output rate distribution per shift. a(equivalent) = a(individua1)(number Of assembly (3.14) stations) Oa(equivalent)= Oa(individua1)-V/(no° Of assembly (3.15) stations) Again, four states of assembly operation were con- sidered: not assembling or assembling for one, two, or three shifts. The decision-making technique for moving from one state to another is discussed in detail while describing the Signal Flow Chart (page 27). 22 The upper and lower control limits (UCL & LCL) were set on the product inventory level on the basis of the pattern presented in Fig. (4). The pattern of product inventory level departed from other patterns discussed earlier in this chapter. A shortage of the product with- out the loss of customer orders was permitted in this case. The unfulfilled orders were registered as a backlog Lu) until the period when the product was available for ship- ment. However, such shortage was discouraged by assigning a penalty for each unit shortage per time interval in the derivation of optimal levels L1 and L2 and consequently the UCL and LCL. #1 I /\ .1 /\_., / A\U\:._._.___ O - i"di)t if \/ V H—TZ-al Timet, days Product inventory level H Fig. (4): Pattern of Product Inventory Level 23 Let c = total variable cost per unit of the product 5i = average daily assembly production di = expected daily demand I = optimal product inventory L1 = maximum product overage level L2 = maximum product shortage level S = an assembly-production ordering cost h = product holding cost per unit—day s = product shortage penalty per unit-day T1 = assembly operation stop lead time T2 = assembly operation start lead time UCL = upper control limit LCL = lower control limit Then , S set up cost per unit ='f And L1 L1 total time during which overage occurs = §—-—§— + 3—- i i i Ll average overage = if hSile h ld' t 't = _ _ 0 ing cos per uni 2d (a,-d )I i i 1 L2 L2 total time during which shortage occurs = _ d -+ g— 24 L 2 average shortage = 3r saiL2 shortage cost per unit = 2a.(5.—a.)1 i i i Sl-ai L2 = I a. - L1 1 sai a.—di 2 shortage cost per unit = 231(5i_ai)1 I a ) - Ll Combining the expressions for set up cost, holding cost and shortage cost yields the total variable cost per unit product as a function of the maximum product inventory and maximum overage level per assembly run. h5.L 2 sa. (5.-5.) i i i S l i 2 =— _ + _ _ _ _ Ca I + 2d.(a.-d.)I 2d.(a.-d.)I I a, L1 (3.16) 1 i i i i i 1 3c aca Setting partial derivatives BI = 0, and EL_ = 0; and solving 1 simultaneous equations for minimum cost value yields, 2Sd. i h+s i I h s a._a. (3.17) l 2351 51-31) The maximum shortage level L and the upper and lower limits 2 can be computed as 25 255i h ai-ai L2 =~( . h: a. ‘3-19’ 1 UCL = L - T (5.- a.) (3.20) 1 l i i = _ + T ‘ 3.21 LCL L2 2di ( ) The Signal Flow Chart The detailed operation of the manufacturing system is schematically presented in the Signal Flow Chart of Fig. (5). At the beginning of each interval*, a customer demand (di) was created using the random normal deviate of daily demand. The product inventory level was then computed as = I + - o Ii (i—l) a(i-i) di (3 22) and the new level was recorded. (The suffix (i-l) designates the previous interval.) It was checked against the upper and lower control limits (UCL & LCL) which were set up ac— cording to the ordering rule derived earlier in this chap- ter. This comparison was essential for arriving at the decision regarding the desired operating state of assembly station. *Each working day will, hereaften be referred to as an interval. f 26 II- ---------------------- "I r-flr ----------------- - ——————————————————————————————— —, I I I I I I I I ' I I I " ' I I I Chet]: all finiihed IP I | Check raw material I par 8 avai abi ity ”.9321. _____ I __ I _ abailability R('1.1)L I 1’ ‘T 'T Z31 "“ " " ‘ " I I I I I _ 3.1 I I I I 12.1. 0 I I I I I I I I I I I l I I I I ' I I I I l I I I I l I a. 5. 6. I I I I 9. 10. 11. I generate desired Operating determine generate I I I I generate desired Operating determine generate ' 2 state SD of assembly line running assembly I I I state SD of jt production running part , I" 1 during it interval state SR production, B. )" ”PG-I)" . line during the 1th interval. state SR production dG-DI IICH) I d I fly I Jl I I I i I I I 13.. 1 t -- -- .. I it _ 1 I . I 5* I ' ra—‘—“ , :v . - ' I . I . ' .«4 I Z'eate (.ompute r: -' :vrjm. 2' 9 YES 0 I ompute I coupare YES 0 m I:::“:; I s -~—-—a3 0 _...I,... . u’um- ' + O i d1 ~ n ~)' I I .....Iventory I . L, 11 I t- .v,_____ I I , IPiL I I I 1... . - : 1 : -, 1 : I~0 . : —- Ln 1 T I I + I com are I + V ”'30“ III-II .I ewe-“<1”?- YES I ' Jag-I11“) Eco'rd 8” I IP p UCL, an order was issued to decrease the existing desired running state (SD) by one shift. How- ever, such an order was implemented only after the speci- fied "stop" lead time. Contrarywise, when Ii < LCL, an order was issued to increase the existing desired running state (SD) by one shift. This order was also executed only after a specified "start" lead time. The status-quo was maintained when UCL > Ii > LCL. Obviously, the desired state was restricted to one of the four operating states mentioned before. The decision to change the existing desired running state was also governed by the following rules: 1. A change amounting to only one shift at a time was permitted. 2. No new decision was made until the previous decision was executed. 3. No new decision was made when, during the previous interval, the actual running state (SR) was short of existing desired running state (SD). The existing desired running state (SD) as well as the actual running state (SR) were recorded every interval. 28 A minimum quantity of each finished part, specified arbitrarily from statistical considerations, was necessary to start an assembly operation shift. The finished parts inventory levels were checked against these minimum require- ments to determine the availability of finished parts in terms of shifts. The existing desired running state was then compared with the available state and the state which was restricting one was put in effect as the actual running state (SR). The assembly production for each shift of the actual running state (SR) was generated using a normal distribu- tion with parameters (Si, oai). The total number of assemblies produced were moved to the storage area at the end of each interval. The computing method for finished part inventory level (IPij) was very similar to the one used for product inven— tory level. IP..=IP. ,+P, ,-, . 13 (l-l)j (l-l)j a1 (3 23) where the suffix j was introduced to represent a part. The computed inventory level (IPij) for each finished part was recorded and compared with corresponding upper and lower control limits specified by preset pattern of inventory. 29 The decision as to increase, decrease, or maintain the existing desired running state (SD) of a production line depended upon whether the inventory level of that part (IPij) was greater than the upper control limit, less than the lower control limit, or neither of the two. Again, the desired state was chosen out of the four optional states specified. The decision was, however, carried out after an appropriate lead time. Other rules governing the above decision were the same as those laid down for similar decisions regarding the existing desired running state of an assembly station. Quite analogous to the previous case, minimum raw material requirements were specified for every part before it could be put into each shift production. The availa— bility of raw material for any part in terms of shifts was determined by comparing the raw material inventory (Ri.) with the minimum requirement for one shift. The limiting state between the existing desired running state (SD) and the available state was chosen as the actual running state (SR) of a production unit. For every part these operating states were recorded, and the production of each shift was obtained from a normal distribution whose parameters average production per shift (Rj) and standard deviation of 30 production rate (on) were specified. The total production (Pij) was shifted to the finished part storage area at the close of the day. Finally, the raw material inventory level for each part was computed as R + r - P.. (3.24) ij = R(i-l)j (i-l)j 13 where r(i-l)j indicated the raw material received on the previously placed order. The resulting raw material level was also recorded every interval. A lower control limit was set as a reordering point, and whenever the raw material inventory level crossed this point an optimal quantity of raw material was ordered. However, to avoid duplication, no new order was issued when a raw material order was pend- ing. All the purchase orders were recorded. The receipt of the raw material after an order was issued, was expected after a variable delivery time (Tj). The variations in delivery time were, however, controlled by a normal distribution. The feed-back network is indicated by dotted lines in the Signal Flow Chart. 31 CHAPTER IV THE SIMULATOR Some Characteristics The simulator consists of a program for the MISTIC computer. The MISTIC computer was chosen because these facilities were the ones most easily available. The MISTIC computer is a parallel, binary, fractional single-address machine. The primary input to the machine is via standard 5 channel teletype punched paper tape and a photoelectric reader with a maximum input speed of 300 characters per second. The present core memory offers space for 4096 words, each word consisting of 40 bits. Instruc- tions are stored in order pairs, the left hand instruction occupying the first 20 bits of the word and the right hand instruction occupying the last 20 bits of the word. The machine obeys 256 order codes which cause MISTIC to perform operations. It takes approximately 65 microseconds for the machine to obey an order and 700 microseconds for multi- plication and division. Output is generally via a paper tape perforator that punches at a rate of 60 characters per second. Complete details may be found in the MISTIC Pro- gramming Manual (16). 32 A large number of random numbers were required for various elements, such as customer demand, assembly and part productions, raw material delivery time etc. This could be done by storing Random Number Tables; but the memory space requirements for this procedure made it im- practical. For the memory space available the most con— venient way was to generate pseudo-random numbers inside the machine itself. Hence a random number generating routine was included in the simulator. Another routine was provided to generate a standard normal deviate using the pseudo-random number. The standard normal deviate was then converted into a specific normal deviate by a sub- routine which also truncated the distribution. The simulator was designed for a system manufacturing at the most 100 parts; all being produced on a production line basis and assembled into a single product. The statistical distributions used were either normal or the ones that can be approximated by a normal distribution. Systems can be compared by varying number of parts; or for a given system configuration it can be tested by varying any one or all of the following parameters: expected cus— tomer daily demand and its standard deviation, average assembly and average part productions, and corresponding 33 standard deviations, various lead times, different patterns of inventory levels, control limits, minimum requirement quantities, average raw material delivery time and its standard deviation, etc. System operation can be simulated for any length of time. However, due to the limitations imposed by the reliability of the MISTIC computer and by the machine time available, a large run was divided into sub-runs of shorter (about 100 intervals) length. The first sub—run was started by the program. At the end of each sub-run the memory was dumped on output tape using a dump routine. Each subsequent sub-run was then started using the dump of the previous sub-run. A counter or a clock, as it is often called, was provided to count the number of intervals of system operation. The input and output were done via paper tape. Output was in decimal numbers. The program was written in decimal number language in a format suitable to Decimal Order Input. It Was translated into machine language by a MISTIC Computer Library routine. Since only integers were used in computations, the fixed point programming method was used. 34 It is interesting to note that about an hour of the MISTIC computer time was sufficient to simulate one year (250 intervals) of overall operation of a system producing 7 parts. The Master Routine The master routine was designed as shown in the flow diagram of Fig. (6). The overall operation of the system was accommodated into one program by providing loops at various places. While it was aimed at designing the flow diagram to be most informative about the master routine it has been simplified at places where confusion was likely to arise due to complicated loops. Same group of orders were used to determine availability of finished parts for assembly operation as well as to determine availability of raw materials for parts production. The SR state for assembly operation was designed as follows: As per SD state a minimum requirement quantity was stored, and compared with the available finished inventory of part no. 1. If it met the requirement, part no. 2 was compared for the same state. If part no. 1 failed to meet the SD state of assembly operation, it was checked for the next lower state. The 35 comparison was continued until the SR state of assembly operation allowable by part no. 1 was determined. Part no. 2 was then compared from this state onward until the SR state allowable by it was determined. In the same manner the process was continued until all the parts (j) were checked. Finally, a state allowable by all the parts was executed as the SR state of assembly operation. After all the data related to the product had been computed the addresses were changed to compute data for part no. 1; and depending upon the existing SD state for part no. 1, the minimum raw material requirement of part no. 1 was compared with the raw material inventory for it. The process of comparison was extended, when necessary, by lowering the state until the allowable SR state of produc- tion for part no. 1 was determined. The corresponding addresses were then incremented for the same sort of com- parison for next part; and in a similar fashion its pro— duction state was determined. Thus, the loops were performed (j—l) times to determine actual part production state SR for each part independently. The output format has been presented in Fig. (7). DECREASE START 36 Store prOjram I Stop c———— Insert para. and data tape and start. la Input parameters and data lb Store product data in $08: temporary locations for computations. f r Transfer to sub-routines to compute di’ store di Compute and store Ii ( - Test counter Cl: is there any lead time ? NO [YES 4b Does lead time end-in this interval? 12.—*10 [YES 5a Test counter C2: increase or decrease SD? 5b J INCREASE Increase SD by one shift; Test, new SD> 3?, if yes set {9 = 3 [5 c Fig Decrease SD by one shift Test, new SD<0?, if yes set SD = 0 (6): FLOW DIAGRAM OF THE MASTER ROUTINE (cont. ) 37 1: t23 otherw1se set C1 = t12 6 Test counter C32 is SD=SR in the previous interval?| NO I 10 YES HES 73 Is 11¢ LCL? NO 7b Is Iia-UCL? NO I 10 YES 8 Set C1 = stop lead time (t) also set C2 = 0 to decrease a shift ‘ I 10 '__.[9a Set C2 = -l to increase a shift YES 9b _ E, r.__.a 18 SD - 9. J No 9‘: Is SD = 3? ii. 11 [No 9d Is SD = 2?, if ys's, set c ._-———»11 SetC =t otherwise part: 1 01 ‘_—-—>14 10 Is SD = 0? ———>YES 14 NO 11 If product: multiply KOj (mm. requ1rement quant1ty) and store F———+lZa store min. requirement quantity Fig. (6): FLOW DIAGRAM OF THE MASTER ROUTINE (cont. ) 38 123 IS SD=3? ‘JES—‘lZd NO 2b Is SD = 2? N0 ' YES cMultiply 2(min. requirement quantity) and store -———>l3 12d Multiply 3(min. requirement quantity) and store F3 Compare available inventory with minimum requirement quantity stored and determine SR l4 Reset addresses and counters for next part SR>015 Is SD: SR?, if yes set counter C3 otherwise set C3— = O AB SR = 0 16 Set SR = 0 address is set for If address is set for product part l . l7Transfer to sub-routine to compute assembly- production for each shift; accumulate and store total assembly production ai 18 Output following: label INTERVAL and number of interval labels D, I, SD, SR ' values of D, I, SD, SR labels PARTS, J, IP, SD, SR, R, ORDER, T ‘———+29 Fig. (6): FLOW DIAGRAM OF THE MASTER ROUTINE (cont.) l9 . 30—_H Increment and output J 20 Compute, store and output 1Pij ___’4a 21 Output SD, SR 22 Transfer to sub-routine to compute part- production for each shift; accumulate and store total part-production Pij 23 Compute, store and output Ri' Set r..= 0 J 1.1 YES 24 . . . 9 ,____. Test counter C4- 18 raw material on order . NO 25 Is Rij-c‘LCL? NO +28 ps5 26 Output label PLACED Transfer to sub-routine to compute T. ~—-——>28 Store and output Tj p J ___427a Is raw material arrival tomorrow? NO YES 27b Store rj in the location specified [ 6 28 Fig. (6): FLOW DIAGRAM OF THE MASTER ROUTINE (cont. ) 39 L 40 YES 28 Test, all the parts (j) done? NO ,29 Store data back from $08 temporary locations 30Store data for next part in $08 temporary locations ——>19 _431 Increment interval (i) counter 32 Reset :addresses and counters for next interval if Q YES 33 Test, all intervals (i) done ? .—N9—. lb j... OFF ——' dump contents of memory using X8-M for next sub-run. Fig. (6): FLOW DIAGRAM OF THE MASTER ROUTINE 41 INTERVAL 00501 D I SD SR 0000641 —0002397 00003 00001 PARTS J IP SD SR R ORDER T 00001 00000139 00003 00003 00003269 00002 00007179 00000 00000 00005823 00003 00003717 00003 00003 00000882 PLACED 0000007 00004 00000370 00002 00002 00000223 00005 00006386 00002 00002 00000698 00006 00003816 00000 00000 00007686 00007 00009140 00000 00000 00002362 (7): The Output Format In Fig. (7) the notations are D = daily demand, I = product inventory level, SD = existing desired operating state, SR = actual running state, R = raw material in- ventory level, T = delivery time, etc. 807: A Sub-routine To Convert Standard Normal Distribution into a Specific Normal Distribution The routine Vll(S): “GeneraUERandom Normal Deviates" described briefly later in this chapter, generates a quantity 2' where z' = z/8 (4.1) 42 and z is a standard normal deviate. The sub-routine SO7 converts 2' into 2 up to a fraction of three significant digits, then computes a specific random normal deviate x by the following formula: x = 02 + u (4.2) Since a negative value of x is not practically feas- ible, this sub-routine truncates the distribution such that x Z 0. To avoid unanticipated high values of x in the order of infinity, the distribution is also truncated to x + 3.20X. The truncated distribution is shown in Fig.(8). / /_I I/ \ -00 d” . __ _ , ‘— + oo 0 x x——> (X+3-20x) Fig. (8): Truncated Normal Distribution The MISTIC Computer Library Routines Used A brief description of the MISTIC Computer Library rou- tines used in the simulator is presented here. Complete details can be obtained from the MISTIC Computer Library. 43 1. Large Decimal Order Input for Core Memory (X4—M): This routine is an input routine designed to accept orders with addresses in decimal and relative form. The program should be written in a suitable format. 2. Generate Random Normal Deviates (VllS): This routine produces a number 2' where z' = Z/8 (4.3) 2 is a random normal deviate whose probability distribution is a standard normal distribution given by 2 —z /2 p(z) dz = (1/ \/2Tr)e ~ dz (4.4) A non-negative random number less than 1 is required for computation of each normal deviate and it is supplied by the routine V128. 3. Generate a Sequence of Positive Random Numbers One ataa Time (V128): It is necessary to input five random numbers initially. This routine, upon a standard entry, generates five pseudo—random numbers and replaces the previous ones. The numbers are generated according to the following recur— sion formula A = A + - + + , n+5 7 n+4 An+3 4An+2 3An+l “(AIR (4 5) h f 40—b' b , . . w ere or a it num er a0 ,a39 “(ao' - . -,a39) = a0, a4, a5. - . a39,al,a2.a3 (4 6) 44 The numbers have been found random by the test applied; and the sequence has been found not to repeat within the first 10 million numbers. This routine supplies one number at a time to VllS with the sign digit of each number set to zero. 4. Print One Number Fractional or Integer in a Manner Determined by a Program Parameter (P4—M): This routine is used to print decimal integers or fractions, with or with— out sign, to a specified number of places with simulated decimal point. 5. Sexadecimal Dump with Sum Check (XS—M): This routine is used to dump contents of memory on output tape. An option has been provided so that this routine will put X4—M on the end of the resulting tape. When the dumped program is read in, the X4—M (D.O.I.) is automatically input after the sum has been checked. Only those memory locations whose contents are non zero are punched out. To obtain a faster read-in the output is in sexadecimal form; and all fifth hole characters except delays are excluded from the dumped program. General Operating Procedure The first sub-run is started by inputing the master program at the end of which a data tape is included. At the 45 end of a sub-run the dump routine X8—M is read in and the contents of the memory, including the program, are output on a paper tape in sexadecimal notations. In this manner the exact detailed operating state of the system is pre— served. The next sub-run is then started using the dump of the present sub—run ending. However, it is necessary to put new value of parameter specified for the total number of intervals that will be over at the end of the sub-run. The new value will be the value specified for the parameter in the previous :mflb-Inni plus the number of intervals to be run in the present sub—run. Thus length of each sub—run can also be varied. To specify the new number of intervals a separate tape is prepared for each sub—run. After the dump, this tape is read in and it replaces the old total of the intervals by the new one. 46 CHAPTER.V A HYPOTHETICAL SYSTEM AND THE INITIAL RUNS Description of the Product A hypothetical factory producing a single simple pro- duct—-a drill press vise illustrated in Fig. (9) and Fig. (10)-ewas chosen for initial study. The drill press vise consists of eleven different parts. Of these, four parts were considered standard items that would definitely be purchased. These parts were the screws, the steel ball, and the spring. The remaining seven parts, viz. vise base, handle, screw, movable jaw, jaw faces, clamping shoe, and locking pin were manufactured on a production line basis.* Design of the Factory 1) The customer demand: The design of the factory was based upon an expected annual demand (D) of 50,000 units. The corresponding expected daily demand (di) was 200 units with a standard deviation (odi) of equal amount. *Some of the data such as man—machine data, the sequence of manufacturing operations for each part, and production cycle times were taken from table 2, pp. 54 and table 4, pp. 55 of "Manufacturing System Synthesis Utilizing a Digital Computer," unpublished Ph.D. Thesis by Wayland P. Smith, Case Institute of Technology, 1960. 0W1? FIGURE '9 FIGURE 10 ASSEMBLED DRILL PRES VISE EXPIDDEDVIWOFDRIILPRESSVISE 47 2) Number of assembly stations: 13 Number of assembly stations = 250—55 48 (5.1) where S and a designate number of operating shifts and ex— pected output per shift per station of product assemblies. Assuming 250 working days per year, in this particular case only one shift operation and one assembly station were found necessary. The data regarding the assembly production and the product inventory control are presented in table 1. TABLE 1 THE PRODUCT DATA Symbol Description Amount Si average daily assembly production 300 units Oai standard deviation of assembly production 15 units di expected daily customer demand 200 units Gdi standard deviation of daily demand 200 units S an assembly-production ordering cost $100 h product holding cost per unit-day $.01 5 product shortage penalty per unit-day $.01 Tldt) assembly operation stop lead time for each shift 1 day Tzitof assembly operation start lead time (O-rl shift) 5 days t12 start lead time l-+-2 shifts 10 days t23 start lead time 2-a-3 shifts 15 days UCL upper control limit 720 units LCL lower control limit 180 units S designed number of shifts 1 49 3) Number of production lines per part: 13 (5.2) 250 Sfij Number of production lines per part = where fij is the output of a production line of jth part per shift. However, the number of parallel production lines (k), and the number of operating shifts were selected to provide also a slack of at least 25 percent in each production line per shift. 4) Minimum requirement quantities of finished parts: A fairly high quantity was specified as minimum requirement for limiting the level of finished parts inventory to non- negative values. Minimum requirement quantity of a finished part per shift = KO.(ai+20ai) (5.3) of assembly operation 3 where kOj = number of jth part required per assembly 5) Lead times: (a) Stop lead time——The lead time for stopping a shift operation was based mainly upon the number of manufacturing operations involved in part production. A stop lead time of one day for the first three operations plus a day for each group of additional four operations was recommended. )* T . = 1 + l/4(n.-3 1] 3 )+ (5.4 *See footnote on page 50. 50 where nj = number of manufacturing operations for jth part. (b) Start lead time--This was also based on similar con- siderations: five days for the first three operations plus a day for each group of additional three operations. T2]. = 5 + l/3(nj-3)+ (5.5)* The smallest time interval considered being one day both type of lead times were approximated to the nearest inte— ger. The lead times were provided mainly to account for the time spent in the paper work, hiring and firing of labor, setting up or tearing down operations etc. The lead times calculated using equations (5.4) and (5.5) were valid only for a change of operating state by one shift. Hence, depending upon the number of operating shifts specified by the design, equivalent lead times were necessary for computations of control limits. The follow— ing discussion should suffice to explain the procedure of arriving at the equivalent lead time in various cases. How- ever, the expressions given below would be true only when the lead time for each shift change is assumed same. *The + sign as a suffix is used to indicate that only the non-negative resultant values of the terms within parentheses were considered. 51 (i) designed number of operating shift--one: equivalent lead time = lead time for one shift (5.6) A glance at Fig. (11) would make it obvious that in case of operating shift equal to one the total production could be stopped or started at a time. (ii) designed number of operating shifts—-two: . . 3 . . equivalent lead time = §'(lead time for one shift) (5.7) A reference would be made to Fig. (12) for explanation. Here the area enclosed by full line represents the actual production stopping or starting operation in the factory. It is clear that this process was done in steps. Now if the cross hatched area was transferred as indicated by the arrow head and sketched as dotted area, it would represent that the production of both the operating shifts was stopped or started simultaneously; and that the time elapsed after an order was issued for such action would be equivalent lead time. (iii) designed number of operating shifts--threef equivalent lead time = 2(lead time for one shift) (5.8) The same procedure is adopted here also and is illustrated in Fig. (13). 52 mumwsm mounH Mom mafia use; ucmHm>finwm "AmHv .me rwwww.mufl\ /Wmmmmmm L museum museum muumum LTI. mQODm ATMI.wmwMWI.LT madam ,Irlm DHHsm _1|u~ UHHsm .AIIH uHHsm A m uanm N suHsm H umHsm sumHsm one use maHs sssH unsHssHssm "ANHV .me H _ .. a § 1.-- ,1 MIMWII unmum mun—mum leIMIHIHIm. mmoum “ J“ m o m N uHHsm H umHnm finlllnm “HHsm _ITIII.H uHHsm uHHsm use use saHa sssH ussHs>Hssm HHHHV .me r_.l pennans uotnanp susssm H “HHsm «EH9 sssH :Hcflmum: uamHm>Havm -o:a 1930; DOInonpOJd “31923“ Japio T paddons UOIJOnpOJd [Biol ssoum H “HHsm _ oEHH puma :Qoum: ucmHm>Hsvw UOIJODPOJJ udonsu Japio 53 The necessary data for all the parts are summarized in table 2. 6) Minimum requirement quantities of raw materials: A fairly high quantity of raw material was recommended for each part to restrict the raw materials inventory level to non—negative values. minimum quantity of a raw material required for each shift of a part production H "U + (A) O (5.9) The raw materials data are presented in table 3. The Initial Runs For experimentation and initial study of the system three runs, each simulating a period of four years (1000 intervals) of system operation, were made at different demand levels. The system was started from a zero initial condition for each run. The demand levels were varied by changing the expected daily demand while keeping the shape of the demand distribution the same. However, the design of the system was based on the demand values of run I. ' The system response to the three demand levels was then examined from various viewpoints. In View of the MISTIC computer reliability limitations, and the machine time available each run was divided into sub—runs of 100 intervals. 54 no Hm H. H. 6N + my M 0mm 0mm owe 0mm 0mm 0mm 0mm ..>uw .wwu .SHE OOOH OOOH ooom OOON oowN OOOH ooom HOH .uHEHH Honucoo HDBOH OOva mev comm moNv ooom O©¢m eonv HUD .uHEHH Honusou momma m m vH OH NH m mH NB .mEHu ommH pnmum Hmuou H H w o w H m H8 .mEHp waH m0pm HMDOD m m n n o m m HMHSm MNu Ho NHu.Hou.mEHu DmmH unmum H H m s m H s use p .msHu 6mmH scum mNQxxfim Hooo.w Hoo.w Noo.w Hoo.m mNoQHw Noo.w a .hmp uHcs Hem umou mcHUHon OQNw OHm comm oomw OONw ovm oo¢m m .umoo msHHmUHo .DOHQ com mam oom mom oms oos mms HHm .psduso NHHms .dxm om wm Hw wN MH mN wH DMHnm flmo.QOHUMH>mU .Uum ucmHm>stm oom mam oom omH osH cos ssH “mm Hm .DSduso .mxm Hmuou om «m mN pH m mN h mcHH .Doum Hem mo.coHumH>m© .Upm oom mam omH mm on cos 6m , m .DSduso .mxw H H m N m H m m .mDMHnm mo .0: UmcmHmmp H H N N N H w x .mmCHH .UOHQ m0 .oc H H N H H H H hox .UmmH .oz GHQ momw 3mh mcHxDmQ mozm Bmh mHnm>OE Boson mecmn omen mam: puma h m m e m N H m ..oc puma dfififl mfimflm WEB N OHQMB 55 OSHH oomH m m mmoooos osw oommN GHQ mconoH h hmm oogH Hooo.w osm omwNH OOSm mmv OOON Hoo.w osw comm momm 3th mom oovH moo.m osw OmmN 3mm mHnw>OE th OOOH Hoo.w osw ooov 3®HUW sms OOOH mmooo.w osm Doom QHUCMS N me OOON OH moo.w osm ommN mmmn H mm m H. om + .mv..>uw .vmu .QHE HUH .HHEHH Houucoo HOBOH Bo.mEHu >Hm>HHmU mo COHDMH>OD .Upm wwmp .8 .mEHu >H®>HH¢D .mxm a .mmUIuHCD Hmm pmoo mCHUHO£ m .umou mQHUMHQ Hmpuo cm H .thuGMDW HmUHO HMEHDQO mama puma h ..Oc unmm £949 mqfiHmmB<2i3ICycle, N Fig. (14): Inside Area and Outside Area per Designed Cycle Under Actual Pattern Cumulative averages of Ai, A0, and (Ai+AO) were plotted as a function of the number of cycles of the designed inventory level. N Z A. Cumulative average of inside _ l l . — (5.10)* area per deSigned cycle N N 2 A0 Cumulative average of outside _ 1 . — (5.11)* area per deSigned cycle N N + Cumulative average of total area i (Ai Ao) per designed cycle under actual = N (5.12)* inventory level pattern where N is the number of cycles. *If the cumulative average converges to a single value as N increases, this would indicate the achievement of a steady-state operation. 59 Cumulative average of inside area per designed cycle indicates the degree of conformance of actual inventory level pattern with that of the designed pattern; while cumulative average of outside area per designed cycle indicates the measure of actual inventory available, but not in conformance with the designed pattern. Cumulative average of total area per designed cycle is used to examine whether the actual inventory levels display any pattern other than the designed pattern. Cumulative average of total actual inventory level per designed cycle for part no. l-—base—-at expected daily demand di = 200 is shown in Fig. (15). It was observed that the actual inventory at di = 200, was stabilizing around 36% of the designed inventory. How- ever, actual inventory at this demand level in conformance with the designed inventory was only 25%. Some improve- ment--from 27% to 58%—-in the level of actual inventory was found as demand decreased from di = 280 to di = 120. Other parts displaying similar behavior were no. 3-—screw, no. 4——movable jaw, no. 5——jaw face. Illustrated in Fig. (16) are the cumulative averages of A., A , and (A +A ) at d, = 200 units for part no. 2—— i o i o i i + A0) Cumulative Average of (A sq. in. for Part No. 1 at 31 a 200 units -—-——- area per designed cycle average total area I I | l 4 8 12 16 cycle, N Fig. 15: Cumulative Average of Total Area Per Designed Cycle Under Actual Inventory Level Pattern 60 A0, and (Af+Ao) sq. in. Cumulative Averages of A1, 3.5 +— 3.0 —- 2.5 H. [\x I, \\ ’ \ 2 0 \\ +- \ .— \ I"... \\ ,—-/ \ /’ \bp”"\/ 1.5 r- ///-' \ /'\ \\’\ /r -. \( '\\ for Part No. 2 1.0 at '31 - 200 —- area per designed cycle average total area 0.5 H. _._.—.. average inside area ‘——--—— average outside area I l J 1 0 4 8 12 16 cycle, N , Fig. (15): Cumulative Averages of Inside Area, Outside Area, and Total Area per Designed Cycle Under Actual Inventory Level Pattern 61 62 handle. Considerable amount of resemblance-—in the range of 66% to 70%——to the designed pattern was shown by the pattern of cumulative average of Ai at all the three demand levels. Total actual inventory level was observed to attain a steady state in the range of 112% to 124% of the designed inventory level; and cumulative average of AC was observed to be in the range of 44% to 58% at all the three demand levels. Part no. 6--Shoe, and part no. 7—- locking pin displayed very similar behavior. As shown in Fig. (17), total actual inventory for the product-—drill press vise--was in total disagreement with the designed inventory pattern. Huge amount of overage-— maximum 900%-—was observed at di = 120. Large amount of shortage--maximum 1500%-—was evident at di = 200, and even more at 51 = 280. No sign of approaching a steady state was indicated by the actual pattern of inventory level at any of the three demand levels. A section of the pattern of inventory level at d = 200 for part no. l-—base—-is illustrated in Fig. (18). Most of the time the finished inventory of part no. 1 remained below LCL at all the three demand levels. Shown in Fig. (19) is the pattern of inventory level at d = 200 units for part no. 2--handle. It shows close resemblance to the ) Cumulative average of total overage area (A10 + A00 sq. in. in. Cumulative average of total Shortage area (Ais + AOS) sq. 63 1'5 _' for_product at d1 : 120 -—- overage area per designed cycle —-—- average total overage 1.0... area /\ ,’ ‘x\ I/ \\ x, “\\H/\\ // 0 5 — r\__/'\/ I I I / I P"’ I --P----——--—--—--————--——-— 0 / .shortage area per designed cycle 0.5 __ average total Shortage area 1.0 L for_Product at d1 = 200 1.5 I I I I O 10 20 30 4O cycle, N Fig. (17): Cumulative Average of Total Area Per Designed Cycle Under Actual Inventory Level Pattern 64 mmmmnnH .oz uumm How Hm>mH huousm>cH mo cuouumm "wH wustm H .Hm>umucH on owe one oNo 0am own omm com _ _ _ _ H _ - _ o .I OOON ADA E . I ooos HUD I oooo :Houuwm Hanuom CON u_flm cuwuuwm pmamemp Ill. L ooom (J1) IaAaq AxonuaauI 65 oHmemuum .02 team .HoH Ho>oH Faggot: mo snout—mm “0H .mHnH H Hat/~35 0H N. owe omo 0N0 00m 00m 0mm 00m H _ _ H o .HOH III. I I 000.N 000$s < HOP . < I ooos I 000.w Ghouumm H9506 I H duouudm pmdemeU 00m .. m. I 000.0H (d1) ISA-9’1 Kiowa/m} 66 designed pattern. Illustrated in Fig. (20) and Fig. (21) are the finished product--drill press vise--inventory level patterns at di = 200, and di = 120 respectively. Huge amount of shortage is observed at di = 200 while large amount of overage is observed at di = 120. 2) Pattern of Inventory Levels of Raw Materials: Typical raw material inventory patterns at d = 200 for part no. l-— base, and part no. 2--handle are exhibited in Fig. (22) and Fig. (23) respectively. For all the parts the slope of raw material consumption was found to be steeper than designed. Consequently, orders for raw materials were placed more frequently than designed during the period When part production was in full swing. However, varying amount of raw material inventory stocks resulted for parts no. 2, no. 6, and no. 7 due to production breaks; hence raw material order placing for these parts was almost as desired. 3) Pattern of Operating Shifts for Product and Parts: Typical operating shift (SR) patterns at di = 200 for part no. l—-base, and part no. 2--handle are shown in Fig. (24) and Fig. (25) respectively. Parts no. 1, no. 3, no. 4 and no. 5 displayed a fluctuating pattern of operating shifts from 0 shift to 3 shifts with frequent 67 me> mmmum HHHunusuuavoum new Ho>wH huouco>cH mo cumuumm "0N .me H .Hw>umucH oHH omo one oHo osm oon omm _ _ _ _ _ _ H P l‘lnl.’ b I .klllll'ZIflllIllIZl‘nlluHI'2IuIlIIIIZIIllIIIIIZIaKIIIIIZIIBIIIIIIZIHIIIIIIZA‘w HUH auouumm stuom H00 cumuuma pmcwH new I ooH . Hs 00m 000NH1 II. 000w: I. ooos-. .II 000¢+ .I 000w+ (I) faaaq Kioauaaul ionpOJg 68 mmH> mmmum HHHuounuosmoum you Hw>mH mucusm>cH mo cumuumm "HN .me H .Hm>uwucH 0Hm 000 0mm 0N0 000 00m 0mm 00m _ _ _ _ _ _ _ oooNH- cumuuwm Heauum .II 000mm cumuuma pmstmmv I H I. .- >I>flha1 J 4:1". . a .. HUH .III II 000v+ HUD I1 000w+ (I) IBAaq Azoauaaul 33np01g 69 ommmHIIH .02 when” .HoH Ho>oH HHHOHHHQEH HmHHoumHZ 3mm .Ho cuofimnm “NN .mHnH H .H.~>.HOHH.HH ohm 00m , 0mm gum 0mm 0mm 03 00m T/ , IIfl— _I o H v. / W m A w s m . I e I 000 NH u. I e I m. A m 404 IL m. I 000 .v M duofimm Hmsuom shown—mm DocmHmop 00m. u Hm 7O oHHoHHmEunN .02 team .HoH H954 >H0ucv>5 HmHHQHmHZ 3.8m Ho cumuumnm “mm .mHnH 0H5 owe 0m0 0N0 00m 00m 0mm 00m HOH I 000.N 000;‘ I ooo.o III I 000.w system Hmsmom 933.6% Dvdemop H II . oom n .s ooo oH 71 ummmmuaH .oz uumm How Hmm-omv ssHHsm oHsH was Ammo sumHsm msHususao Ho ssssussm Hssuus "sH .wHH H .He>umucH ohm oom omm osn omm omm on - oom _ _ _ H. _ _ _ _ j s .1 H .1 N _ (I m oou u Hm . (I o :1 H In N E . (us) SJJIHS SUTJFJBdO (us-as) SJJIHS aIPI 72 mHmammsuN .oz uumm How Hem-omo suHHHm oHsH oss Ammo sumHsm wsHusHsao Ho sassuusm Hssuos "mu .st H .Hm>umuaH okm osm omm ; osm omm own oHn oom fl _ H H Ll H _ A it s E s O H (as) sngtqs Burnsiado N H (us-as) SJJIQS 8191 N 73 steady operating state at 0 shift, or 3 shifts. Less fluctuation was observed in the pattern of operating shifts for parts no. 2, no. 6, and no. 7. A given operating state was maintained for these parts for a considerably longer time at each shift level. The most unsteady behavior exhibited was by assembly operation shifts as shown in Fig. (26). Large fluctuations between 0 shift to 2 shifts, and occasionally 3 shifts were observed. All of these fluctuations were caused mainly by the shortage of raw materials for parts production and the shortage of finished parts for assembly operations. 4) Pattern of Idle Shifts for Product and Parts: The patterns of idle time were also observed to be highly fluctuating. A great deal of idleness was found for part no. 1 as shown in Fig. (24). The behavior of parts no. 3, no. 4, and no. 5 was similar to that of part no. 1. Parts no. 2, as shown in Fig. (25), and part no. 6 exhibited less idle time. The least amount of idle time occurred for part no. 7. A large amount of idleness was exhibited by the product as shown in Fig. (26). The main reason for occurrence of idle time was one cited for fluctuations in operating shifts: raw materials and finished parts shortages. 74 0pm 03> mmonnH HHHHan—odponnm 8H 36.69 33m 22 Has Ems Exam 33230 Ho sasstsm H88... “om .erH H .HsisHsH oom omm osm o8 omm on oom _ _ _ H _ L H L __o I H I H I m H oom u .m lo I H I N m (as) sums Butieiedo (HS'CIS) sums eIpI 75 CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK Conclusions From the limited experience gained from this study the following conclusions were drawn. 1. The designed pattern of raw material inventory level was found crucial in the production of parts. The parts having high optimal quantity of raw material compared to production rate exhibited close resemblance to the designed pattern of finished part inventory level with considerably less idle time. The parts having low optimal quantity of raw material compared to production rate displayed very low degree of conformance with the designed pattern of finished part inventory level; and large amount of idle time was incurred. This indicated that design based on only expected demand considerations would not always be "near optimal" design for many parts crucial in the final assembly. 2. On final product considerations, the system--for the specific design configuration--did not attain a steady state of operation. Many variations from the designed pattern were observed and much idle time was incurred due 76 to the shortage of one finished part or another. 3. Slight improvement in the degree of conformance of various system components with the designed patterns was observed as demand decreased. Recommendations for Further WOrk The study undertaken here is merely the start of a vast field of experimentation by simulation of manufacturing systems. The next step should be to design raw material inventory patterns on production rates instead of expected demand values. Replication of a typical system run should also be carried out to insure that the system behavior is not dominated by a particular series of random numbers. Another interesting area would be investigation of the effects of different values of lead times on system per- formance. The amount and degree of synchronization of various lead times could be crucial to the behavior of a manufacturing system. Using the present simulator, manufacturing systems of different size--a maximum of 100 parts system——could be simulated for any desired period of time. A selected con— figuration can be tested for different demand distributions; and to meet a known demand level the system configuration 77 can best be designed and selected by changing one or more of the system parameters such as patterns of inventory levels, lead times, raw material ordering rules and related delivery times, etc. With some modification in the simu- lator a retrospective simulation can also be carried out. The approach and methodology developed here could be used to design and test systems producing parts also on job shop basis and sub-contracting basis. The study could be made more realistic by providing overtime practice, and introducing element of cost as one of the measures of per- formance of system operation. However, such experimentation would need additional memory space and a faster computer than one used in this study. 10. ll. 78 LIST OF REFERENCES Arrow, K. J., Karlin, S., Scarf, H., Studies ig_the Mathematical Theory gf_Inventory and Production, Stanford, California, Stanford University Press, 1958. Bellman, R. E., Dynamic Programming, Princeton, N.J., Princeton University Press, 1957. Brown, R. G., "A General Purpose Inventory--Control Simulation," Report g£_System Simulation Symposium, Baltimore, Maryland, Waverly Press, Inc., 1958. Campbell, D. P., Process Dynamics, New York, N. Y., John Wiley and Sons, Inc., 1958. Canning, R. G., "Electronic Scheduling Machine Equip- ments," Management Science, Research Report No.29, March 1955. Churchman, C. W., Arcoff, R. L., Arnoff, E. L., Introduction tg_0perations Research, New York, N. Y., John Wiley and Sons, Inc., 1957. Conway, R. W., Johnson, B. M., and Maxwell, W. L., "An Experimental Investigation of Priority Dis- patching," The Journal gf_Industrial Engineering, May-June, 1960, Vol. 11, No. 3, pp. 221-229. Conway, R. W., Johnson, B. M., and Maxwell, W. L., "Some Problems of Digital Systems Simulation," Management Science, October, 1959, Vol. 6, No. 1, pp. 92-110. Forrester, J. W., "Industrial Dynamics," Harvard Business Review, July-August, 1958, Vol. 36, No. 4, pp. 37—66. Forrester, J. W., "Advertising: A Problem in Indus- trial Dynamics," Harvard Business Review, March-April, 1959, Vol. 37, No. 2, pp. 100-110. Gass, S. 1., Linear Programming, New York, N. Y., McGraw-Hill Book Co., 1958. 12. 13. 14. 15. l6. 17. 18. 19. 20. 21. 22. 79 Grabbe, E. M., Ramo, S., WOoldridge, D. E., Handbook g§_Automation, Computation and Control, Vol. I, New York, N. Y., John Wiley and Sons, Inc., 1958. Impact g§_Feedback Control Concepts in the Study g§_ Economic and Business Systems, New York, N. Y., The Foundation for Instrumentation Education and Research, Inc., October, 1960. Jackson, J. R., "Queues with Dynamic Priority Disci— pline," Management Science, Vol. 8, No. 1, October, 1961. Magee, J. F., Production Planning and Inventory Control, New York, N. Y., McGraw-Hill Book Co., 1958. MISTIC Programming Manual, Prepared by the Computer Laboratory Staff, Michigan State University, East Lansing, Michigan, 1958. Robinson, P. J., "Cases in Simulation-—A Research Aid as a Management Demonstration Piece," Report g§_System Simulation Symposium, Baltimore, Maryland, Waverly Press, Inc., 1958. Rowe, A. J., "Toward a Theory of Scheduling ," The Journal g£_Industrial Engineering, March-April, 1960, Vol. 11, No. 2, pp. 125-136. Rowe, A. J., and Jackson, J. R., "Research Problems in Production Routing and Scheduling," Management Science, Research Report No. 46, October, 1956. Sasieni, Maurice, Yaspan, Arthur, Friedman, Lawrence, Operations Research--Methods and Problems, New York, N. Y., John Wiley and Sons, Inc., 1959. Satty, T. L., Elements of Queueing Theory, New York, N. Y., McGraw-Hill Book Co., 1961. Smith, W. P., Manufacturing System Synthesis Utilizing g_Diqital Computer, Unpublished Ph.D. Thesis, Case Institute of Technology, Cleveland, Ohio, 1960. 23. 24. 80 Vazsonyi, Andrew, Scientific Programming pp Business and Industry, New York, N. Y., John Wiley and Sons, Inc., 1958. Whitin, T. M., The Theogy p§_Inventory Management, Princeton, N. J., Princeton University Press, 1957. V381 USE UI‘ILY MICHIGAN STATE UNIVERSITY LIBRARIES 01 3 46 0516 II 3 1293