iii iv ................................ ................................ ................................ .......................... ................................ ................................ ................................ ....................... ................................ ................................ ................................ ........ ................................ ................................ ................................ .... ................................ ................................ ................................ ....... ................................ ................................ .................. ................................ ................................ .......................... ................................ ................................ ................................ ..... ................................ ............................. ........... ................................ ................................ ....... ................................ ................................ ....... ................................ ................................ ................... ................................ ................................ .................. ................................ ................................ .......... ................................ ................................ ........... ................................ ................................ ....................... ................................ ............................. ..................... ................................ ................................ . ................................ ......................... ................................ ................................ ............. ................................ ................................ ................................ .... ................................ ................................ ................................ .............................. ................................ ................................ .................... ................................ ................................ ................................ ................................ ............... ......................... ................................ ................................ ................................ ............................. v ................................ ................................ ............................ ................................ ................................ .......... ................................ ................................ ................................ ............................... vi ................................ ................................ ............. ................................ ........ ................................ ................................ ......... ................................ ................................ ................................ ................................ ............ ................................ ....................... ................................ ................................ ....................... ................................ ................................ ........................ ................................ ................................ ........................ ................................ ................................ ........................ ................................ ................................ ...................... ................................ ................................ ...................... ................................ ................................ ...................... vii 1 CHAPTER 1 INTRODUCTION 1.1 2 3 1.2 4 5 CHAPTER 2 LITERATURE REVIEW 2.1 6 7 2.2 (1) 8 (2) (3) (4) (5) (6) 9 2.3 10 Schwartz and Voß (2007) developed a mixed integer programming model for network design of a supply chain with possible postponement of assembly or packaging. Their model minimizes total costs (i.e., variable shipping costs, variable processing costs, and fixed infrastructure costs) with the following constraints: (i) material flow balance, (ii) demand satisfaction, (iii) limited supply, (iv) limited transportation capacity, and (v) limited infrastructure capacity. Shao and Ji (2008) presented an optimization model wit h the objective of minimizing total inventory costs and constrained by (i) a threshold for average customer waiting time, and (ii) the fil l rate within a target waiting time window. 11 2.4 12 13 CHAPTER 3 INVENTORY IN SUPPLY CHAIN 3.1 14 15 3.2 3.2.1 16 3.2.2 17 3.2.3 3.3 18 19 CHAPTER 4 PROBLEM STATEMENT AND MATHEMATICAL MODELING 4.1 I. II. 20 4.2 21 22 23 CHAPTER 5 COMPUTATIONAL RESULTS 24 1 2 3 4 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 Retailer Capacity 25 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 Retailer Lead time (in weeks) 26 1 2 3 4 0 0.5 1 1.5 2 2.5 3 Retailer Additional cost (in $ per unit) 27 1 2 3 4 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 Retailer Unit cost (in $ per unit) 1 2 3 4 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% Retailer h 28 1 2 3 4 75% 76% 77% 78% 79% 80% 81% 82% 83% 84% 85% 86% 87% 88% 89% 90% 91% 92% 93% 94% 95% 96% 97% 98% 99% Retailer CSL 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer (1,2) 29 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer (1,3) 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer qv (1,4) 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer (2,3) 30 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer (2,4) 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Retailer (3,4) 31 32 CHAPTER 6 CONCLUSION S 33 34 35 APPENDIX A 36 37 38 APPENDIX B 39 1 option minlp=shot 2 sets 3 i products /1/ 4 j retailers /1*4/; 5 alias (j, m); 6 *known 7 parameters 8 L lead time in terms of weeks /9/ 9 CSL desired cycle service level /0.95/ 10 h_fr annualy holding cost fraction /0.3/ 11 cc(i,j,m) correlation coefficient 12 /1. 1. 2 0.0 13 1. 1. 3 0.0 14 1. 1. 4 0.0 15 1. 2. 3 0.0 16 1. 2. 4 0.0 17 1. 3. 4 0.0/ 18 Add_cost additional cost per unit of product 19 /1/ 20 C(i) unit cost of i in terms of dollars 21 /1 1000/ 22 Cap(i) weekly packaging capacity of product i 23 /1 2200/; 24 $funclibin stolib stodclib 25 function inv_nor /stolib.icdfnormal/; 26 Scalar FCSL; 27 FCSL = inv_nor(CSL,0,1); 28 *bsic 29 Table ave_dem(j,i) average demand of product i b eing sent to retailer j per week 30 1 40 31 1 1000 32 2 1000 33 3 100 34 4 100 ; 35 Table sta_dev(j,i) SD of product i being sent to retailer j 36 1 37 1 500 38 2 100 39 3 50 40 4 10 ; 4 1 binary variable x(j,i); 42 *Option I without postponement 43 Variables 44 ss(j,i) safety stock of product i being sent to retailer j 45 H(j,i) holding cost of ss(ij) in termss of dollars 46 TC_I total cost of option I in terms of dollars; 47 Equations 48 safety_sto(j,i) safety stock of product i being sent to retailer j 49 Hol_cost(j,i) holding cost of ss(ij) in termss of dollars 50 Total_cost_I total cost of option I in terms of dollars; 51 safety_sto(j,i) .. ss(j,i) =e= FCSL*sqrt(L)*sta_dev(j,i); 52 Hol_cost(j,i) .. H(j,i) =e= ss(j,i)*C(i)*h_fr; 53 Total_cost_I .. TC_I =e= sum((j,i),(1 - x(j,i))*H(j,i)); 54 *Option II with postponement 55 Variables 56 ave_dem_a(i) average demand of portion of product i 57 sta_dev_a(i) SD of portion of product i 58 ss_a(i) safety stock of portion of product i 59 H_a( i) holding cost of ss_a(i) 60 TC_II total cost of portion of product i; 61 Equations 62 AD_a(i) average demand of portion of product i 63 SD_a(i) standard deviation of portion of product i 64 safety_inv_a(i) safety stock of portion of product i 65 Hol_cost_a(i) holding cost of portion of product i 66 Total_cost_II total cost of product i; 67 AD_a(i) .. ave_dem_a(i) =e= sum(j,x(j,i)*ave_dem(j,i)); 68 SD_a(i) .. sta_dev_a(i) =e= sqrt(sum(j,power(x(j,i)*sta_dev(j,i),2))+2*sum((j,m)$(ord(j)j 42 z_2 = z_2+2*(x(1,i)*x(1,j)*cc_base(i,j )*std_dev(i,1)*std_dev(j,1)); 43 end 44 end 45 H_a=inv_nor*sqrt(L)*sqrt(z_1+z_2)*c_base*h_base; 46 AC=AC+(52*ca_base*ave_dem(i,1)*x(1,i)); 47 TC_II=H_a+AC; 48 end 49 TC=TC_I+TC_II; 50 if TC_Min(1,L)==0 51 TC_Min(1,L)=TC; 52 elseif TC_Min(1,L)>TC 53 TC_Min(1,L)=TC; 54 x_min=x; 55 end 56 end 57 end 58 end 59 end 60 fprintf('When lead time is: %d \ n',L) 61 x_min 62 fprintf('minmum cost is: %d \ n', TC_Min(1,L)); 63 end 45 46 47 48