A major retail firm is considering a major change in itsdistribution system. It is considering relocating its distributioncenters such that all retail stores can be replenished within 24hours of a request for merchandise.
The table below is a matrix of cover coefficients for 10 storesand 10 potential sites for distribution centers. If store i can bereplenished within 24 hours from site j, then a_ij=1; otherwisea_ij=0. The cost of installation of the distributions centers varyfrom zone to zone and are given in the DC cost row. The firm wantsto find the optimal location of the distributioncenters. Â
Store i | Distribution Center Site |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
2 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
4 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
5 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
6 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
7 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
8 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
9 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
10 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
DC COST | 193 | 721 | 822 | 156 | 607 | 593 | 246 | 385 | 309 | 867 |
1-Provide a mathematical formulation of above model
2-Provide a mathematical formulation given a budget restrictionof 300.
3-Provide a mathematical formulation given a coverage targetmore than 85% (firms wants to cover at least 85% of the stores)
3-Solve the 3 models using Lindo/Excel Solver or anyoptimization software you know
