A major retail firm is considering a major change in its distribution system. It is considering...

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Mechanical Engineering

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 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

Answer & Explanation Solved by verified expert

3.7 Ratings (422 Votes)

Solution1 Let xi is the binary integer in such a way thatxj 1 when the site j 1210 isselected and xj 0 otherwiseMinimize Z 193x1 721x2 822x3 156x4 607x5 593x6 246x7 385x8 309x9 867x10Subject to for i 1 2 10xij 01From abovetable Result See Answer

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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