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  3. a major retail firm is considering a major change

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

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Question

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.  

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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