A supermarket chain has five stores in different regions of a country. These sto

Question

A supermarket chain has five stores in different regions of a country. These stores may make agreements with several transportation companies which can provide shuttle service for their customers. The following table shows the regions covered by these supermarkets, the cost of shuttle service and the benefits of having the corresponding shuttle service. Shuttle service cost Benefit of shuttle service Regions covered 1,2.4 2,3,6 4,5,6 5,7.8 6,8,9 Store 12 10 14 19 16 Formulate an integer programming model such that the shuttle service is provided in the whole country at minimum cost.

Explanation / Answer

Integer program:

Decision variables: Let Xi is a binary variable such that if Xi=1, then shuttle service is contracted by store i, otherwise if Xi=0, then shuttle service is not contracted by store i.

Objective: Min 3X1+4X2+3X3+7X4+5X5

s.t.

X1 = 1   (to cover region 1)

X1+X2 >= 1 (to cover region 2)

X2 >= 1   (to cover region 3)

X1+X3 >= 1 (to cover region 4)

X3+X4 >= 1 (to cover region 5)

X2+X3+X5 >= 1 (to cover region 6)

X4 >= 1 (to cover region 7)

X4+X5 >= 1 (to cover region 8)

X5 >= 1 (to cover region 9)

X1, X2, X3, X4, X5 = 0,1

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