Suppose that Yi is a binary variable which takes a value of 1 if a warehouse is

Question

Suppose that Yi is a binary variable which takes a value of 1 if a warehouse is opened in city i and 0 otherwise. There are 4 candidate cities. Fixed cost of opening warehouse in city i is 200, 230, 400, 185 for cities i=1, 2, 3 and 4, respectively. The objective is to minimize the total cost of opening warehouses subject to the constraints listed below. Formulate each of the items below using an integer programming approach:

a) Objective function

b) If the warehouse in city 2 is opened, then the warehouse in city 3 can not be opened.

c) At most three, at least two warehouses should be opened.

d) Either the city 3 warehouse or the city 2 warehouse must be opened.

e) If the city 4 warehouse is open, then the warehouses in city 1 and city 2 should also be opened.

Explanation / Answer

a) Objective function: Min 200Y1 + 230Y2 + 400Y3 + 184Y4

b) Y2 + Y3 <= 1

c) Y1 + Y2 + Y3 + Y4 <= 3

Y1 + Y2 + Y3 + Y4 >= 2

d) Y2 + Y3 = 1

e) 2Y4 - Y1 - Y2 <= 0

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