Reference no: EM132916105
Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.
The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
DC A B C D 1 1 3 3 2 2 2 4 1 3 3 3 2 2 3 The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.
Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4.
Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3.
The constraint for distribution center 1 is:
X11 + X12 + X13 + X14 ≥ 500.
X11 + X12 + X13 + X14D + 500y1 ≤ 0.
X11 + X12 + X13 + X14 - 500y1 ≤ 0.
X11 + X12 + X13 + X14 ≤ 500.
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