Mack\'s wants to locate two new receiving warehouses adjacent to two of its exis

Question

Mack's wants to locate two new receiving warehouses adjacent to two of its existing eight stores in the state. The distance matrix between the store locations is given below Assume that demands are identical in each store and that there are no capacity constraints 120 78 170 14 140 120 24 200 140 230 16 320 45 115 20 45 110 190 130 175 85 35 10 65 140 130 60 90 a) Find the total distance covered by trucks carrying product from warehouses to the stores if the two warehouses are located adjacent the two stores that are farthest apart (15 points) b) Is it better to locate the warehouses adjacent to the two stores closest to each other instead? (15 points)

Explanation / Answer

a) The two stores that are farthest apart are 2 and 6 having a distance of 320 between them. Distance matrix between the 2 warehouses and the 8 stores is as follows

Warehouse that is nearest to a store supplies to that store. so stores 1, 2, 4 and 7 get supply from warehouse adj store 2 and stores 3, 5, 6 and 8 get supply from warehouse adj store 6.

Total distance covered by trucks = 120+0+45+140+10+0+45+60 = 420

b) Stores 5 and 6 are closest to each other, having a distance of 10 between them. Distance matrix between the 2 warehouses and the 8 stores is as follows

Warehouse that is nearest to a store supplies to that store. so stores 1, 2, 3, 4, 5 and 7 get supply from warehouse adj store 5 and stores 6 and 8 get supply from warehouse adj store 6.

Total distance covered by trucks = 24+16+20+130+0+0+65+60 = 315.

This distance is lesser than earlier. Therefore it is better to locate the warehouses adjacent to the two stores closest to each other.

1 2 3 4 5 6 7 8 wh adj. store 2 120 0 170 140 16 320 45 115 wh adj. store 6 200 320 45 175 10 0 130 60

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