A company needs to locate three departments (X, Y, and Z) in the three areas (I,

Question

A company needs to locate three departments (X, Y, and Z) in the three areas (I, II, and III) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.50 per load meter moved. An analyst has prepared the following flow and distance matrices:

1. What are total weekly costs for an optimum layout?

Multiple Choice

$2,600

$6,200

$3,600

$8,200

$7,200

2.

Which layout will minimize the total distance loads will be moved each week?

Multiple Choice

X in 1; Y in 2; Z in 3

Y in 1; X in 2; Z in 3

X in 1; Z in 2; Y in 3

Z in 1; X in 2; Y in 3

Z in 1; Y in 2; X in 3

Distances (meters) From/To I II III I - 10 20 II - 10 III -

Explanation / Answer

Step-1: Find the total flow of the pairs

Step-2: We are given three sets of distances - 10, 10, and 20. it is obvious that when we allocate minimum distance to the maximum load, the total load distance is minimized. The logical allocation should be -

Step-3: This is only possible when we allocate like this -

Step-4: Find the cost by multiplying the total flow distance with $0.5

i.e. 5200 x $0.5 = $2600

Pairs Flow X-Y 0+30 = 30 Y-Z 150+130 = 280 Z-X 80+100 = 180

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