The Johnny Ho manufacturing company in Columbus Ohio is putting out four new ele

Question

The Johnny Ho manufacturing company in Columbus Ohio is putting out four new electronic components. each of hos four plants ahs the capacity to add one more porduct to its current line of elecronic parts. The unit manufacturing costs for porducing the different parts at the four plants are shown in the accompnaying table

0.11

The optimal assignment of plants to componets that minimizes the cost is what for all four plants?

The cumulative cost for the optimal assignment of plants to components=

component 1 2 3 4 c53 0.14 0.13 0.09 0.1 c81 0.03 0.04 0.06 0.07 d5 0.4 0.36 0.32 0.33 d44 0.19 0.12 0.15

0.11

Explanation / Answer

The above problem can be solved by Hungarian algorithm.

We start with subtracting the row minimum from each row.

0

we subtract the column minimum from each column,

We will now determine the minimum number of lines (horizontal or vertical) that are required to cover all zeros in the matrix. We find here there are 3 lines to cover all zeroes but matrix size is 4. Hence we need to create additional zero in the above matrix.

we find that the smallest uncovered number is 0.01. We subtract this number from all uncovered elements and add it to all elements that are covered twice. This results in the following matrix:

0

Now we assign each component to the four plants by assigning each zero to each plant such that the cost is minimized.

Based on this

c53 component should go to plant 3.

c81 component should go to plant 1.

d5 component should go to plant 4..

d44 component should go to plant 2.

The cumulative cost for the optimal assignment of plants is 0.57.

component 1 2 3 4 subtraction c53 0.14 0.13 0.09 0.1 (-0.09) c81 0.03 0.04 0.06 0.07 (-0.03) d5 0.4 0.36 0.32 0.33 (-0.032) d44 0.19 0.12 0.15 0.11 (-0.11)

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