Answer to Question #173500 in Operations Research for ANJU JAYACHANDRAN

Question

6. (a) A company has 5 jobs to be processed by 5 mechanics. The following table gives the 

return in rupees when the th i job is assigned to the th j mechanic. i,( j = ,2,1 K ).5,

How should the jobs be assigned to the mechanics so as to maximize the overall 

return?

Jobs 

1 2 3 4 5 

1 22 28 30 18 30 

Mechanics 2 30 34 18 11 26 

3 31 17 23 20 27 

 4 12 28 31 26 26 

 5 19 23 30 25 29

Answer 1

The given problem is balanced minimization problem.

Step-1: Initial Solution

 (a) Row reduction

(b) Column reduction

Step-2: Optimally Test

 we draw minimum number of straight lines to cover maximum zeroes.

Since the number of lines\neq No. of rows/column, optimal solution is not posiible.we further improve the matrix.

Here The minimum uncovered cell element is 1, we shall processed further with the steps stated above, finally we get the following matrix-

we again draw minimum no. of straight lines to cover maximum zeros.

Since the no. of line=No. of rows/columns =5 , optimal solution is possible.

Step-3: Assignment 

Final Answer