Maximal Assignment Problem
Sample Assignment Problem
A company has 5 tasks to be performed. The following matrix presents the return in terms of rupees on allotting ith ( i = 1, 2, 3, 4, 5 ) machine to the jth job ( j = A, B, C, D, E ). Assign the five jobs to the five machines in order to maximize the total expected profit.
Jobs
Machines
A
B
C
D
E
1
5
11
10
12
4
2
6
3
14
7
9
8
Answer
Subtract all the elements from the uppermost element
Highest element = 14
0
Row Reduced matrix
I Modified Matrix
N < n i.e. 3 < 5
II Modified Matrix
N < n i.e. 4 < 5
III Modified Matrix
N = n
Zero assignment
Optimal assignment 1 - C 2 - E 3 - D 4 - B 5 - A
Maximum profit = 10 + 5 + 14 + 14 + 7 = Rs. 50
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