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Question
A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:
|
Jobs
|
Machines |
|||
|
P |
Q |
R |
S |
|
|
Processing Cost (Rs.)
|
||||
|
A |
31 |
25 |
33 |
29 |
|
B |
25 |
24 |
23 |
21 |
|
C |
19 |
21 |
23 |
24 |
|
D |
38 |
36 |
34 |
40 |
How should the jobs be assigned to the four machines so that the total processing cost is minimum?
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Solution
We can express the matrix form
`[(31,25,33,29), (25,24,23,21), (19,21,23,24), (38,36,34,40)]`
Subtracting the smallest element in each row from every element of it,
`[(6,0,8,4), (4,3,2,0), (0,2,4,5), (4,2,0,6)]`
Subtracting the smallest element In each column from very element of it.
`[(6,0,8,4), (4,3,2,0), (0,2,4,5), (4,2,0,6)]`
All the zeros of the above matrix are covered with minimum number of lines as below :
No. of lines = No. of rows/columns
Assignment of jobs :
A → Q, B → S, C → P, D → R
Minimum cost = 25 + 21 + 19 + 34
= Rs 99
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