Page 176 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 8: Assignment Problem – Unbalanced

8. Determine an optimum assignment schedule for the following assignment problem. The Notes
cost matrix is –

Machine
Job 1 2 3 4 5 6

A 11 17 8 16 20 15
B 9 7 12 6 15 13
C 13 16 15 12 16 8
D 21 24 17 28 26 15
E 14 10 12 11 15 6

If job C cannot be assigned to machine 6, will the optimum solution change?
9. A company has 6 jobs to be processed by 6 machines. The following table gives the return
th
th
in rupees when the i job is assigned to the j machine (I, J = 1…….6). How should the jobs
be assigned to the mechanics so as to maximize the overall return?
Jobs
Machine 1 2 3 4 5 6
1 9 22 58 11 19 27
2 43 78 72 50 63 48
3 41 28 91 37 45 33
4 74 42 27 49 39 32
5 36 11 57 22 25 18
6 13 56 53 31 17 28

10. A company is faced with the problem of assigning 4 machines to 6 different jobs (one
machine to one job only). The profits are:
Job Machine
A B C D
1 3 6 2 6
2 7 1 4 4
3 3 8 5 8
4 6 4 3 7
5 5 2 4 3
6 5 7 6 4

11. A process can be carried out an anyone of 6 machines. The average time taken by any
operator on any specific machine is tabulated in the given matrix. It is proposed to buy a
new machine to replace one of the existing ones for operations. To carry out the process on
this machine average times have been estimated and entered in the matrix. Is it
advantageous at this stage to use the new machine? If so, which of the original machines
should be replaced and how should the operators be allocated?

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