Q51211c A machine operator has to perform three operations — turning, threading and knurling — on a number of different jobs. The time required to perform these operations (in minutes) for each job is given below in Table no. 1. Determine the order in which the jobs should be processed in order to minimize the total time required to perform all the jobs. Also find the minimum elapsed time.

Job 1 2 3 4 5 6
Turning 3 12 5 2 9 11
Threading 8 6. 4 6 3 1
Knurling 13 14 9 12 8 13
Table no. 1 Sequence Problem

Solution:

Initially, check whether the given problem satisfies the condition or not. We have three separate machines for Turning, Threading, and Knurling, so let these three machines be Ml, M2 and M3 respectively.

Check the condition for,

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Since either one of the conditions is satisfied, the problem can now be converted into two- machine type.

Assuming imaginary machines as M4 and M5

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Table No. 2 Problem Converted to 2-Machine Type

Now using the algorithm for n jobs and two machines, the optimal sequence is shown in Table 3.

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Table No. 3 Optimal Sequence

Find the total elapsed time and idle time for machine M1, M2 and M3. These are shown in Table 4, below:

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Table No. 4 Final Optimal Sequence Table

From the above table, we find that

Total elapsed time               =              77 min.

Idle Time for Machine M1  =               35 min.

Idle Time for Machine M2  =               49 min.

Idle Time for Machine M3  =                8 min.

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