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Two Jobs ‘m’ Machine Case

Two Jobs ‘m’ Machine Case

  1. 1.   Two axis to represent job 1 and 2 are drawn at right angles to each other. Same scale is used for X and Y axis. X-axis represents the processing time and sequence of job 1 and Y axis represents the processing time and sequence of job 2. The processing time on machines are, laid out in the technological order of the problem.
  2. 2.   The area which represents processing times of jobs 1 and 2 and is common to both the jobs is shaded. As processing of both the jobs on same machine is not feasible, the shaded area represents the unfeasible region in the graph.
  3. 3.   The processing of both the jobs 1 and 2 are represented by a continued path which consists of horizontal, vertical and 45 degree diagonal region. The, path starts at the lower left comer and stops at upper right comer and the shaded area is avoided. The path is not allowed to pass through shaded area which as brought out in step II represents both the jobs being processed simultaneously on the same machine.

Any vertical movement represents that job 2 is in progress and job 1 is waiting to be processed. Horizontal movement along the path indicates that 1 is in progress and job 2 is idle waiting to be processed. The diagonal movement of the path indicates that both the jobs are being processed on
different machines simultaneously.

  1. 4.   A feasible path maximizes the diagonal movement minimizes the total processing time.
  2. 5.   Minimum elapsed time for any job = processing time of the job + idle time of the same job.

Example 7.11 The operation time of two jobs 1 and 2 on 5 machines M1, M2, M3, M4 and given in the following table. Find out the optimum sequence in which the jobs should be processed so that the total time used is minimum. The technological order of use of machine for job 1 is M1, M2, M3, M4 and M5 for job 2 is M3, M1, M4, M5 and M2.

Job

1

M1

M2

M3

M4

M5

1

2

3

5

1

Job

2

M3

M1

M4

M5

M2

3

4

2

1

5

 

Job 1 proceeds job 2 on machine M1, job 1 proceeds job 2 on machine M2, job 2 preceeds job 1 on machine M3, job 1 proceeds job 2 on M4 and job 2 proceeds job 1 on M5.

The minimum processing time for job 1 and 2, Total processing time for job 1 + idle time for Job 1 = 12 + 3 = 15 hours.

Total processing time for job 2 + idle time for job 2 = 15 + 0 = 15 hours. 

Example 7.12. Two parts A and B for a product need processing of their operations through six machines at stations S1, S2, S3, S4, S5 and S6. The technological order of these parts and the manufacturing time on the machines are as given below.

Part A Technological Order

S3

S1

S5

S6

S4

S2

Time (hours)

2

3

4

5

6

1

Part B Technological Order

S2

S1

S5

S6

S3

S4

Time (hours)

3

2

5

3

2

3

 

Determine the optimal sequencing order to minimize the total processing time for part A and B.

Sol. Let us construct the two dimensional graph let X-axis represent Job A and Y-axis represent Job B.

Total elapsed time = 23

Part A=21+2 (idle time)=23

Part B=18+(2+2+1) idle time=23

Example 7.13 There are two job to be performed on 5 machines. The following data is available. Find out the minimum total time in sequence.

Job 1 Sequence time (Hours)

M1

M2

M3

M4

M5

2

3

4

6

2

Job 2 Sequence time (Hours)

M3

M1

M4

M5

M2

4

5

3

2

6

 

Sol. Let us draw X-axis representing job 1 and Y-axis representing job 2, Horizontal lines represent job 1 being processed when job 2 is waiting to be processed. Horizontal line indicates job 2 is being processed and job 1 is idle. 

Fig. 7.5

Idle time for job 1 = 3

Idle time for job 2 = 0

Total elapsed time = 20 hours