Page 208 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 10: Sequencing Problems and Replacement Theory

Notes
Table 10.21: Final Optimal Sequence Table
Job Machine I Machine II Idle Time Idle
Sequence A Time
Time In Time Out Time In Time Out
B
J1 0 2 2 8 0 2
J2 2 6 8 15 0 0
J6 6 10 15 26 0 0
J3 10 19 26 30 0 0
J5 19 26 30 33 0 0
J4 26 32 33 36 0 0
36-32=4
4 2
The total elapsed time is 36 hours

Idle time for Machine I is 4 hours
Idle time for Machine II is 2 hours

Self Assessment

State true or false
4. One machine – one job is not an assumption in solving sequencing problems

5. If there are two least processing times for machine A and machine B, priority is given for
the processing time which has lowest time of the adjacent machine.
6. There can be four types of sequencing problems depending upon number of jobs and
number of machines.

10.3.2 Type II: Processing n Jobs through Three Machines

In this type, we have three machines instead of two with n jobs. All the jobs are to be processed
through three machines, say M , M and M .
1 2 3
Considering n jobs (say 1,2,3….n) to be processed on three machines M , M and M in the order
1 2 3
M , M , M , the processing time is t , t ,….. t and t , t ….. t as shown in Table 10.22
1 2 3 11 12 ln 31 32 3n
Table 10.22: Sequence Problem

Machines Job
1 2 3 …. n
M1 t 11 t 12 T 13 …. t ln
M2 t 21 t 22 T 23 …. t 2n
M3 t 31 t 32 T 33 …. t 3n

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