Page 216 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 10: Sequencing Problems and Replacement Theory

Notes
Calculation of weighted average cost of machine B
N Rn V RnV RnV C+RV V TC/V
n-1
n-1
n-1
n-1
n-1
n-1
1 1,200 1.0000 1,200 1,200 3,700 1.0000 3,700
2 1,200 0.9091 1,090.9 2,290 4,790.9 1.9091 2,509.5
3 1,200 0.8264 991.68 3,282.6 5,782.6 2.7355 2,113.91
4 1,200 0.7513 901.56 4,184.16 6,684.16 3.4868 1,799.55
5 1,200 0.6830 819.6 5,033.76 7,503.76 4.1698 1,916.99
6 1,200 0.6209 745.08 5,748.8 8,248.8 4.7907 1,721.84
7 1,400 0.5645 790.3 6,539.14 9,039.14 5.3552 1,687.92
8 1,600 0.5132 821.12 7,360.26 9,860.3 5.8682 1,680.29
9 1,800 0.4665 839.7 8,199.96 10,699.96 6.3349 1,689.05
10 2,000 0.4241 848.2 9,048.16 11,548.16 6.7590 1,708.56

Inference

It becomes evident from the table that the weighted average cost of machine B is lower than the
weighted average cost of machine A. Hence, it can be arrived at a decision that machine B is
better than machine A.

!
Caution If the weighted average cost of X and X are equal then both the machines are
1 2
equally good.
10.6 Summary

 Sequencing problems can be considered with situations where there is a selection of an
appropriate order for a series of different jobs to be done on a finite number of service
facilities.
 A sequencing problem involves jobs in a manufacturing unit, aircraft waiting for landing
and clearance, maintenance scheduling in a manufacturing company, customers in an
electricity department, and so on.
 Consider the sequencing problems in respect of the jobs to be performed in an organization
and study the different method of their feasible solution.
 This type of sequencing problems may be divided in two strata. In the first one, there are
n jobs to be completed; each job requires processing on some or all of the m different
machines.

 Then find out the effectiveness of each of the sequences that are technically correct &
feasible and select a sequence which optimizes the total effectiveness of the system.
 To explain, the timings of processing of the n jobs on each of the m machines, in a particular
defined order, may be given and the time for completing the jobs may be the measure of
effectiveness.
 Arrange the sequence(s) for which the total time consumed by the machines in processing
all the jobs.

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