Page 209 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes The optimal solution can be obtained if either one of the following conditions is satisfied:
Condition 1: Minimum time on row 1 should be greater than or equal to maximum time on row 2
i.e., Min tlj > Max t2j, j = 1,2,….n
(or)
Condition 2: Minimum time on row 3 should be greater than or equal to maximum time on row 2
i.e., Min t3j > Max t2j, j = 1,2,….n

Algorithm

Step 1: Check whether the given processing time for all the three machines satisfy either one or
both the conditions. If the condition is satisfied, go to Step 2, else the model fails.

Step 2: Convert the three machine types into two machines by introducing two imaginary
machines M and M .
x y
Where, M = M + M and
x 1 2
M =M + M
y 2 3
Step 3: For the imaginary machines M and M , determine the optimal sequence using the
x y
algorithm for Type 1 (i.e., n job and two machines).
Step 4: Find the total elapsed time and the idle time for all the three machines.

Example: 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 10.23. 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.

Table 10.23: Sequence Problem
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

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 M , M and M
l 2 3
respectively.
Check the condition for,

Minimum time for M > Maximum time M
1 2
i.e., 2 > 8 does not satisfy the condition.
(or)
Minimum time for M > Maximum time on M
3 2
i.e., 8 > 8 satisfies the condition.

204 LOVELY PROFESSIONAL UNIVERSITY