Question

There are 5 jobs to be processed on 4 machines. The processing time for each job on each machines is shown in table. What will be the correct sequence of jobs to minimize total elapsed time to complete the jobs?

Jobs should be processed on machines in processing order of $M_1{M}_2{M}_3{M}_4$.

• A. S - T - Q - P - R
• B. T - S - R - P - Q
• C. Q - P - R - S - T
• D. R - P - Q - T - S

Answer 1

The correct option is D R - P - Q - T - S

$\text{Minimum processing time on}{M}_1\text{is = 7}$

$\text{Minimum processing time on}{M}_2\text{is = 5}$

$\text{Minimum processing time on}{M}_3\text{is = 6}$

$\text{Minimum processing time on}{M}_4\text{is = 6}$

$\text{Minimum}{M}_{1j}\ge \text{Maximum}{M}_{2j}\text{,}\text{Maximum}{M}_{3j}$

$\text{Minimum}{M}_{2j}\ge \text{Maximum}{M}_{2j}\text{,}\text{Maximum}{M}_{3j}$

We can reduce this problem to n jobs on 2 machines.

$\text{Processing times}{M}_{1j}+M_{2j}+M_{3j}\text{and}{M}_{4j}+M_{2j}+M_{3j}$
$\text{for each job and solving the problem.}$


$\text{R - P - Q - T - S}$

$\text{Hence the required optimum sequence is R - P - Q - T - S}$