Question

Solve the following problem of sequencing for minimizing the total elapsed time and idle time for both the machines.

Job	P	Q	R	S	T	U
M1	1	4	6	3	5	2
M2	3	6	8	8	1	5

The optimal sequence of the jobs as follows:

Total elasped time is obtained as follows:

Job sequence	Machine A		Machine B		Idle time for Machine B
	Time In	Time Out	Time In	Time Out
P	${\displaystyle \square }$	1	1	${\displaystyle \square }$	${\displaystyle \square }$
U	${\displaystyle \square }$	3	4	${\displaystyle \square }$	${\displaystyle \square }$
S	${\displaystyle \square }$	6	9	${\displaystyle \square }$	${\displaystyle \square }$
Q	${\displaystyle \square }$	10	17	${\displaystyle \square }$	${\displaystyle \square }$
R	${\displaystyle \square }$	16	23	${\displaystyle \square }$	${\displaystyle \square }$
T	${\displaystyle \square }$	21	31	${\displaystyle \square }$	${\displaystyle \square }$

Total elapsed time T = ${\displaystyle \square }$ minutes

Idle time for Machine A = T – ${\displaystyle \square }$ = ${\displaystyle \square }$ minutes

Idle time for Machine B = ${\displaystyle \square }$

Answer 1

Job	P	Q	R	S	T	U
M1	1	4	6	3	5	2
M2	3	6	8	8	1	5

The optimal sequence of the jobs as follows:

P

U

S

Q

R

T

Total elapsed time is obtained as follows:

Job sequence	Machine A		Machine B		Idle time for Machine B
	Time In	Time Out	Time In	Time Out
P	0	1	1	4	1
U	1	3	4	9	0
S	3	6	9	17	0
Q	6	10	17	23	0
R	10	16	23	31	0
T	16	21	31	32	0

Total elapsed time T = 32 minutes

Idle time for Machine A = T – 21 = 11 minutes

Idle time for Machine B = 1