Question

Problem 16-17 Given the following information on job times and due dates Job Time Due Date (Hours) (Hours) Job 3.5 2.0 4.5 5.0 2.5 6.0 18 20 Determine the optimal processing sequence using (1) First come, first served, (2) Shortest processing time, (3) Earliest due date, and (4) Critical ratio. a-1. Sequence for First come, first served (Click to select) Sequence for Shortest processing time Click to select) Sequence for Earliest due date (Click to select) Click to select) Sequence for Critical ratio a-2. For each method, find the average job flow time and the average job tardiness. (Round your answers to 2 decimal places.) First Come, First Served Shortest Processing Earliest Due Date Critical Ratio Average fow time Average job tardiness

Answer 1

a-1
1
The processing sequence is the sequence for which jobs should be processed first
If the sequence is first come, first served. In this case we would go as per the sequence given
Therefore, sequence for first come, first served would be a-b-c-d-e-f
2
If the processing sequence is job which takes shortest processing time. In this case the jobs which take lower time are processes first
Therefore, sequence would be b-e-a-c-d-f
3
If the processing sequence is job which has earliest due date, in this case the jobs which has lowest due date is processed first
Therefore, sequence would be e-b-a-c-f-d
4
Calculation of CR ratio so as to determine the processing sequence
Calculating iitial critical ratios at hour 0
Job	Processing time (hours)	Due date (hours)	Critical ratio calculation	CR
a	3.5	7	(7-0)/3.5	2.00
b	2	6	(6-0)/2	3.00
c	4.5	18	(18-0)/4.5	4.00
d	5	22	(22-0)/5	4.40
e	2.5	4	(4-0)/2.5	1.60	lowest
f	6	20	(20-0)/6	3.33
Job e is scheduled first
At hour 0 + 2.5 = 2.50 Job e completed, the critical ratio calculation is
Job	Processing time (hours)	Due date (hours)	Critical ratio calculation	CR
a	3.5	7	(7-2.5)/3.5	1.29	lowest
b	2	6	(6-2.5)/2	1.75
c	4.5	18	(18-2.5)/4.5	3.44
d	5	22	(22-2.5)/5	3.90
f	6	20	(20-2.5)/6	2.92
Job a is scheduled second
At hour 2.50 + 3.50 = 6 Job a completed, the critical ratio calculation is
Job	Processing time (hours)	Due date (hours)	Critical ratio calculation	CR
b	2	6	(6-6)/2	0.00	lowest
c	4.5	18	(18-6)/4.5	2.67
d	5	22	(22-6)/5	3.20
f	6	20	(20-6)/6	2.33
Job b is scheduled third
At hour 6+2 = 8 job b is completed, the critical ratio calculation is
Job	Processing time (hours)	Due date (hours)	Critical ratio calculation	CR
c	4.5	18	(18-8)/4.5	2.22
d	5	22	(22-8)/5	2.80
f	6	20	(20-8)/6	2.00	lowest
Job f is scheduled fourth
At hour 8+6 = 14, job f is completed, the critical ratio calculation is
Job	Processing time (hours)	Due date (hours)	Critical ratio calculation	CR
c	4.5	18	(18-14)/4.5	0.88888889	lowest
d	5	22	(22-14)/5	1.6
Job c is scheduled fifth
Therefore, job d is scheduled sixth
The processing sequence would be e-a-b-f-c-d
a-2
First come first served
We will have to calculate flow time and tardy hours
Job flow time is the cumulative job time of processing sequence
Tardy time = Flow time - due date
Job	Job time (hours)	Due date (hours)	Flow time	Tardy days
a	3.5	7.0	3.5	0.0
b	2.0	6.0	5.5	0.0
c	4.5	18.0	10.0	0.0
d	5.0	22.0	15.0	0.0
e	2.5	4.0	17.5	13.5
f	6.0	20.0	23.5	3.5
	23.5		75.0	17
Average job flow time = Total job flow time/Number of jobs			23.50/6	12.50
Average job tardiness = Total job tardiness/Number of jobs			17/6	2.83
Shortest processing time
sequence is b-e-a-c-d-f
Job	Job time (hours)	Due date (hours)	Flow time	Tardy days
b	2	6	2	0
e	2.5	4	4.5	0.5
a	3.5	7	8	1
c	4.5	18	12.5	0
d	5	22	17.5	0
f	6	20	23.5	3.5
	23.5		68	5
Average job flow time = 77/6		11.33
Average job tradiness = 5/6		0.83
Earliest due date
Therefore, sequence would be e-b-a-c-f-d
Job	Job time (hours)	Due date (hours)	Flow time	Tardy days
e	2.5	4	2.5	0
b	2	6	4.5	0
a	3.5	7	8	1
c	4.5	18	12.5	0
f	6	20	18.5	0
d	5	22	23.5	1.5
	23.5		69.5	2.5
Average job flow time = 69.5/6		11.58
Average job tradiness = 5/6		0.42
Critical ratio
The processing sequence would be e-a-b-f-c-d
Job	Job time (hours)	Due date (hours)	Flow time	Tardy days
e	2.5	4	2.5	0
a	3.5	7	6	0
b	2	6	8	2
f	6	20	14	0
c	4.5	18	18.5	0.5
d	5	22	23.5	1.5
	23.5		72.5	4
Average job flow time = 72.5/6		12.08
Average job tradiness = 3.5/6		0.67
	First come first served	Shortest processing time	Earliest due date	Critical ratio
Average flow time	12.50	11.33	11.58	12.08
Average job tradiness	2.83	0.83	0.42	0.67