(Solved Homework): Consider a single-machine, five-job, job sequencing problem such that all jobs have a ready…

Consider a single-machine, five-job, job sequencing problem such that all jobs have a ready time of zero and preempting jobs is not permitted. The remaining characteristics of the five jobs, listed in the order they were received, can be found in the table below. Determine and evaluate the job sequence that minimizes total weighted completion time.

Expert Answer

Answer


	Job Number	Processing Time	Due Date	Weight
	J	P	D	W
	1	3	4	6
	2	6	8	3
	3	8	12	1
	4	4	15	9
	5	2	11	2

Here we are going to use 4 rules which are given below to find the completion times and total weighted completion times to find the shortest total weighted completion times.

1	FCFS	First Come First Service
2	DDATE	Nearest Due Date
3	Slack	Minimum Slack
4	SPT	Smallest Process Time

FCFS
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Weighted Completion Time
	J	P	D	W	S	C=S+P	WC=W*C
	1	3	4	6	0	3	18
	2	6	8	3	3	9	27
	3	8	12	1	9	17	17
	4	4	15	9	17	21	189
	5	2	11	2	21	23	46
	Total Weighted Completion Time						297
DDATE
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Weighted Completion Time
	J	P	D	W	S	C=S+P	WC=W*C
	1	3	4	6	0	3	18
	2	6	8	3	3	9	27
	5	2	11	2	9	11	22
	3	8	12	1	11	19	19
	4	4	15	9	19	23	207
	Total Weighted Completion Time						293
Slack
Minimum Slack=Due Date – Today’s Date-Processing Time

	Job Number	Processing Time	Due Date	Weight	Slack
	J	P	D	W	S=D-0-P
	1	3	4	6	1
	2	6	8	3	2
	3	8	12	1	4
	4	4	15	9	11
	5	2	11	2	9

	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Weighted Completion Time
	J	P	D	W	S	C=S+P	WC=W*C
	1	3	4	6	0	3	18
	2	6	8	3	3	9	27
	3	8	12	1	9	17	17
	5	2	11	2	17	19	38
	4	4	15	9	19	23	207
	Total Weighted Completion Time						307

SPT
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Weighted Completion Time
	J	P	D	W	S	C=S+P	WC=W*C
	5	2	11	2	0	2	4
	1	3	4	6	2	5	30
	4	4	15	9	5	9	81
	2	6	8	3	9	15	45
	3	8	12	1	15	23	23
	Total Weighted Completion Time						183

As we can make out here total weighted completion time is achieved through SPT and is 183

Now this question has a condition that preempting is not allowed that means we cannot make any thing before due date .

FCFS
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Adjusted Completion Time as per due date	Weighted Completion Time
	J	P	D	W	S	C=S+P	AC	WC=W*AC
	1	3	4	6	0	3	4	24
	2	6	8	3	4	10	10	30
	3	8	12	1	10	18	18	18
	4	4	15	9	18	22	22	198
	5	2	11	2	22	24	24	48
	Total Weighted Completion Time							318
DDATE
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Adjusted Completion Time as per due date	Weighted Completion Time
	J	P	D	W	S	C=S+P	AC	WC=W*AC
	1	3	4	6	0	3	4	24
	2	6	8	3	4	10	10	30
	5	2	11	2	10	12	12	24
	3	8	12	1	11	12	20	20
	4	4	15	9	19	20	24	216
	Total Weighted Completion Time							314
Slack
Minimum Slack=Due Date – Today’s Date-Processing Time

	Job Number	Processing Time	Due Date	Weight	Slack
	J	P	D	W	S=D-0-P
	1	3	4	6	1
	2	6	8	3	2
	3	8	12	1	4
	4	4	15	9	11
	5	2	11	2	9

	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Adjusted Completion Time as per due date	Weighted Completion Time
	J	P	D	W	S	C=S+P	AC	WC=W*C
	1	3	4	6	0	3	4	24
	2	6	8	3	4	10	10	30
	3	8	12	1	10	18	18	18
	5	2	11	2	17	18	20	40
	4	4	15	9	19	20	24	216
	Total Weighted Completion Time							328

SPT
	Job Number	Processing Time	Due Date	Weight	Start Time	Completion Time	Adjusted Completion Time as per due date	Weighted Completion Time
	J	P	D	W	S	C=S+P	AC	WC=W*C
	5	2	11	2	0	2	11	22
	1	3	4	6	2	11	14	84
	4	4	15	9	5	14	18	162
	2	6	8	3	9	18	24	72
	3	8	12	1	15	24	32	32
	Total Weighted Completion Time							372

If we go by this shortest total weighted completion will be 314 if we go by due date and job sequence will be 12534

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