Question

Evan Schwartz has six jobs waiting to be processed through his machine. Processing time (in days) and due date information for each job are as follows:

Job	Processing Time	Due Date
A B C D E F	2 1 5 3 4 7	3 2 12 4 8 11

Sequence the jobs by FCFS, SPT, SLACK, and DDATE. Calculate the mean flow time and mean tardiness of the six jobs under each sequencing rule. Which rule would you recommend?

Answer 1

ANSWER

FCFS: Process the jobs in order of their arrival, A, B, C, D, E.

Job	Processing time	Flow time	Due date	Tardiness
a	2	2	3	0
b	1	3	2	1
c	4	7	12	0
d	3	10	4	6
e	4	14	8	6
f	5	19	11	8
		55		21

Mean flow time = total flow time/ no. of jobs

                                   = 55/6 = 9.17

Mean Tardiness = total tardiness/ no. of jobs

                                = 21/6 = 3.50

SPT: Sequence the jobs by smallest processing time.

Job	Processing time	Flow time	Due date	Tardiness
b	1	1	2	0
a	2	3	3	0
d	3	6	4	2
c	4	10	12	0
e	4	14	8	6
f	5	19	11	8
		53		16

Mean flow time = 53/6 = 8.83

Mean Tardiness = 16/6 = 2.67

SLACK: Sequence the jobs by minimum slack. The slack for each job is calculated as: (due date - today's date) - remaining processing time.

Job	Processing time			Due date		Slack
a	2			3		0
b	1			2		0
c	4			12		7
d	3			4		0
e	4			8		3
f	5			11		5
Job		Processing time	Flow time		Due date		Tardiness
a		2	2		3		0
b		1	3		2		1
d		3	6		4		2
e		4	10		8		2
f		5	15		11		4
c		4	19		12		7
			55				16

Mean flow time = 55/6 = 9.17

Mean Tardiness = 16/6 = 2.67

DDATE: Sequence the jobs by earliest due date

Job	Processing time	Flow time	Due date	Tardiness
b	1	1	2	0
a	2	3	3	0
d	3	6	4	2
e	4	10	8	2
f	5	15	11	4
c	4	19	12	7
		54		15

Mean flow time = 54/6 = 9

Mean Tardiness = 15/6 = 2.50

Process DDate method is recommended as it has the lowest Mean tardiness.

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