Question

: A forensic audit firm has five audit jobs remaining at a point in time. The audits are labeled as jobs 1, 2, 3, 4 and 5. The respective audit times (in days) and the remaining days before the due date are given in the table below.

Audit job	Time required	Due (at the end of) day
1	11	61
2	29	45
3	31	31
4	1	33
5	2	32

1. Determine the job sequence using each of these priority rules: (1) CR, (2) SPT, (3) EDD
2. Determine the performance of each rule using (1) average flow time, (2) average days late, and 3) average work in progress
3. Determine the sequence which will minimize the total number of late jobs

Answer 1

Answer a=

1=Critical ratio=Time remaining until due date/ Remaining processing time

Audit job	Time required	Due (at the end of) day	Critical Ratio Calculation
1	11	61	(61-0)/11=5.55
2	29	45	(45-0)/29=1.55
3	31	31	(31-0)/31=1 (lowest)
4	1	33	(33-0)/1=33
5	2	32	(32-0)/2=16

So we will place Job 3 first which will be completed a 31 days.

Audit job	Time required	Due (at the end of) day	Critical Ratio Calculation
1	11	61	(61-31)/11=2.73
2	29	45	(45-31)/29=0.48(lowest)
3
4	1	33	(33-31)/1=2
5	2	32	(32-31)/2=0.5

So we will place Job 2 second which will be completed a 31+29=60 days

Audit job	Time required	Due (at the end of) day	Critical Ratio Calculation
1	11	61	(61-60)/11=0.09
2
3
4	1	33	(33-60)/1=-27
5	2	32	(32-60)/2=-14

So we will place Job 4 third which will be completed a 31+29+1=61 days

Audit job	Time required	Due (at the end of) day	Critical Ratio Calculation
1	11	61	(61-61)/11=0.0
2
3
4
5	2	32	(32-61)/2=-14.5

So we will place Job 5forth and the final sequence will be

3-2-4-5-1

2=In case of the shortest processing time, we will arrange the jobs in the ascending order to processing time. So the sequence will be

4-5-1-2-3

3= In case of the earliest due date, the job with a least due date will be placed first followed by second and so on. So the sequence is=3- 5-4-2-1

Answer b=

CR:			Job time		Flow time		Due date		Days
	Job		(days)		(days)		(days)		tardy
	3		31		31		31		0
	2		29		60		45		15
	4		1		61		33		28
	5		2		63		32		31
	1		11		74		61		13
			74		289				87

Average job flow time = Total job flow time / Number of jobs = 289 / 5= 57.8 days.

Average job tardiness = Total job tardiness / Number of jobs = 87/ 5 = 17.4 days.

Average number of jobs = Total flow time / Makespan = 289 / 74 = 3.9jobs

SPT			Job time		Flow time		Due date		Days
	Job		(days)		(days)		(days)		tardy
	4		1		1		33		0
	5		2		3		32		0
	1		11		14		61		0
	2		29		43		45		0
	3		31		74		31		43
			74		135				43

Average job flow time = Total job flow time / Number of jobs = 135 / 5= 27 days.

Average job tardiness = Total job tardiness / Number of jobs = 43/ 5 = 8.6 days.

Average number of jobs = Total flow time / Makespan = 135/74 = 1.8 jobs

EDD			Job time		Flow time		Due date		Days
	Job		(days)		(days)		(days)		tardy
	3		31		31		31		0
	5		2		33		32		1
	4		1		34		33		1
	2		29		63		45		18
	1		11		74		41		6
			74		235				26

Average job flow time = Total job flow time / Number of jobs = 235 / 5= 47 days.

Average job tardiness = Total job tardiness / Number of jobs = 26/ 5 = 5.2 days.

Average number of jobs = Total flow time / Makespan = 235/74 = 3.1 jobs

Answer C= EDD will minimize the total number of late jobs