Question

Problem 1: 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 10 28 30 Due (at the end of day 60 45 30 32 31 le a) Determine the job sequence using each of these priority rules: (1) CR, (2) SPT and (3) EDD b) Determine the performance of each rule using (1) average flow time, (2) average days late, and 3) average work in progress C) Apply the appropriate method to determine the sequence which will minimize the total number of late jobs.

Answer 1

a)

(1)

Critical ratio = Due date/ Time required for processing

As per sequencing rule, jobs with lowest critical ratio are sequenced first and so on.

Job 1 -> CR = 60/ 10 =6

Job 2 -> CR = 45/28 = 1.61

Job 3 -> CR = 30/30 = 1

Job 4 -> CR = 32/1 = 32

Job 5 -> CR = 31/ 2 =15.5

So we will sequence Job 3 first then 2, 1, 5 and 4.

Sequence	Time required	Due day	Flow time	Lateness (flow time- due date), -ve is 0
3	30	30	30	0
2	28	45	30+28=58	58-45=13
1	10	60	58+10=68	68-60=8
5	2	31	68+2=70	70-31=39
4	1	32	70+1=71	71-32=39

Average flow time= Total flow time/ number of jobs= (30+58+68+70+71)/5 = 59.4 days

Average days late = Total lateness/ number of jobs = (0+13+8+39+39)/ 5 =19.8 days

Average work in progress = Total flow time/ total time required = (30+58+68+70+71)/ (1+2+10+28+30) = 4.18

(2)

SPT is shortest processing time. As per this rule, sequencing is done such that job with shortest processing time is scheduled first and so on.

Sequence	Time required	Due day	Flow time	Lateness (flow time- due date), -ve is 0
4	1	32	1	0
5	2	31	1+2=3	0
1	10	60	3+10=13	0
2	28	45	13+28=41	0
3	30	30	41+30=71	71-30=41

Average flow time= Total flow time/ number of jobs= (1+3+13+41+71)/5 = 25.8 days

Average days late = Total lateness/ number of jobs = 41/ 5 =8.2 days

Average work in progress = Total flow time/ total time required = (1+3+13+41+71)/ (1+2+10+28+30) = 1.82

(3)

EDD is earliest due date. Sequencing is done with jobs due first and so on.

Sequence	Time required	Due day	Flow time	Lateness (flow time- due date), -ve is 0
3	30	30	30	0
5	2	31	30+2=32	32-31=1
4	1	32	32+1=33	33-32=1
2	28	45	33+28=61	61-45=16
1	10	60	61+10=71	71-60=11

Average flow time= Total flow time/ number of jobs= (30+32+33+61+71)/5 = 45.4 days

Average days late = Total lateness/ number of jobs = (0+1+1+16+11)/ 5 = 5.8 days

Average work in progress = Total flow time/ total time required =(30+32+33+61+71)/ (1+2+10+28+30) = 3.20

(b)

All performance measures against each rule are calculated in section (a)

(c)

Now the objective is to minimize the total number of late jobs in the sequence. Looking at the above performance data for each rule, we can access that SPT rule has lowest number of late job (1). Hence, SPT is an appropriate method to minimize the total number of late jobs.

Sequence as per SPT is 4-5-1-2-3.

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