Question

A Northern British Columbia lumberyard has four jobs on order, as shown in the following table. Today is day 205 on the yard’s schedule.

Job	Due Date	Remaining Time (Days)
A	212	6
B	209	3
C	214	10
D	210	8

In what sequence would the jobs be ranked according to the following decision rules:

a) FCFS

b) SPT

c) LPT

d) EDD

e) Critical ratio

Which is best and why? Which has the minimum lateness?

Answer 1

a)

Using FCFS decision rule, the order of jobs is as follows –

Sequence	Job
1	A
2	B
3	C
4	D

Job Sequence	Processing Time (in Days)	Due Date (Days remaining)	Flow Time (in Days)	Days Late = Flow Time - Due Date (in Days) (0 if negative)
A	6	212 – 205 = 7	0 + 6 = 6	0
B	3	209 – 205 = 4	6 + 3 = 9	5
C	10	214 – 205 = 9	9 + 10 = 19	10
D	8	210 – 205 = 5	19 + 8 = 27	22
Total	27		61	37

Average lateness using FCFS rule = Days Late / Total Number of Jobs = 37 / 4 = 9.25 days.

b)

Using SPT decision rule, the order of jobs is as follows –

Sequence	Job
1	B
2	A
3	D
4	C

       

Job Sequence	Processing Time (in Days)	Due Date (Days remaining)	Flow Time (in Days)	Days Late = Flow Time - Due Date (in Days) (0 if negative)
B	3	4	0 + 3 = 3	0
A	6	7	3 + 6 = 9	2
D	8	5	9 + 8 = 17	12
C	10	9	17 + 10 = 27	18
Total	27		56	32

Average lateness using SPT rule = Days Late / Total Number of Jobs = 32 / 4 = 8 days.

c)

Using LPT decision rule, the order of jobs is as follows –

Sequence	Job
1	C
2	D
3	A
4	B

Job Sequence	Processing Time (in Days)	Due Date (Days remaining)	Flow Time (in Days)	Days Late = Flow Time - Due Date (in Days) (0 if negative)
C	10	9	0 + 10 = 10	1
D	8	5	10 + 8 = 18	13
A	6	7	18 + 6 = 24	17
B	3	4	24 + 3 = 27	23
Total	27		79	54

Average lateness using LPT rule = Days Late / Total Number of Jobs = 54 / 4 = 13.50 days.

d)

Using EDD decision rule, the order of jobs is as follows –

Sequence	Job
1	B
2	D
3	A
4	C

    

Job Sequence	Processing Time (in Days)	Due Date (Days remaining)	Flow Time (in Days)	Days Late = Flow Time - Due Date (in Days) (0 if negative)
B	3	4	0 + 3 = 3	0
D	8	5	3 + 8 = 11	6
A	6	7	11 + 6 = 17	10
C	10	9	17 + 10 = 27	18
Total	27		58	34

Average lateness using EDD rule = Days Late / Total Number of Jobs = 34 / 4 = 8.5 days.

(e) Critical ratio.

Job	Remaining Job Time (in Days)	Due Date (Days remaining)	Critical ratio = (Remaining time until due date) / (Remaining job time)	Priority
A	6	7	7 / 6 = 1.17	3
B	3	4	4 / 3 = 1.33	4
C	10	9	9 / 10 = 0.9	2
D	8	5	5 / 8 = 0.625	1

So the job sequence = D – C – B – A.

Job Sequence	Processing Time (in Days)	Due Date (Days remaining)	Flow Time (in Days)	Days Late = Flow Time - Due Date (in Days) (0 if negative)
D	8	21	0 + 8 = 8	3
C	10	16	8 + 10 = 18	9
A	6	15	18 + 6 = 24	17
B	3	17	24 + 3 = 27	23
Total	27		77	52

Average lateness using Critical Ratio rule = Days Late / Total Number of Jobs = 52 / 4 = 13 days.

Here SPT decision rule is the best as it has minimum lateness, i.e., 8 days.