Processing times (including setup times) and due dates for six jobs waiting to be processed at a work center are given in the following table. Determine the sequence of jobs, average flow time, average tardiness, and average number of jobs at the work center, for each of these rules:

a. FCFS

b. SPT

c. EDD

d. CR

Job Processing Time (days) Due Date (days from present time)

A 2 7

B 8 16

C 4 4

D 10 17

E 5 15

F 12 18

Assume jobs arrived in the order shown.

Question

Processing times (including setup times) and due dates for six jobs waiting to be processed at a work center are given in the following table. Determine the sequence of jobs, average flow time, average tardiness, and average number of jobs at the work center, for each of these rules:

a. FCFS

b. SPT

c. EDD

d. CR

Job	Processing Time (days)	Due Date (days from present time)
A	2	7
B	8	16
C	4	4
D	10	17
E	5	15
F	12	18

Assume jobs arrived in the order shown.

a. FCFS

b. SPT

c. EDD

d. CR

Job	Processing Time (days)	Due Date (days from present time)
A	2	7
B	8	16
C	4	4
D	10	17
E	5	15
F	12	18

Assume jobs arrived in the order shown.

Accepted Answer

a. The FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see table):

(1) Average flow time: 120/6 = 20 days.

(2) Average tardiness: 54/6 = 9 days.

(3) The makes pan is 41 days. Average number of jobs at the work center: 120/41 = 2.93.

	(1)	(2)	(3)	(2) -(3)
Job Sequence	Processing Time	Flow Time	Due Date	Days Tardy [0 if negative]
A	2	2	7	0
B	8	10	16	0
C	4	14	4	10
D	10	24	17	7
E	5	29	15	14
F	[latex]\underline{12} [/latex]	[latex]\underline{41} [/latex]	18	[latex]\underline{23} [/latex]
	41	120		54

The flow time column indicates cumulative processing time , so summing these times and dividing by the total number of jobs processed indicates the average time each job spends at the work center. Similarly, find the average number of jobs at the center by summing the flow times and dividing by the total processing time.

b. Using the SPT rule, the job sequence is A-C-E-B-D-F (see the following table). The resulting values for the three measures of effectiveness are

(1) Average flow time: 108/6 = 18 days.

(2) Average tardiness: 40/6 = 6.67 days.

(3) Average number of jobs at the work center: 108/41 = 2.63.

	(1)	(2)	(3)	(2)-(3)
Job Sequence	Processing Time	Flow Time	Due Date	Days Tardy [0 if negative]
A	2	2	7	0
C	4	6	4	2
E	5	11	15	0
B	8	19	16	3
D	10	29	17	2
F	[latex]\underline{12} [/latex]	[latex]\underline{41} [/latex]	18	[latex]\underline{23} [/latex]
	41	108		40

c. Using earliest due date as the selection criterion, the job sequence is C-A-E-B-D-F . The measures of effectiveness are as follows (see table):

(1) Average flow time: 110/6 = 18.33 days.

(2) Average tardiness: 38/6 = 6.33 days.

(3) Average number of jobs at the work center: 110/41 = 2.68.

	-(1)	(2)	(3)	(2) -(3)
Job Sequence	Processing Time	Flow Time	Due Date	Days Tardy [0 if negative]
C	4	4	7	0
A	2	6	4	0
E	5	11	15	0
B	8	19	16	3
D	10	29	17	12
F	[latex]\underline{12} [/latex]	[latex]\underline{41} [/latex]	18	[latex]\underline{23} [/latex]
	41	110		38

d. Using the critical ratio we find

Job Sequence	Processing Time	Due Date	Critical Ratio Calculation
A	2	7	( 7 - 0)/ 2 = 3.5
B	8	16	(16 - 0)/ 8 = 2.0
C	4	4	( 4 - 0)/ 4 = 1.0 (lowest)
D	10	17	(17 - 0)/10 = 1.7
E	5	15	(15 - 0)/ 5 = 3.0
F	12	18	(18 - 0)/12 = 1.5

At day 4[C completed], the critical ration are

Job Sequence	Processing Time	Due Date	Critical Ratio Calculation
A	2	7	( 7 - 16)/ 2 = - 4.5 (lowest
B	8	16	(16 - 16)/ 8 = 0.0
C	—	—	—
D	10	17	(17 - 16)/10 = 0.1
E	5	15	(15 - 16)/ 5 = 0.2
F	12	18	( 18 - 4)/12 = 1.17 (lowest)

At day 16[C and F completed], the critical ration are

Job Sequence	Processing Time	Due Date	Critical Ratio Calculation
A	2	7	( 7 - 16)/2 = - 4.5 (lowest
B	8	16	(16 - 16)/ 8 = 0.0
C	—	—	—
D	10	17	(17 - 16)/10 = 0.1
E	5	15	(15 - 16)/ 5 = -0.2
F	—	—	—

At day 18 [C, F, and A completed], the critical ratios are

Job Sequence	Processing Time	Due Date	Critical Ratio Calculation
A	—	—	—
B	8	16	(16 - 18)/ 8 = - 0.25
C	—	—	—
D	10	17	(17 - 18)/10 = - 0.10
E	5	15	(15 - 18)/ 5 = - 0.60 (lowest)
F	—	—	—

At day 23 [C, F, A, and E completed], the critical ratios are

Job Sequence	Processing Time	Due Date	Critical Ratio Calculation
A	—	—	—
B	8	16	(16 - 23)/ 8 = - 0.875 (lowest
C	—	—	—
D	10	17	(17 - 23)/10 = - 0.60
E	—	—	—
F	—	—	—

The job sequence is C-F-A-E-B-D, and the resulting values for the measures of effectiveness are as follows:

(1) Average flow time: 133/6 = 22.17 days.

(2) Average tardiness: 58/6 = 9.67 days.

(3) Average number of jobs at the work center: 133/41 = 3.24.

	(1)	(2)	(3)	(2) -(3)
Sequence	Processing Time	Flow Time	Due Date	Days Tardy
C	4	4	4	0
F	12	16	18	0
A	2	18	7	11
E	5	23	15	8
B	8	31	16	15
D	[latex]\underline{10} [/latex]	[latex]\underline{41} [/latex]	17	[latex]\underline{24} [/latex]
	41	133		58

The results of these four rules are summarized in Table 16.4

TABLE 16.4
Comparison of the four rules for Example 2

Rule	Average Flow Time (days)	Average Tardiness (days)	Average Number of Jobs at the Work Center
FCFS	20·00	9·00	2.93
SPT	18·00	6.67	2.63
EDD	18.33	6.33	2.68
CR	22.17	9.67	3.24

Question 16.2: Processing times (including setup times) and due dates for s...

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