PRIORITY RULES FOR DISPATCHING. Five architectural rendering jobs are waiting to be assigned at Avanti Sethi Architects. Their work (processing) times and due dates are given in the following table. The firm wants to determine the sequence of processing according to (1) FCFS, (2) SPT, (3) EDD, and

Question

PRIORITY RULES FOR DISPATCHING. Five architectural rendering jobs are waiting to be assigned at Avanti Sethi Architects. Their work (processing) times and due dates are given in the following table. The firm wants to determine the sequence of processing according to (1) FCFS, (2) SPT, (3) EDD, and (4) LPT rules. Jobs were assigned a letter in the order they arrived. Today is day 1, and work begins today.

JOB	JOBWORK (PROCESSING) TIME (DAYS)	JOB DUE DATE (DAYS)
A	6	8
B	2	6
C	8	18
D	3	15
E	9	23

APPROACH [latex]\blacktriangleright[/latex] Each of the four priority rules is examined in turn. Four measures of effectiveness can be computed for each rule and then compared to see which rule is best for the company.

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex]
1. The FCFS sequence shown in the next table is simply A–B–C–D–E.

JOB SEQUENCE	JOBWORK (PROCESSING) TIME	FLOW TIME	JOB DUE DATE	JOB LATENESS
A	6	6	8	0
B	2	8	6	2
C	8	16	18	0
D	3	19	15	4
E	9	28	23	5
	28	77		11

The FCFS rule results in the following measures of effectiveness:

a. Average completion time = [latex]\frac{Sum of total flow time}{Number of jobs} = \frac{77 days}{5} = 15.4[/latex] days

b. Utilization metric = [latex]\frac{Total job work (processing) time}{Sum of total flow time} = \frac{28}{77}[/latex] = 36.4%

c. Average number of jobs in the system = [latex]\frac{Sum of total flow time}{Total job work (processing) time} = \frac{77 days}{28 days} = 2.75[/latex] jobs

d. Average job lateness = [latex]\frac{Total late days}{Number of jobs} = \frac{11}{5} = 2.2[/latex] days

2. The SPT rule shown in the next table results in the sequence B–D–A–C–E. Orders are sequenced according to processing time, with the highest priority given to the shortest job.

JOB SEQUENCE	JOBWORK (PROCESSING) TIME	FLOW TIME	JOB DUE DATE	JOB LATENESS
B	2	2	6	0
D	3	5	15	0
A	6	11	8	3
C	8	19	18	1
E	9	28	23	5
	28	65		9

Measurements of effectiveness for SPT are:

a. Average completion time = [latex]\frac{65}{5} = 13[/latex] days

b. Utilization metric = [latex]\frac{28}{65}[/latex] = 43.1%

c. Average number of jobs in the system = [latex]\frac{65}{28} = 2.32[/latex] jobs

d. Average job lateness = [latex]\frac{9}{5} = 1.8[/latex] days

3. The EDD rule shown in the next table gives the sequence B–A–D–C–E. Note that jobs are ordered by earliest due date first.

JOB SEQUENCE	JOBWORK (PROCESSING) TIME	FLOW TIME	JOB DUE DATE	JOB LATENESS
B	2	2	6	0
A	6	8	8	0
D	3	11	15	0
C	8	19	18	1
E	9	28	23	5
	28	68		6

Measurements of effectiveness for EDD are:

a. Average completion time = [latex]\frac{68}{5} = 13.6[/latex] days

b. Utilization metric = [latex]\frac{28}{68}[/latex] = 41.2%

c. Average number of jobs in the system = [latex]\frac{68}{28} = 2.43[/latex] jobs

d. Average job lateness = [latex]\frac{6}{5} = 1.2[/latex] days

4. The LPT rule shown in the next table results in the order E–C–A–D–B.

JOB SEQUENCE	JOBWORK (PROCESSING) TIME	FLOW TIME	JOB DUE DATE	JOB LATENESS
E	9	9	23	0
C	8	17	18	0
A	6	23	8	15
D	3	26	15	11
B	2	28	6	22
	28	103		48

Measures of effectiveness for LPT are:

a. Average completion time = [latex]\frac{103}{5} = 20.6[/latex] days

b. Utilization metric = [latex]\frac{28}{103}[/latex] = 27.2%

c. Average number of jobs in the system = [latex]\frac{103}{2} = 3.68[/latex] jobs

d. Average job lateness = [latex]\frac{48}{5} = 9.6[/latex] days

The results of these four rules are summarized in the following table:

RULE	AVERAGE COMPLETION TIME (DAYS)	UTILIZATION METRIC (%)	AVERAGE NUMBER OF JOBS IN SYSTEM	AVERAGE LATENESS (DAYS)
FCFS	15.4	36.4	2.75	2.2
SPT	13.0	43.1	2.32	1.8
EDD	13.6	41.2	2.43	1.2
LPT	20.6	27.2	3.68	9.6

INSIGHT [latex]\blacktriangleright[/latex] LPT is the least effective measurement for sequencing for the Avanti Sethi firm. SPT is superior in 3 measures, and EDD is superior in the fourth (average lateness).
LEARNING EXERCISE [latex]\blacktriangleright[/latex] If job A takes 7 days (instead of 6), how do the 4 measures of effectiveness change under the FCFS rule? [Answer: 16.4 days, 35.4%, 2.83 jobs, 2.8 days late.]
RELATED PROBLEMS [latex]\blacktriangleright[/latex] 15.15, 15.17a–d, 15.18, 15.19 (15.15 alternate, 15.24 are available in MyOMLab)
EXCEL OM Data File Ch15Ex5.xls can be found in MyOMLab.
ACTIVE MODEL 15.1 This example is further illustrated in Active Model 15.1 in MyOMLab.

Question 15.EX.5: PRIORITY RULES FOR DISPATCHING. Five architectural rendering...

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