Chapter 14, Problem 11PA

A

Summary Introduction

Interpretation: Under the given scenario, the sequence that promises a minimized average lateness is to be derived.

Concept Introduction: The process of planning the ordering of the activities involves based on the elements such as, priority, set up time and such other is referred to as sequencing.

Explanation of Solution

Under the given order rule:

Job

1

2

3

4

5

6

7

8

Job	Processing Time	Flow Time	Due Date	Lateness	Tardiness
1	7	7	21	-14	0
2	3	10	7	3	3
3	5	15	8	7	7
4	2	17	5	12	12
5	6	23	17	6	6
6	9	32	16	16	16
7	14	46	38	8	8
8	4	50	12	38	38
	Average	25.00		9.50	11.25

Average Flow Time will be;

  $=\frac{7+10+15+17+23+32+46+50}{8}=\frac{200}{8}=25.00$

The average lateness will be;

  $=\frac{-14+3+7+12+6+16+8+38}{8}=\frac{76}{8}=9.50$

The average tardiness will be;

  $=\frac{0+3+7+12+6+16+8+38}{8}=\frac{90}{8}=11.25$

Under the SPT rule:

Job

4

2

8

3

5

1

6

7

Job	Processing Time	Flow Time	Due Date	Lateness	Tardiness
4	2	2	5	-3	0
2	3	5	7	-2	0
8	4	9	12	-3	0
3	5	14	8	6	6
5	6	20	17	3	3
1	7	27	21	6	6
6	9	36	16	20	20
7	14	50	38	12	12
	Average	20.38		4.88	5.88

Under the EDD rule:

Job

4

2

3

8

6

5

1

7

Job	Processing Time	Flow Time	Due Date	Lateness	Tardiness
4	2	2	5	-3	0
2	3	5	7	-2	0
3	5	10	8	2	2
8	4	14	12	2	2
6	9	23	16	7	7
5	6	29	17	12	12
1	7	36	21	15	15
7	14	50	38	12	12
	Average	21.13		5.63	6.25

The comparisons will be as follows:

	AFT	AL	AT
FCFS	25.00	9.50	11.25
SPT	20.38	4.88	5.88
EDD	21.13	5.63	6.25

Upon observing the above derived observations, it can be concluded that the sequence that minimizes the AL is EDD:

4

2

3

8

6

5

1

7

B

Summary Introduction

Interpretation: Under the given scenario, the sequence that promises a minimized average tardiness is to be calculated.

Concept Introduction: The process of planning the ordering of the activities involves based on the elements such as, priority, set up time and such other is referred to as sequencing.

Explanation of Solution

Upon observing the above derived observations, it can be concluded that the sequence that minimizes the AT is SPT:

4

2

8

3

5

1

6

7

C

Summary Introduction

Interpretation: In a generalized manner, the logic is to be placed into a procedure that aids in accomplishing these objects for most of the time.

Concept Introduction: The process of planning the ordering of the activities involves based on the elements such as, priority, set up time and such other is referred to as sequencing.

Explanation of Solution

The logic here is so simple. Supposing that the flow time need to be minimized then the SPT need to be implemented. The advantage of the SPT here is that it minimizes the average job flow time and WIP inventory and also thereby maximizes the resource allocation.

On the other hand, the EDD rule minimizes the average tardiness and lateness and in that it does the best job.

Once the data of processing time, the due date of the single machine are accomplished and the tardiness can easily be minimized, the firm does the best.