A manufacturing shop with a single workstation (machine) produces 6 products (jo

Question

A manufacturing shop with a single workstation (machine) produces 6 products (jobs). The following table shows the estimated processing times, weights and due dates of these jobs.

Job 1 2 3 4 5 6

Processing time (days) 2 5 3 6 4 4

Due date 6 36 8 23 13 15

(a) Assume that each job has the same weight and jobs are divided into three groups in which the following processing orders among the jobs should be satisfied.

Group 1: Job 1, Job 6 Group 2: Job 2, Job 5 Group 3: Job 3, Job 4

Further assume that all jobs in a group should be should be processed together before switching over to another group of jobs. The management of the manufacturing shop wants to minimize the total weighted work-inprocess inventory of jobs. Which scheduling performance criterion and scheduling rule (approach) should be used in order to determine the optimal sequence of jobs that minimizes the total cost? Apply this scheduling rule, and calculate the cost of the resulting schedule?

Explanation / Answer

As the management of manufacturing shop wants to minimize the total weighted work in process inventory of jobs.then WSPT rule (Weighted shortest processing time) is to be used.

WSPT rule

In this rule, job iwth shortes "processing time per unit of importance" is considered first, then ext and so on. It means arranging processing time per unit of importance in ascending order, the job sequence could be found.

2/1=2 (I)

Using WSPT rule the sequence of jobs will be

Respective flow time=

2,

(2+3)=5

(5+4)=9

(9+4)=13

(13+5)=18

(18+6)=24

Mean flow time =(2+5+9+13+18+24)/6=11.833 or 12units.

Weighted mean flow time=71/6=12 units

Basic assumptions

1. only one operation is carried out on a machine at a time.

2. processing times are known and do not change.

3. processing times are independent of order of processing the job.

4. the time required in moving jobs from one machine to another is neglibily small.

5. each operation once started must be performed till completion.

6. each preceding operation must be completed,before beginning of the next immediate operation.

7. only one machine of each type is available

8. a job is processed as soon as possible, but only in the order specified.

9. same order of jobs is maintained over each machine. for example if n jobs are to be processed on two machines A B in order A to B, then each job should go to machine A first then to machine B.

JOB PROCESSING TIME time/importance weight 1 2

2/1=2 (I)

2 5 5/1=5 (V) 3 3 3/1=3 (II) 4 6 6/1=6 (VI) 5 4 4/1=4 (3.5rank) 6 4 4/1=4 (3.5 rank)

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