1. A manufacturing shop with a single workstation (machine) produces 6 products
ID: 363308 • Letter: 1
Question
1. 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
(b) Assume that the manufacturing shop has to pay $50 per each job completed after its due date, and wants to
minimize the total cost. 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?
Job
1
2
3
4
5
6
Processing time (days)
2
5
3
6
4
4
Due date
6
36
8
23
13
15
Explanation / Answer
1 (b)
Here job lateness or tardiness is of prime importance since the manufacturing shop has to shell out $ 50 for every job finishing after its due date. Therefore, Earliest Due Date (EDD) scheduling rule will be used to minimize the total cost.
Earliest Due Date Scheduling Rule:
Job with earliest due date is carried out first.
Job Sequence
Processing Time
(in Days)
Due Date
(in Days)
Flow Time
(in Days)
Days Tardy = Flow Time - Due Date
(in Days) (0 if negative)
1
2
6
0 + 2 = 2
0
3
3
8
2 + 3 = 5
0
5
4
13
5 + 4 = 9
0
6
4
15
9 + 4 = 13
0
4
6
23
13 + 6 = 19
0
2
5
36
19 + 5 = 24
0
Total
24
72
0
(i) Average job flow time = 72 / 6 = 12 days.
(ii) Average tardiness = 0 / 6 = 0.
(iii) Makespan = Total completion time of all the jobs = 24 days.
(iv) Average number of jobs at the work center = Total flow time / Makespan = 72 / 24 = 3.
The tardiness or lateness for each job is zero as flow time of every job is less than its due date.
So, the manufacturing shop does not have to pay any extra money because of lateness. Hence, this sequence is the optimum sequence as it minimizes the total cost.
Optimum sequence = 1-3-5-6-4-2.
The cost of the resulting schedule = $ 0 (as no money has to be paid for any delay).
Job Sequence
Processing Time
(in Days)
Due Date
(in Days)
Flow Time
(in Days)
Days Tardy = Flow Time - Due Date
(in Days) (0 if negative)
1
2
6
0 + 2 = 2
0
3
3
8
2 + 3 = 5
0
5
4
13
5 + 4 = 9
0
6
4
15
9 + 4 = 13
0
4
6
23
13 + 6 = 19
0
2
5
36
19 + 5 = 24
0
Total
24
72
0
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