Question

(assuming all jobs are currently in queue at their first operation) and do the following 1a. For the following set of jobs find the sequence that minimizes average completion time; 1b. For the following set of jobs find the sequence that minimizes the number of tardy jobs.

Job	Processing Time	Due Date
1	15	20
2	8	30
3	11	32
4	6	40
5	14	50
6	7	50
7	3	65
8	9	75

Answer 1

Job	Processing Time	Due Date
1	15	20
2	8	30
3	11	32
4	6	40
5	14	50
6	7	50
7	3	65
8	9	75

1a. For the following set of jobs find the sequence that minimizes average completion time;

To minimize average completion time, we put all jobs based on the shortest processing time rule,

The sequence will be 7-4-6-2-8-3-5-1

The completion times would be (3, 9, 16, 24, 33, 44, 58, 73)

Average completeion time = (3+9+16+24+33+44+58+73)/8 = 32.5

1b. For the following set of jobs find the sequence that minimizes the number of tardy jobs.

Step 1)

To minimize the number of tardy jobs, we put all jobs based on the EDD sequence,

The EDD sequence will be 1-2-3-4-5-6-7-8

The completion times would be (15, 23, 34, 40, 54, 61, 64, 73)

The tardiness for each job is (0, 0, 2, 0, 4, 11, 0, 0)

Step 2)

The first tardy job is job 3,

The largest processing time between 1 to 3 is job 1 with time = 11.

So we remove job 1 from sequence.

Step 3)

The new sequence is 2-3-4-5-6-7-8

The completion times would be (8, 19, 25, 39, 46, 49, 58)

The tardiness for each job is (0, 0, 0, 0, 0, 0, 0)

So the optimal sequence is 2-3-4-5-6-7-8-1

With the number of tardy jobs (N_t) = 1.