Problem 1. The Taylor Machine Shop rebores engine blocks. Currently, five engine blocks are waiting for processing. At any time, the company has only one engine expert on duty who can do this type of work. The engine problems have been diagnosed, and the processing times for the jobs have been estimated. Expected completion times have been agreed upon with the shops customers. The accompanying table shows the current situation. Determine the schedule for the engine expert by using (a) the FCFS rule, (b) the SPT rule, (c) the EDD rule, and (d) the CR rule. For each rule, calculate the average flow time, average tardiness, and number of tardy jobs. If average past due is most important, which rule should be chosen?

Engine Block	Processing time (days)	Due date (days)
Ranger	8	10
Explorer	6	12
Bronco	15	20
Econoline 150	3	18
Thunderbird	12	22

Problem 2: Jane Reed bakes breads and cakes in her home for parties and other affairs on a contract basis. Jane has only one oven for baking. One particular Monday morning she finds that she has agreed to complete five jobs for that day. Her husband John will make the deliveries, which require about 15 minutes each. Suppose that she begins baking at 8:00 A.M.

Job	Time required	Promised time
1	1.2 hr	11:30 A.M.
2	40 min	10:00 A.M.
3	2.2 hr	11:00 A.M.
4	30 min	1:00 P.M.
5	3.1 hr	12:00 NOON
6	25 min	2:00 P.M.

Determine the sequence in which she should perform the jobs in order to minimize the number of tardy jobs.

Problem 3. Eight jobs are to be processed through a single machine. The processing times and due dates are given here.

Job	1	2	3	4	5	6	7	8
Processing time	2	3	2	1	4	3	2	2
Due date	5	4	13	6	12	10	15	19

Furthermore, assume that the following precedence relationships must be satisfied:

2 6 3

1 4 7 8

Determine the sequence in which these jobs should be done in order to minimize the maximum lateness subject to the precedence restrictions.

Problem 4. Consider a problem with five jobs (A, B, C, D, and E) and two machines M1 and M2. All five jobs consist of two operations each. The first operation of each job is processed on machine M1; and the second operation is processed on machine M2. The following table gives the processing times in hours for each operation of each job.

Job	Machine 1	Machine 2
A	8	3
B	5	7
C	6	9
D	4	1
E	7	6

Problem 5. Shahi Export House has to process five jobs through three stages of production, i.e., cutting, sewing, and pressing. Processing times are given in the following table:

Job_i	Cutting A_i	Sewing B_i	Pressing C_i
1	3	3	5
2	8	4	8
3	7	2	10
4	5	1	7
5	2	5	6

Determine an order in which these items should be processed so as to minimize the total processing time.