Question

The following jobs are waiting to be processed at the same machine center. Jobs are logged as they​ arrive:

Job   Date Received   Due Date   Duration (days)
A             275                    312                  16
B             275                    325                  40
C      275                     314                   5
D            275                     315                   3
E            275                      313                  8

All dates are specified as manufacturing planning calendar days. Assume that all jobs arrive on day 275. Assume each job starts at the beginning of the day and finishes at the end of the day​ (a job that begins on day 275 and takes 8 days will finish on day​ 282, and the next job begins in the morning of day​ 283). Compute all times based on initiating work on day 275.

​a) Using the FCFS​ (first come, first served​ ) decision rule for sequencing the​ jobs, the order is​ (assume that jobs came in the order in which they are listed in the​ table):

Sequence                    Job

1                    ?

2                    ?

3                    ?

4                    ?

5                    ?

the average tardiness for the sequence developed using the EDD rule= ?? days

The percentage utilization for the sequence developed using the EDD rule =??% round 2 dec

using the SPT decision rule for sequencing the jobs, the order is a,e,b,c,d

the average tardiness for the sequence developed using the SPT rule = ?? days

the percentage utilization for the sequence developed using the SPT rule = ??% round 2 dec.

using the LPT decision rule for sequencing the jobs, the order is d,c,b,e,a

the average tardiness for the sequence developed using the LPT rule = ?? days . round 2 dec.

the percentage utilization for the sequence developed using the LPT rule = ??% round 2 dec

Answer 1

(a)

As it is FCFS, the sequence will be A – B – C – D – E.

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For EDD, the earliest due date job is taken first. So sequence will be A – E – C – D – B.

EDD
Job	Date received	Due date	Duration	Flow time Duration of existing job + flow time of previous job	Date of completion Date received + Duration – 1	Lateness Maximum of 0 and (Date of completion – Due date)
A	275	312	16	16	275 + 16 - 1 = 290	290 – 312 = -22 = 0
E	275	313	8	16 + 8 = 24	298	0
C	275	314	5	24 + 5 = 29	303	0
D	275	315	3	32	306	0
B	275	325	40	72	346	21
Total			72	173	1543	21

Average tardiness = Total tardiness/number of jobs = 21/5 = 4.20

% utilization = Total Duration/Total flow time = 72/173 * 100 = 41.618 = 41.62%

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SPT stands for Shortest Processing time. The sequence will be D – C – E – A – B

SPT
Job	Date received	Due date	Duration	Flow time	Date of completion	Lateness
D	275	315	3	3	277	0
C	275	314	5	8	282	0
E	275	313	8	16	290	0
A	275	312	16	32	306	0
B	275	325	40	72	346	21
Total			72	131	1501	21

Average tardiness = 21/5 = 4.2

% utilization = 72/131 * 100 = 54.96%

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LPT stands for longest processing time. Here, the sequence is done based on the longest to shortest duration of work. Sequence will be B -A – E – C – D

LPT
Job	Date received	Due date	Duration	Flow Time	Date of completion	Lateness
B	275	325	40	40	314	0
A	275	312	16	56	330	18
E	275	313	8	64	338	25
C	275	314	5	69	343	29
D	275	315	3	72	346	31
Total			72	301	1671	103

Average tardiness = 103/5 = 20.6

% utilization = 72/301 * 100 = 23.92%

Hope the answer will help. In the case of doubt, please comment. I have tried my best to explain.