Question

15.13 The following jobs are waiting to be processed at Rick Carlson’s machine center. Carlson’s machine center has a relatively long backlog and sets fresh schedulesevery 2 weeks, which do not disturb earlier schedules. Below are the jobs received during the previous 2 weeks. They are ready to be scheduled today, which is day 241(day 241 is a work day). Job names refer to names of clients and contract numbers.
Job Date Job Received Production Days Needed Date Job Due
BR-02 228 15 300
CX-01 225 25 270
DE-06 230 35 320
RG-05 235 40 360
SY-11 231 30 310

a) Complete the table below. (Show your supporting calculations)
b) Which dispatching rule has the best score for flow time?
c) Which dispatching rule has the best score for utilization metric?
d) Which dispatching rule has the best score for lateness?
e) Which dispatching rule would you select? Support your decision

Answer 1

a.

To complete: The table given below.

Given information:

It is given that C machine center schedules for every 2 weeks. Today is 241st working day, and they are all set to schedule the jobs for next 2 weeks.

Job	Date job received	Production days needed	Date job due
B	228	15	300
C	225	25	270
D	230	35	320
R	235	40	360
S	231	30	310

Explanation:

Early due date:

The job with the earliest due date is selected first and the rest of the jobs are taken in an ascending order.

The order of selection of jobs using early due date method is:

Job sequence	Date job due
C	270
B	300
S	310
D	320
R	360

Table no: 1

Note: Flow time is the cumulative addition of production days needed / processing time (column 3).

Note: In column 6, the date job due (from column 5) is reduced by 240 since the job is started from day 241.

Note: In column 7, when subtracting flow time (column 4) and job starting date (column 6), assign 0 instead of negative numbers.

It is calculated that the total late days are 50. Refer to Table no: 1.

It is given that the total number of jobs is 5.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 1.

It is calculated that the sum of total flow time is 385 days. Refer to Table no: 1.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 1.

It is calculated that the sum of total flow time is385 days. Refer to Table no: 1.

Shortest processing time:

The job with shortest processing time is taken first and the rest of the jobs are taken in an ascending order.

The order of selection of jobs using shortest processing time method is:

Job sequence	Production days needed
B	15
C	25
S	30
D	35
R	40

Table no: 2

Note: Flow time is the cumulative addition of production days needed / processing time (column 3).

Note: In column 6, the date job due (from column 5) is reduced by 240 since the job is started from day 241.

Note: In column 7, when subtracting flow time (column 4) and job starting date (column 6), assign 0 instead of negative numbers.

It is calculated that the total late days are 60. Refer to Table no: 2.

It is given that the total number of jobs is 5.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 2.

It is calculated that the sum of total flow time is 375 days. Refer to Table no: 2.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 2.

It is calculated that the sum of total flow time is 375 days. Refer to Table no: 2.

Longest processing time:

The job with the longest processing time is taken first and the rest of the jobs are taken in a descending order.

The order of selection of jobs using longest processing time method is:

Job sequence	Production days needed
R	40
D	35
S	30
C	25
B	15

Table no: 3

Note: Flow time is the cumulative addition of production days needed / processing time (column 3).

Note: In column 6, the date job due (from column 5) is reduced by 240 since the job is started from day 241.

Note: In column 7, when subtracting flow time (column 4) and job starting date (column 6), assign 0 instead of negative numbers.

It is calculated that the total late days are 220. Refer to Table no: 3.

It is given that the total number of jobs is 5.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 3.

It is calculated that the sum of total flow time is 495 days. Refer to Table no: 3.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 3.

It is calculated that the sum of total flow time is 495 days. Refer to Table no: 3.

First come first serve method:

The processes for the job are done according to the order they arrive.

The order of selection of jobs using first come first serve method is:

Job sequence	Date job received
B	228
C	225
D	230
R	235
S	231

Table no: 4

Note: Flow time is the cumulative addition of production days needed / processing time (column 3).

Note: In column 6, the date job due (from column 5) is reduced by 240 since the job is started from day 241.

Note: In column 7, when subtracting flow time (column 4) and job starting date (column 6), assign 0 instead of negative numbers.

It is calculated that the total late days are 85. Refer to Table no: 3.

It is given that the total number of jobs is 5.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 4.

It is calculated that the sum of total flow time is 390 days. Refer to Table no: 4.

It is calculated that the total production days needed (processing time) is 145 days. Refer to Table no: 4.

It is calculated that the sum of total flow time is 390 days. Refer to Table no: 4.

Therefore, the completed table is:

b.

To determine: The dispatching rule that has the best score for flow time.

Given information:

It is given that C machine center schedules for every 2 weeks. Today is 241st working day, and they are all set to schedule the jobs for next 2 weeks.

Job	Date job received	Production days needed	Date job due
B	228	15	300
C	225	25	270
D	230	35	320
R	235	40	360
S	231	30	310

Explanation:

Now, find the dispatching rule that has best score for flow time.

Flow time shows the time taken for all the processes in the job. Least value denotes quick processing and completion of jobs, which is the best option. SPT has the least score for flow time compared to all other methods.

c.

To determine: The dispatching rule that has the best score for utilization metric.

Given information:

It is given that C machine center schedules for every 2 weeks. Today is 241st working day, and they are all set to schedule the jobs for next 2 weeks.

Job	Date job received	Production days needed	Date job due
B	228	15	300
C	225	25	270
D	230	35	320
R	235	40	360
S	231	30	310

Explanation:

Now, find the dispatching rule that has best score for utilization metric.

Utilization metric shows how effectively the jobs are done. Higher the score higher is the effectiveness. SPT has the highest score; therefore, it must be chosen.

d.

To determine: The dispatching rule that has the best score for lateness.

Given information:

It is given that C machine center schedules for every 2 weeks. Today is 241st working day, and they are all set to schedule the jobs for next 2 weeks.

Job	Date job received	Production days needed	Date job due
B	228	15	300
C	225	25	270
D	230	35	320
R	235	40	360
S	231	30	310

Explanation:

Now, find the dispatching rule that has best score for lateness.

Average job lateness shows the delay in the processing of the job. Lower the score quicker the jobs are done. EDD has the least score for average job lateness.

e.

To determine: The best dispatching rule.

Given information:

It is given that C machine center schedules for every 2 weeks. Today is 241st working day, and they are all set to schedule the jobs for next 2 weeks.

Job	Date job received	Production days needed	Date job due
B	228	15	300
C	225	25	270
D	230	35	320
R	235	40	360
S	231	30	310

Explanation:

Now, find the best dispatching rule.

Either SPT or EDD can be chosen, since SPT has the best score for flow time and utilization rate and EDD has the best score for job lateness.