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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Lab 7 Short Term Scheduling
Objectives of this laboratory:
1. Student is able to define loading jobs, assignment method, and sequencing
jobs.
2. Student is able to apply the assignment method for loading jobs.
3. Student is able to define and describe each of the priority sequencing rules.
4. Student is able to apply the priority rules and the critical ratio methods for
sequencing jobs.
Before we start this laboratory exercise, let familiarize our self with several terms that
are commonly used in Short Term Scheduling realm.
What is Loading Jobs?
• Loading Jobs means the assignment of jobs to work or processing centers
so that costs, idle time or completion times are kept to a minimum.
What is assignment method?
• Assignment method is a special class of linear programming models that
involves assigning tasks or jobs to resources so that (most often objectives)
the total costs or time required can be minimized.
What is sequencing Jobs?
• Sequencing Jobs is the determination of the order in which jobs should be
done at each work center.
Assignment Method
Let say that there are three printing jobs that need to be processed at three different
types of printing machines. To print specific jobs at each printing machine (typesetter)
will cost a certain amount of money as refer to the table below.
Typesetter
Job
A
B
C
R-34
$11
$14
$6
S-66
$8
$10
$11
T-55
$9
$12
$7
The question is which job to assign to which machine in order to minimize the total
cost for all the printing processes?
So, the assignment method involves adding and subtracting appropriate numbers in
the table to find the lowest opportunity cost for each assignment. There are four steps
in the assignment method.
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Step 1a:
Subtract the smallest number in each row from every numbers in the row.
Typesetter
Job
A
B
C
R-34
$11 - $6
$14 - $6
$6 - $6
S-66
$8 - $8
$10 - $8
$11 - $8
T-55
$9 - $7
$12 - $7
$7 - $7
Typesetter
Job
A
B
C
R-34
5
8
0
S-66
0
2
3
T-55
2
5
0
Step 1b:
Than, subtract the smallest number in each column from every numbers in the
column.
Typesetter
Job
A
B
C
R-34
5-0
8-2
0-0
S-66
0-0
2-2
3-0
T-55
2-0
5-2
0-0
Typesetter
Job
A
B
C
R-34
5
6
0
S-66
0
0
3
T-55
2
3
0
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Step 2:
Draw the minimum number of vertical and horizontal straight lines needed to
cover all zeros. Because two lines suffice, the solution is not optimal.
Typesetter
Job
A
B
C
R-34
5
6
0
S-66
0
0
3
T-55
2
3
0
Smallest uncovered number
Step 3:
Subtract the smallest uncovered number from every other uncovered number
and add it to numbers at the intersection of two lines.
Typesetter
Job
A
B
C
R-34
5 -2
6-2
0
S-66
0
0
3+2
T-55
2-2
3-2
0
Typesetter
Job
A
B
C
R-34
3
4
0
S-66
0
0
5
T-55
0
1
0
Than return to step 2
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Typesetter
Job
A
B
C
R-34
3
4
0
S-66
0
0
5
T-55
0
1
0
Because three lines are necessary, an optimal assignment can be made.
Assign R-34 to C
Assign S-66 to B
Assign T-50 to A
The total cost is = $6 + $10 + $9 = $25
Sequencing Jobs
a) Priority Rules
Rules used to determine the sequence of jobs in process oriented facilities.
There are four priority rules for dispatching jobs:
•
First come, first served (FCFS)
o Jobs are completed in the order they arrived.
•
Shortest processing time (SPT)
o Jobs with the shortest processing times are assigned first.
•
Earliest due date (EDD)
o Earliest due date jobs are performed first.
•
Longest processing time (LPT)
o Jobs with the longest processing time are completed first.
There are four types of result in measuring the effectiveness of the priority rules
•
Average completion time =
Sum of total flow time
Number of jobs
o The lower the better
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
•
Utilization =
PPK Pembuatan
2008/2009
Total job work ( proces sin g ) time
Sum of total flow time
o The higher the better
•
Average number on jobs in the system =
Sum of total flow time
Total job work ( proces sin g ) time
o The lower the better
•
Average job lateness =
Total late days
Number of jobs
o The lower the better
Example:
Let say we have five jobs that need to be set prioritize which one run first and
which is next and so on.(Refer to table below)
A
Job Work (Processing)
Time (Days)
6
B
2
6
C
8
18
D
3
15
E
9
23
Job
Job Due Date (Days)
8
Let choose the first come, first served priority rule (FCFS). Sort the job
sequence based on FCFS.
A
Job Work
(Processing)
Time
6
B
2
6+2=8
6
8–6=2
C
8
8 + 8 = 16
18
16 – 18 = 0
D
3
16 + 3 = 19
15
19 – 15 = 4
E
9
19 + 9 = 28
23
28 – 23 = 0
Total
28
77
Job Sequence
Flow Time
Job Due Date
Job Lateness
6
8
6–8=0
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
•
•
•
PPK Pembuatan
2008/2009
Average completion time =
Sum of total flow time
Number of jobs
Average completion time =
77 days
= 15.4 days
5
Utilization =
Total job work ( proces sin g ) time
Sum of total flow time
Utilization =
28
= 36.4%
77
Average number on jobs in the system =
•
Sum of total flow time
Average number on jobs in the system =
Total job work ( proces sin g ) time
77 days
= 2.75 jobs
28 days
Average job lateness =
Total late days
Number of jobs
Average job lateness =
11
= 2.2 days
5
The results of these four rules are summarized in the following table:
FCFS
Average
Completion
Time (Days)
15.4
36.4
Average
Number of
Jobs in System
2.75
SPT
13.0
43.1
2.32
1.8
EDD
13.6
41.2
2.43
1.2
LPT
20.6
27.2
3.68
9.6
Rule
Utilization
(%)
Average
lateness (Says)
2.2
For this example the shortage processing time (SPT) is superior in 3 measures of
effectiveness.
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Critical Ratio
A sequencing rule that is an index number computed by dividing the time
remaining until due date by the work time remaining. Critical ratio is dynamics and
easy to update and it tends to perform better than FCFS, SPT, EDD or LPT on the
average job lateness criterion.
Critical Ratio =
Time remaining
Due date − Today ' s date
=
Workdays remaining
Work (lead ) time remaining
If the critical ratio is exactly 1.0 meaning the job is on schedule, if the value of critical
ratio is greater than 1.0 means the job is ahead and if the value of critical ratio is
glower than 1.0 means the job is falling behind schedule.
Example:
Today is day 25 on Zyco Medical Testing laboratories’ production schedule. Three
jobs are on order, as shown in table below:
Job
Due Date
Workdays Remaining
A
30
4
B
28
5
C
27
2
Job
Critical Ratio
Priority Order
Solution:
A
B
C
30 − 25
= 1.25
4
28 − 25
= 0.60
5
27 − 25
= 1.00
2
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
Exercises:
1) The Orange Top Cab Company has a taxi waiting at each of four cabstands in
Evanston, Illinois. Four customers have called and requested service. The
distances, in miles, from the waiting taxis to the customers are given in the
following table. Find the optimal assignment of taxis to customers so as to
minimize total driving distance to the customers. [5 marks]
Customer
Cab Site
A
B
C
D
Stand 1
7
3
4
8
Stand 2
5
4
6
5
Stand 3
6
7
9
6
Stand 4
8
6
7
4
Note: All the solutions / calculations must be constructed using Microsoft Excel program.
2) The following jobs are waiting to be processes at the same machine center. Jobs
are logged as they arrive:
Job
Due Date
Duration (days)
A
313
7
B
312
15
C
325
30
D
314
10
E
314
6
In what sequence would the jobs be ranked according to the following decision rules:
a) FCFS
b) EDD
c) SPT
d) LPT
All dates are specified as manufacturing planning calendar days. Assume that all jobs
arrive on day 275. Which decision is best and why? [10 marks]
Note: All the solutions / calculations must be constructed using Microsoft Excel program.
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EPT 432 Operation Management
Lab 7 – Short Term Scheduling
PPK Pembuatan
2008/2009
3) The following 5 overhaul jobs are waiting to be processed at Avianic’s Engine
Repair Inc. These jobs were logged as they arrived. All dates are specified as
planning calendar days. Assume that all jobs arrived on day 180; today’s date is
200.
Job
Due date
Duration (days)
103
214
10
205
223
7
309
217
11
412
219
5
517
217
15
Using the critical ratio scheduling rule, in what sequence would the jobs be
processed? [5 marks]
Note: All the solutions / calculations must be constructed using Microsoft Excel program.
Total marks = _______ / 20 marks
GOOD LUCK
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