pert 09 penjadwalan jangka pendek (2) assignment method
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PERT 09 Penjadwalan Jangka Pendek (2)
� Assignment Method
� Pengurutan Pekerjaan
� Teori Keterbatasan
�Assigns tasks or jobs to resources
�Type of linear programming model
– Objective
• Minimize total cost, time etc.
– Constraints
• 1 job per resource (e.g., machine)
• 1 resource (e.g., machine) per job
Assignment Method
Assignment Method - Four Steps
1 Subtract the smallest number in each row from every number in that row; then subtract the smallest number in every column from every number in that column
2 Draw the minimum number of vertical and horizontal straight lines necessary to cover all zeros in the table
– If the number of lines equals either the number of rows or the number of columns, then you can make an optimal assignment (Step 4)
– Otherwise:
3 Subtract the smallest number not covered by a line from every other uncovered number. Add the same number to any number(s) lying atthe intersection of any two lines. Return to Step 2
4 Optimal assignments will always be at the zero locations of the table
Assignment Method – Type Setter Example
$7$12$9T-50
$11$10$ 8S-66
$ 6$14$11R-34
CBATypesetter
Job
Initial set-up
Step 1a & 1b
052T-50
320S-66
085R-34
CBATypesetter
Job
032T-50
300S-66
065R-34
CBATypesetter
Job
Step 1aStep 1b
Step 2
032T-50
300S-66
065R-34
CBATypesetter
Job
Smallest uncovered
number
Step 3
010T-50
500S-66
043R-34
CBATypesette
r
Job
Make assignments
Production Control Production
Which job do
I run next?
Dispatch List
Order Part Due Qty
XYZ 6014 123 100
ABC 6020 124 50
Job Packet
Job XYZ
Order
release
Sequencing Challenge
�Specifies order jobs will be worked
�Sequencing rules
– First come, first served (FCFS)
– Shortest processing time (SPT)
– Earliest due date (EDD)
– Longest processing time (LPT)
– Critical ratio (CR)
– Johnson’s rule
Sequencing
Priority Rules for Dispatching Jobs
First come, first served
The first job to arrive at a work center is processed first
Earliest due date
The job with the earliest due date is processed first
Shortest processing time
The job with the shortest processing time is processed first
Longest processing time
The job with the longest processing time is processed first
Critical ratio
The ratio of time remaining to required work time remaining is calculated, and jobs are scheduled in order of increasing ratio.
FCFS
EDD
SPT
LPT
CR
�Process first job to arrive at a work
center first
�Average performance on most
scheduling criteria
�Appears ‘fair’ & reasonable to customers
– Important for service organizations
• Example: Restaurants
First Come, First Served Rule
Shortest Processing Time Rule
�Process job with shortest processing time
first.
�Usually best at minimizing job flow and
minimizing the number of jobs in the
system
�Major disadvantage is that long jobs may be
continuously pushed back in the queue.
Longest Processing Time Rule
�Process job with longest processing time
first.
�Usually the least effective method of
sequencing.
�Process job with earliest due date first
�Widely used by many companies
– If due dates important
– If MRP used
• Due dates updated by each MRP run
�Performs poorly on many scheduling
criteria
Earliest Due Date Rule
♦♦Ratio of time remaining to work time Ratio of time remaining to work time
remainingremaining
�Process job with smallest CR first
�Performs well on average lateness
CRTime remaining
Work days remaining
Due date - Today' s date
Work (lead ) time remaining
=
=
Critical Ratio (CR)
Advantages of the Critical RatioScheduling Rule
Use of the critical ratio can help to:
– determine the status of a specific job
– establish a relative priority among jobs on a
common basis
– relate both stock and make-to-order jobs on a
common basis
– adjust priorities and revise schedules
automatically for changes in both demand
and job progress
– dynamically track job progress and location
Criteria to Evaluate Priority Rules
Jobs#
times ΣFlowtime completion Average =
times Flow
times Process nUtilizatioΣ
Σ=
times Process
times Flow system the in jobs of number AverageΣ
Σ=
jobs of Number
times Late lateness job AverageΣ
=
Job Sequencing Example
239E
153D
188C
62B
86A
Job Due
Date (day)
Job Work
Processing
time in days
Job
FCFS
ValueParameter
2.2 daysAverage job
lateness
2.75 jobsAverage number
of jobs in the
system
36.4%Utilization
15.4 daysAverage
completion time
E
D
C
B
A
Sequence
SPT
ValueParameter
1.8 daysAverage job
lateness
2.32 jobsAverage number
of jobs in the
system
43.1%Utilization
13 daysAverage
completion time
E
C
A
D
B
Sequence
EDD
ValueParameter
1.2 daysAverage job
lateness
2.43 jobsAverage number
of jobs in the
system
41.2%Utilization
13.6 daysAverage
completion time
E
C
D
A
B
Sequence
LPT
ValueParameter
9.6 daysAverage job
lateness
3.68 jobsAverage number
of jobs in the
system
27.2%Utilization
20.6 daysAverage
completion time
B
D
A
C
E
Sequence
Summary
Average
Lateness
(Days)
Average Number
of Jobs in the
System
Utilization
(%)
Average
Completion
Time (days)
Rule
9.63.6827.220.6LPT
1.22.4341.213.6EDD
1.82.3243.113.0SPT
2.22.7536.415.4FCFS
Critical Ratio (CR)
0.39
0.20
0.44
0.33
0.75
Critical
Ratio
239E
153D
188C
62B
86A
Job Due
Date
(day)
Job Work
Processing
time in
days
Job
D
B
E
C
A
Sequence
�Used to sequence N jobs through 2
machines in the same order
© 1995 Corel Corp.
© 1995 Corel
Corp.
Saw Drill
Job AJob A
Job BJob B
Job CJob C
Jobs (N = 3)
Johnson’s Rule
Johnson's Rule - Scheduling N Jobs on Two Machines
� All jobs are to be listed, and the time each requires on a machine shown.
� Select the job with the shortest activity time. If the shortest time lies with the first machine, the job is scheduled first; if with the second machine, the job is scheduled last.
� Once a job is scheduled, eliminate it.
� Apply steps 2-3 to the remaining jobs,working toward the center of the sequence.
List jobs &
activity times
Select job with
shortest time
Machine?
Schedule
FIRST
Schedule
LAST
Eliminate job
from list
Jobs left?Break
arbitrarily
Ties?
YesYes
11
22
YesYes
StopNoNo
NoNo
Johnson’s Rule Steps
Johnson’s Rule - Example
710D
127E
48C
63B
25A
Work Center 2
(Lathe)
Work Center 1
(Drill Press)
Job
Johnson’s Rule - Example
AStep 1
ABStep 2
ACBStep 3
ACDBStep 4
ACDEBStep 5
Graphical Depiction of Job Flow
A
C ADEB
CDEBWork
center 1
Work
center 2
0 3 10 20 28 33
0 3 9 10 20 22 28 29 33 35Time =>
Time =>
B E D C A
= Job completed= Idle
Limitations of Rule-Based Dispatching Systems
� Scheduling is dynamic; therefore, rules need to be revised to adjust to changes in process, equipment, product mix, etc.
� Rules do not look upstream or downstream; idle resources and bottleneck resources in other departments may not be recognized
� Rules do not look beyond due dates
Finite Scheduling System
� Deals with factors limiting company’s
ability to achieve goals
� Types of constraints
– Physical
• Example: Machines, raw materials
– Non-physical
• Example: Morale, training
� Limits throughput in operations
Theory of Constraints
Theory of ConstraintsA Five Step Process
� Identify the constraints
� Develop a plan for overcoming the identified constraints
Focus resources on accomplishing the constraints identified in step 2
Reduce the effects of the constraints by off-loading work or by expanding capability
� Once one set of constraints is overcome, return to the first step and identify new constraints
�Bottleneck work centers have less
capacity than prior or following
work centers
�They limit production output
© 1995
Corel
Corp.
Bottleneck Work Centers
Techniques for Dealing With Bottlenecks
1. Increase the capacity of the constraint
2. Ensure well-trained and cross-trained employees are available to operate and maintain the work center causing the constraint
3. Develop alternate routings, processing procedures, or subcontractors
4. Move inspections and tests to a position just before the constraint
5. Schedule throughput to match the capacity of the bottleneck
The 10 Commandments for Correct Scheduling
1. Utilization of a non-bottleneck resource is determined not by its own capacity but by some other constraint in the system
2. Activating a resource is not synonymous with utilizing a resource
3. An hour lost at a bottleneck is an hour lost of the whole system
4. An hour saved at a non-bottleneck is a mirage
5. The transfer batch may not, and many times should not, be equal to the process batch
The 10 Commandments for The 10 Commandments for Correct SchedulingCorrect Scheduling
6. The amount processed should be verifiable and
not fixed
7. Capacity and priority need to be considered
simultaneously, not sequentially
8. Damage from unforeseen problems can be
isolated and minimized
9. Plant capacity should not be balanced
10. The sum of the local optimums is not equal to the
global optimum
Repetitive Manufacturing - Advantages of Level Material Use
�Lower inventory levels, releasing capital for other uses
� Faster product throughput
� Improved component quality and hence improved product quality
�Reduced floor space requirements
� Improved communication among employees because they are closer together
� Smoother production process because large lots have not “hidden” the problems
Scheduling for Services
� Appointment systems - doctor’s office
� Reservations systems - restaurant, car
rental
� First come, first served - deli
� Most critical first - hospital trauma room
Cyclical Scheduling
� Plan a schedule equal in weeks to the number
of people being scheduled
� Determine how many of each of the least
desirable off-shifts must be covered each
week
� Begin the schedule for one worker by
scheduling the days off during the planning
cycle (at a rate of 2 days per week on average)
Cyclical Scheduling - Continued
� Assign off-shifts for the first worker
� Repeat this pattern for each other worker, but
offset by one week from the previous
� Allow each worker to pick his/her “slot” or
“line” in order of seniority
� Mandate that any changes from the chosen
schedule are strictly between the personnel
wanting to switch