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