Chapter 16Scheduling

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 16: Learning Objectives

Instructor Slides

You should be able to:

1. Explain what scheduling involves and the importance of good scheduling

2. Describe scheduling needs in high-volume and intermediate-volume systems

3. Describe scheduling needs in job shops

4. Use and interpret Gantt charts, and use the assignment method for loading

5. Give examples of commonly used priority rules

6. Summarize some of the unique problems encountered in service systems, and describe some of the approaches used for scheduling service systems

16-2

Scheduling

Scheduling: Establishing the timing of the use of equipment,

facilities and human activities in an organization

Effective scheduling can yield Cost savings Increases in productivity Other benefits

Instructor Slides 16-3

Scheduling Context

Instructor Slides

Scheduling is constrained by multiple system design decisions System capacity

Product and/or service design

Equipment selection

Worker selection and training

Aggregate planning and master scheduling

16-4

High Volume Systems

Instructor Slides

Flow System High-volume system in which all jobs follow the same

sequence

Flow system scheduling

Scheduling for flow systems

The goal is to achieve a smooth rate of flow of goods or customers through the system in order to get high utilization of labor and equipment

Workstation 1

Workstation 2

Output

16-5

High-Volume: Scheduling Difficulties

Instructor Slides

Few flow systems are entirely dedicated to a single product or service Each product change requires

Slightly different inputs of parts

Slightly different materials

Slightly different processing requirements that must be scheduled into the line

Need to avoid excessive inventory buildup

Disruptions may result in less-than-desired output

16-6

High-Volume Success Factors

Instructor Slides

The following factors often dictate the success of high-volume systems:• Process and product design• Preventive maintenance• Rapid repair when breakdowns occur• Optimal product mixes• Minimization of quality problems• Reliability and timing of supplies

16-7

Intermediate-Volume Systems

Instructor Slides

Outputs fall between the standardized type of output of high-volume systems and the make-to-order output of job shops

Output rates are insufficient to warrant continuous production Rather, it is more economical

to produce intermittently Work centers periodically

shift from one product to

another

16-8

Intermediate-Volume Systems

Three basic issues: Run size of jobs

The timing of jobs

The sequence in which jobs will be produced

Instructor Slides

up

p

H

DSQ

2

O

16-9

Q

Qp

Imax

Productionand usage

Productionand usage

Productionand usage

Usageonly

Usageonly

Cumulativeproduction

Amounton hand

Time

Intermediate-Volume Systems

Instructor Slides

Important considerations Setup cost

Usage is not always as smooth as assumed in the economic lot size model

Alternative scheduling approach Base production on a master schedule developed from

customer orders and forecasted demand

16-10

Low-Volume Systems

Instructor Slides

Job shop scheduling (Loading and Sequencing) Scheduling for low-volume systems with many

variations in requirements Make-to-order products

Processing requirements

Material requirements

Processing time

Processing sequence and steps

A complex scheduling environment It is impossible to establish firm schedules until actual job

orders are received

16-11

Low-Volume Systems: Loading

Instructor Slides

Loading the assignment of jobs to processing centers Gantt chart

Used as a visual aid for loading and scheduling purposes

Purpose of the Gantt chart is to organize and visually display the actual or intended use of resources in a time framework

Managers may use the charts for trial-and-error schedule development to get an idea of what different arrangements would involve

16-12

Gantt Charts

Load chart A Gantt chart that shows the loading and idle times for a group

of machines or list of departments

Instructor Slides 16-13

Loading Approaches

Infinite loading Jobs are assigned to workstations without regard to the

capacity of the work center

Finite loading Jobs are assigned to work centers taking into account the work

center capacity and job processing times

Instructor Slides

1 2 3 4 5 6

over overCapacity

Infinite loading

1 2 3 4 5 6

Capacity

Finite loading

16-14

Scheduling Approaches

Instructor Slides

· Forward scheduling· Scheduling ahead from some point in time.· Used when the question is:

· “How long will it take to complete this job?· Backward scheduling

· Scheduling backwards from some due date· Used when the question is:

· “When is the latest this job can be started and still be completed on time?”

16-15

Gantt Charts

Schedule chart A Gantt chart that shows the orders or jobs in progress and

whether they are on schedule

Instructor Slides 16-16

Assignment

Instructor Slides

Assignment model A linear programming model for optimal assignment of

tasks and resources

Hungarian method Method of assigning jobs by a one-for-one matching to

identify the lowest cost solution

16-17

Hungarian Method

Instructor Slides

1. Row reduction: subtract the smallest number in each row from every number in the row

a. Enter the result in a new table

2. Column reduction: subtract the smallest number in each column from every number in the column

a. Enter the result in a new table

3. Test whether an optimum assignment can be made

a. Determine the minimum number of lines needed to cross out all zeros

b. If the number of lines equals the number of rows, an optimum assignment is possible. Go to step 6

c. Else, go to step 4

16-18

Hungarian Method (contd.)

Instructor Slides

4. If the number of lines is less than the number of rows, modify the table:

a. Subtract the smallest number from every uncovered number in the table

b. Add the smallest uncovered number to the numbers at intersections of cross-out lines

c. Numbers crossed out but not at intersections of cross-out lines carry over unchanged to the next table

5. Repeat steps 3 and 4 until an optimal table is obtained

6. Make the assignments

a. Begin with rows or columns with only one zero

b. Match items that have zeros, using only one match for each row and each column

c. Eliminate both the row and the column after the match 16-19

Example

Cost

Worker Row minimu

mA B C D

1 8 6 2 4 2

Job 2 6 7 11 10 6

3 3 5 7 6 3

4 5 10 12 9 5Instructor Slides 20

1. Row reduction: subtract the smallest number in each row from every number in the row

Example

Cost

Worker Row minimu

mA B C D

1 6 4 0 2 2

Job 2 0 1 5 5 6

3 0 2 4 3 3

4 0 5 7 4 5Instructor Slides 21

1. Row reduction: subtract the smallest number in each row from every number in the row

ExampleCost Worker Row

minimum

A B C D

1 6 4 0 2 2Job 2 0 1 5 5 6

3 0 2 4 3 3

4 0 5 7 4 5Column Minimum

0 1 0 2

Instructor Slides 222. Column reduction: subtract the smallest number in each column from every number in the column

ExampleCost Worker Row

minimum

A B C D

1 6 3 0 0 2Job 2 0 0 5 3 6

3 0 1 4 1 3

4 0 4 7 2 5Column Minimum

0 1 0 2

Instructor Slides 232. Column reduction: subtract the smallest number in each column from every number in the column

ExampleCost

Worker

A B C D

1 6 3 0 0

Job 2 0 0 5 3

3 0 1 4 1

4 0 4 7 2

Instructor Slides 243. Determine the minimum number of lines needed to cross out all zerosBecause # of lines =3 < 4, optimal solution has not been found.

ExampleCost

Worker

A B C D

1 7 3 0 0

Job 2 1 0 5 3

3 0 0 3 0

4 0 3 6 1

Instructor Slides 25

a. Subtract the smallest number from every uncovered number in the table

b. Add the smallest uncovered number to the numbers at intersections of cross-out lines

ExampleCost

Worker

A B C D

1 7 3 0 0

Job 2 1 0 5 3

3 0 0 3 0

4 0 3 6 1

Instructor Slides 26

Determine the minimum number of lines needed to cross out all zeros

a. Now, no matter how you draw, a minimum of 4 lines is needed. So optimal solution can be found from the table.

ExampleCost

Worker

A B C D

1 7 3 0 0

Job 2 1 0 5 3

3 0 0 3 0

4 0 3 6 1

Instructor Slides 27

Pick out zeros so that each line and column has one and only one zero. The corresponding assignment is optimal:

1-C 2-B 3-D 4-A

Low-Volume Systems: Sequencing

Instructor Slides

Sequencing Determine the order in which jobs at a work

center will be processed

Priority rules Simple heuristics used to select the order in which

jobs will be processed The rules generally assume that job setup cost

and time are independent of processing sequence Job time

Time needed for setup and processing of a job

16-28

Priority Rules

FCFS - first come, first served: Jobs are processed in the order in which they arrive at a machine or work center.

SPT - shortest processing time: Jobs are processed according to processing time at a machine or work center, shortest job first.

EDD - earliest due date: Jobs are processed according to due date, earliest due date first.

CR - critical ratio: Jobs are processed according to smallest ratio of time remaining until due date to processing time remaining.

S/O* - slack per operation: Jobs are processed according to average slack time (time until due date minus remaining time to process). Compute by dividing slack time by number of remaining operations, including the current one.

Rush* - emergency or preferred customers first.Instructor Slides 16-29

Priority Rules: Assumptions

Instructor Slides

The set of jobs is known; no new orders arrive after processing begins and no jobs are canceled

Setup time is independent of processing time Setup time is deterministic Processing times are deterministic There will be no interruptions in processing such

as machine breakdowns or accidents

16-30

Priority Rules: Local v. Global

Local priority rules: FCFS, SPT, EDD Focus on information pertaining to a single workstation

when establishing a job sequence

Global priority rules: CR, S/O Incorporate information from multiple workstations when

establishing a job sequence

Instructor Slides 16-31

Sequence: Performance Metrics

Instructor Slides

Common performance metrics: Job flow time

This is the amount of time it takes from when a job arrives until it is complete

It includes not only processing time but also any time waiting to be processed

Job lateness This is the amount of time the job completion time is

expected to exceed the date the job was due or promised to a customer

Tardiness = max {0, lateness}, 0 if lateness<0 Makespan

The total time needed to complete a group of jobs from the beginning of the first job to the completion of the last job

Average number of jobs Jobs that are in a shop are considered to be WIP inventory

16-32

Example

Job Processing Time (days)

Due Date (days from present time)

A 2 7

B 8 16

C 4 4

D 10 17

E 5 15

F 12 18

Instructor Slides 33

*Jobs arrived in the order shown (A,B,C,D,E,F)

Example

Sequence

Processing Time (days)

Due Date

Flow Time

Tardiness

# of remaining jobs

A 2 7

B 8 16

C 4 4

D 10 17

E 5 15

F 12 18

Average ? ?

Instructor Slides 34

Example

Sequence

Processing Time (days)

Due Date

Flow Time

Tardiness

# of remaining jobs

A 2 7 2 0 6

B 8 16 10 0 5

C 4 4 14 10 4

D 10 17 24 7 3

E 5 15 29 14 2

F 12 18 41 23 1

Total 41 120 54

Average 20 9 2.93

Instructor Slides 35

Example

Makespan =2+8+4+10+5+12=41 (days)

Average Flow Time= (2+10+14+24+29+41)/6 =20 (days)

Average Tardiness= (0+0+10+7+14+23)/6 = 9 (days)

Average # of remaining jobs= Total Flow Time/ Total Processing Time (e.g. 120/41 2.93)

Instructor Slides 36

FCFS is simple to use.SPT minimizes average flow time.EDD minimizes average tardiness.CR is quite well in terms of minimizing average tardiness

Example: CR

Job Processing Time

Due Date Critical Ratio

A 2 7 (7-0)/2=3.5

B 8 16 (16-0)/8=2

C 4 4 (4-0)/4=1

D 10 17 (17-0)/10=1.7

E 5 15 (15-0)/5=3

F 12 18 (18-0)/12=1.5

Instructor Slides 37

Order:C

Example: CR

Job Processing Time

Due Date Critical Ratio

A 2 7 (7-4)/2=1.5

B 8 16 (16-4)/8=1.5

D 10 17 (17-4)/10=1.3

E 5 15 (15-4)/5=2.2

F 12 18 (18-4)/12=1.17

Instructor Slides 38

Order:C->F

Example: CR

Job Processing Time

Due Date Critical Ratio

A 2 7 (7-16)/2=-4.5

B 8 16 (16-16)/8=0.0

D 10 17 (17-16)/10=0.1

E 5 15 (15-16)/5=-0.2

Instructor Slides 39

Order:C->F->A

Example: CR

Job Processing Time

Due Date Critical Ratio

B 8 16 (16-18)/8=-0.25

D 10 17 (17-18)/10=-0.1

E 5 15 (15-18)/5=-0.6

Instructor Slides 40

Order:C->F->A->E

Example: CR

Job Processing Time

Due Date Critical Ratio

B 8 16 (16-23)/8=-0.875

D 10 17 (17-23)/10=-0.60

Instructor Slides 41

Order:C->F->A->E->B->D

Scheduling Difficulties

Instructor Slides

Variability in Setup times

Processing times

Interruptions

Changes in the set of jobs

Except for small job sets, there is no method for identifying an optimal schedule

Scheduling is not an exact science (heuristics) It is an ongoing task for a manager

16-42

Minimizing Scheduling Difficulties

Set realistic due dates Focus on bottleneck operations

First, try to increase the capacity of the operations If that is not possible

Schedule bottleneck operations first Then, schedule non-bottleneck operations around the

bottleneck operations

Consider lot splitting of large jobs (smaller lot size) Often works best when there are large differences in job

times

Instructor Slides 16-43

Service Operation Problems

Instructor Slides

Service scheduling often presents challenges not found in manufacturing These are primarily related to:

1. The inability to store or inventory services

2. The random nature of service requests

Service scheduling may involve scheduling:

1. Customers

2. Workforce

3. Equipment

16-44

Scheduling Service Operations*

Instructor Slides

Scheduling customers: Demand Management Appointment systems

Controls customer arrivals for service

Reservation systems

Enable service systems to formulate a fairly accurate estimate demand on the system for a given time period

Scheduling the workforce: Capacity Management Cyclical Scheduling

Employees are assigned to work shifts or time slots, and have days off, on a repeating basis 16-45

Operations Strategy*

Instructor Slides

If scheduling is done well: Goods and services can be made or delivered in a

timely manner

Resources can be used to best advantage

Customers will be satisfied

It is important to not overlook the importance of scheduling to strategy and competitive advantage

16-46