Chapter 16 Scheduling McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Download ReportTranscript Chapter 16 Scheduling McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 16
Scheduling
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 16: Learning Objectives
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
Instructor Slides
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
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
Instructor Slides
16-4
High Volume Systems
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
Instructor Slides
Workstation
2
Output
16-5
High-Volume: Scheduling Difficulties
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
Instructor Slides
16-6
High-Volume Success Factors
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
Instructor Slides
16-7
Intermediate-Volume Systems
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
Instructor Slides
16-8
Intermediate-Volume Systems
Three basic issues:
Run size of jobs
The timing of jobs
The sequence in which jobs will be produced
Q
Production
and usage
Usage
only
Production
and usage
Usage
only
Production
and usage
Qp
Cumulative
production
Imax
2DS
QO
H
Amount
on hand
Instructor Slides
Time
p
p u
16-9
Intermediate-Volume Systems
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
Instructor Slides
16-10
Low-Volume Systems
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
Instructor Slides
16-11
Low-Volume Systems: Loading
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
Instructor Slides
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
Infinite loading
over
Capacity
1
over
2
3
4
5
6
2
3
4
5
6
Finite loading
Capacity
1
Instructor Slides
16-14
Scheduling Approaches
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?”
Instructor Slides
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
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
Instructor Slides
16-17
Hungarian Method
1.
Row reduction: subtract the smallest number in each row from
every number in the row
a.
2.
Column reduction: subtract the smallest number in each column
from every number in the column
a.
3.
Enter the result in a new table
Enter the result in a new table
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
Instructor Slides
16-18
Hungarian Method (contd.)
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
Instructor
Slides
c.
Eliminate
both the row and the column after the match
16-19
Example
Cost
Worker
Row
minimum
A
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
5
1. Row reduction: subtract the smallest number in each row from
every number in the row
Instructor Slides
20
Example
Cost
Worker
Row
minimum
A
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
5
1. Row reduction: subtract the smallest number in each row from
every number in the row
Instructor Slides
21
Example
Cost
Worker
Job
Column
Minimu
m
Row minimum
A
B
C
D
1
6
4
0
2
2
2
0
1
5
5
6
3
0
2
4
3
3
4
0
5
7
4
5
0
1
0
2
2. Column reduction: subtract the smallest number22in each column
from every number in the column
Instructor Slides
Example
Cost
Worker
Job
Column
Minimu
m
Row minimum
A
B
C
D
1
6
3
0
0
2
2
0
0
5
3
6
3
0
1
4
1
3
4
0
4
7
2
5
0
1
0
2
2. Column reduction: subtract the smallest number23in each column
from every number in the column
Instructor Slides
Example
Cost
Job
Worker
A
B
C
D
1
6
3
0
0
2
0
0
5
3
3
0
1
4
1
4
0
4
7
2
3. Determine the minimum number of lines needed to cross out all zeros
24
Because # of lines =3 < 4, optimal solution has not been
found.
Instructor Slides
Example
Cost
Worker
Job
a.
Instructor Slides
b.
A
B
C
D
1
7
3
0
0
2
1
0
5
3
3
0
0
3
0
4
0
3
6
1
Subtract the smallest number from every uncovered number in the
table
Add the smallest uncovered number to the numbers
at
25
intersections of cross-out lines
Example
Cost
Job
Instructor Slides
Worker
A
B
C
D
1
7
3
0
0
2
1
0
5
3
3
0
0
3
0
4
0
3
6
1
Determine the minimum number of lines needed to cross out all
zeros
a. Now, no matter how you draw, a minimum of 426lines is needed.
So optimal solution can be found from the table.
Example
Cost
Job
Instructor Slides
Worker
A
B
C
D
1
7
3
0
0
2
1
0
5
3
3
0
0
3
0
4
0
3
6
1
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
27
Low-Volume Systems: Sequencing
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
Instructor Slides
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
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
Instructor Slides
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
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
Instructor Slides
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
*Jobs arrived in the order shown (A,B,C,D,E,F)
Instructor Slides
33
Example
Sequenc
e
Processing Due
Time (days) Date
A
2
7
B
8
16
C
4
4
D
10
17
E
5
15
F
12
18
Average
Instructor Slides
Flow Time Tardines
s
?
# of remaining
jobs
?
34
Example
Sequenc
e
Processing Due
Time (days) Date
Flow Time Tardines
s
# 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
20
9
Average
Instructor Slides
2.93
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)
FCFS is simple to use.
SPT minimizes average flow time.
EDD minimizes average tardiness.
CR is quite well in terms of minimizing average tardiness
Instructor Slides
36
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
Order:
C
Instructor Slides
37
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
Order:
C->F
Instructor Slides
38
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
Order:
C->F->A
Instructor Slides
39
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
Order:
C->F->A->E
Instructor Slides
40
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
Order:
C->F->A->E->B->D
Instructor Slides
41
Scheduling Difficulties
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
Instructor Slides
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
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
Instructor Slides
16-44
Scheduling Service Operations*
Scheduling customers: Demand Management
Appointment systems
Reservation systems
Controls customer arrivals for service
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
Instructor Slides
16-45
Operations Strategy*
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
Instructor Slides
16-46