Section Objectives

1

• Section Objectives
• After completing this section, you should be able
  to
• 1. Explain what scheduling involves and the
  importance of good scheduling.
• 2. Discuss scheduling needs in high volume
  systems.
• 3. Discuss scheduling needs in job shops.
• 4. Use and interpret Gantt charts, and use the
  assignment for loading.
• 5. Discuss and give examples of commonly used
  priority rules.
• 6. Discuss some of the unique problems
  encountered in service systems and describe some
  of the approaches used for scheduling service
  systems.

2

• Scheduling High-Volume Systems
• Involves allocating workloads to specific
  centres and determining the sequence in which the
  operations are to be performed.
• High volume systems are frequently referred to as
  flow systems. Examples
• products - autos, radios, televisions, computers,
  appliances
• processes - petroleum refining, sugar refining,
  mining, manufacture of fertilizers
• services - cafeteria lines, news broadcasts, mass
  inoculations
• Major aspect of the design of high volume systems
  is line balancing. Some of the problems
  associated with scheduling flow systems
• few systems completed devoted to a single product
  - each change involves slightly different inputs.
  This amounts to scheduling the inputs, the
  process and the outputs.
• disruptions to the system that generate less than
  the desired amount of output.

3

• Factors That Affect the Success of High Volume
  Systems
• 1. Process and product design
• 2. Preventative maintenance.
• 3. Rapid repair when breakdowns occur.
• 4. Optimal product mixes.
• 5. Minimization of quality problems.
• 6. Reliability and timing of supplies.

4

• Scheduling of Intermediate-Volume Systems
• Distinguished from high-volume systems by lower
  volumes and, therefore, it is more economical to
  process these items intermittently.
• Two basic questions
• 1. What run size to use?
• 2. What sequence should jobs be processed?
• Run size to minimize setup and inventory costs
• This approach works well with a single product,
  but less well for multiple products because setup
  costs can be dependent on the order of processing.

(2DS) / H1/2
Qo
p / (p - u)1/2
x
5

• A second approach is to use runout time. This
  concept is given by
• Runout time Current inventory / Demand rate
• Runout time indicates how long it will be before
  a given item stocks out.
• Product A has a runout time of 4.0 weeks, product
  B has a runout time of 1.2 weeks and product C
  has a runout time of 2.5 weeks. Therefore, the
  processing order would be B-C-A.

Inventory Demand Runout Time Product
(units) (units/week) (weeks)
A 400 divided by 100
4.0 B 120 divided by
100 1.2 C 50
divided by 20 2.5
6

• Scheduling Low-Volume Systems
• Different from high- and intermediate-volume
  systems because
• products are made to order
• orders differ in terms of
• processing requirements
• materials needed
• processing time
• processing sequence and setups
• Two basic issues for schedulers
• 1. How to distribute the workload among centres?
  The loading problem!
• 2. What job processing sequence to use? The
  sequencing problem!
• Loading - the assignment of jobs to work centres.
  Two main approaches to loading
• 1. Gantt charts
• 2. Assignment method
• Sequencing - order in which jobs are assigned

7

• Loading
• 1. Gantt charts - designed to organize and
  clarify the actual or intended use of resources
  in a time framework. In most cases, a time scale
  is represented horizontally, resources to be
  scheduled are listed vertically and the use of
  resources is reflected in the body of the chart.
  Types of Gantt charts include
• a. Load chart - shows loading and idle times for
  a group of machines or a list of departments.

Gantt load chart
Work Centre
Mon.
Tue.
Wed.
Thur.
Fri.
1
Job 3
Job 4
Job 3
Job 7
2
3
Job 1
Job 6
Job 7
4
Job 10
Processing
Centre not available
8
b. Schedule chart - used to monitor the progress
of jobs
Stage
1
2
3
4
5
6
Design

Prototype

Coding

Testing

Manufacture

Scheduled

Actual progress
9

b. Schedule chart - monitors the progress of
jobs. Vertical axis shows the orders or jobs in
progress, and the horizontal axis shows
time.
Gantt schedule chart
Work Centres
Mon.
Tue.
Wed.
Thur.
Fri.
Sat.
1. Machining
D
E
2. Fabrication
C
D
3. Assembly
B
C
D
E
4. Test
B
D
4. Packaging
A
B
C
Actual job progress on plan
Planned job duration
Nonproductive work - repairs, changeovers, etc.
10

• 2. Assignment method - a special-purpose linear
  programming model that is useful in situations
  that call for assigning tasks or other work
  requirements to resources.

Using VAM to solve machine scheduling
Machine
A
B
C
D
Row difference
Job
8
L
2
6
2
4
1
L
1/3
6
7
11
10
2
L
2/1
3
5
7
6
3
L
4
5
10
12
9
4
2
1/2
5
2/3/4
Column difference
The optimal solution is to assign job 1 to
machine C, job 2 to machine B, job 3 to machine
D and job 4 to machine A
11

• Sequencing
• When a number of jobs are waiting for processing,
  priority rules may be used to select the order in
  which the jobs will be processed. Some common
  priority rules
• FCFS (first come, first served) - jobs are
  processed in the order they arrive at a machine
  or work centre.
• SPT (shortest processing time) - jobs are
  processed according to processing time at a
  machine or work centre, shortest job first.
• DD (due date) - jobs are processed according to
  the due date, earliest due date first.
• CR (critical ratio) - jobs are processed
  according to smallest ratio of due date top
  processing time.
• 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.
• The effectiveness of any given sequence can be
  judged by one of three measures
• 1. Average completion time
• 2. Average job lateness
• 3. Average number of jobs at a work centre

12
Processing times (including setup times) and due
dates for six jobs waiting to be processed at a
work centre are given in the following table.
Determine the sequence of processing according to
each of these rules a. FCFS b. SPT c. DD d.
CR Processing Due date Job time (days)
(days) A 2 7 B
8 16 C 4 4 D
10 17 E 5 15 F
12 18 41 Assume jobs
arrived in the order shown.
Sequencing - Illustration 1
13
Sequencing - Illustration 1 Solution for
First Come First Served
The FCFS sequence is simply A-B-C-D-E-F. The
measures of effectiveness are (1) Average
completion time 120 / 6 20 days (2) Average
job lateness 54 / 6 9 days (3) Average
number of jobs at the work centre 120 / 41
2.93
(1) (2) (3) (2) - (3) Job
Processing Flow
Due Days Sequence Time
Time Date
Late A 2 2 7 0 B 8
10 16 0 C 4 14 4 10
D 10 24 17 7
E 5 29 15 14
F 12 41 18 23
41 120 54
14
Sequencing - Illustration 1 Solution for
Shortest Processing Time
The SPT sequence is A-C-E-B-D-F. The measures of
effectiveness are (1) Average completion time
108 / 6 18 days (2) Average job lateness 40
/ 6 6.67 days (3) Average number of jobs at
the work centre 108 / 41 2.63
(1) (2) (3) (2) - (3) Job
Processing Flow
Due Days Sequence Time
Time Date
Late A 2 2 7 0 C 4
6 4 2 E 5 11 15 0
B 8 19 16 3
D 10 29 17 12
F 12 41 18 23
41 108 40
15
Sequencing - Illustration 1 Solution for Due
Date
The DD sequence is C-A-E-B-D-F. The measures of
effectiveness are (1) Average completion time
110 / 6 18.33 days (2) Average job lateness
38 / 6 6.33 days (3) Average number of jobs at
the work centre 110 / 41 2.68
(1) (2) (3) (2) - (3) Job
Processing Flow
Due Days Sequence Time
Time Date
Late C 4 4 4 0 A 2
6 7 0 E 5 11 15 0
B 8 19 16 3
D 10 29 17 12
F 12 41 18 23
41 110 38
16
Sequencing - Illustration 1 Solution for
Critical Ratio
The CR sequence is C-F-D-B-E-A. The measures of
effectiveness are (1) Average completion time
160 / 6 26.67 days (2) Average job lateness
85 / 6 14.17 days (3) Average number of jobs
at the work centre 160 / 41 3.90
(1) (2) (3)
(4) (3) - (4) Job Critical
Processing Flow
Due Days Sequence
Ratio Time Time
Date Late
C 1.0 4 4
4 0 F 1.5 12
16 18 0 D
1.7 10 26 17
9 B 2.0 8
34 16 18 E 3.0
5 39 15 24
A 3.5 2 41
7 34 41
160 85
17
Sequencing - Illustration 1 Summary and
Decision
Optimal
Average Average Average Number Completion
Lateness of Jobs at the Rule Time (days)
(days) Work Centre FCFS 20.00
9.00 2.93 SPT 18.00 6.67
2.63 DD 18.33 6.33
2.68 CR 26.67 14.17 3.90
18
Use the S / O rule to schedule the following
jobs. Note that processing time includes the
time remaining for the current and subsequent
operations. In addition, we will need to know
the number of operations remaining, the current
one. Remaining Remaining
Processing Due date Number of Job time
(days) (days) Operations A 4
14 3 B 16 32
6 C 8 8 5
D 20 34 2 E
10 30 4 F 18
30 2 76 Assume jobs arrived
in the order shown.
Sequencing - Illustration 2
19
Sequencing - Illustration 2 - Solution
(1)
(2)
(3) (4) (5) (6)
Remaining Remaining
Remaining Processing Due date
Number of Job time (days)
(days) Slack Operations
Ratio Rank A 4
14 10 3 3.33
3 B 16 32
16 6 2.67
2 C 8 8
0 5 0 1
D 20 34
14 2 7.00 6 E
10 30 20 4
5.00 4 F 18
0 12 2
6.00 5
(2) - (1)
(3) / (4)
The indicated sequence (see column 6) is
C-B-A-E-F-D
20
Scheduling - Additional Illustration 1
The following table contains information
concerning four jobs that are awaiting processing
at a work centre. a. Sequence the
jobs using (1) FCFS, (2) SPT, (3) DD and (4) CR.
Assume the list is by order of arrival. b. For
each of the methods in part a, determine (1) the
average completion time, (2) the average
lateness and (3) the average number of jobs at
the work centre. c. Is one method superior to
the others? Explain.
Job Time Due Date Job (days)
(days) A 14 7 B
10 16 C 7 4 D
6 17
21
Scheduling - Additional Illustration 2
The following table shows orders to be processed
at a machine shop as of 8 a.m. Monday. The jobs
have different operations they must go through.
Processing times are in days. Jobs are listed in
order of arrival. a. Determine the
processing sequence at the first work centre
using each of the following rules (1) FCFS
and (2) S / O. b. Compute the effectiveness of
each rule using each of these measures (1) the
average completion time, (2) the average lateness
and (3) the average number of jobs at the work
centre. c. Is one method superior to the other?
Explain.
Processing Remaining Time Due
Date Number of Job (days)
(days) Operations A 8 20
2 B 10 18 4 C
5 25 5 D 11
17 3 E 9 35
4
22
Scheduling - Additional Illustration 3
Machine
A
B
C
D
Job
E
14
18
20
17
1
18
14
15
19
16
2
17
12
16
15
14
3
17
11
13
14
12
4
14
5
10
16
15
14
13
Use the assignment method to obtain a plan that
will minimize the processing costs in the above
table under these conditions a. The combination
2-D is undesirable. b. The combinations 1-A and
2-D are undesirable.