CG3500 - Production Planning
Lecture 9
College of the North Atlantic, Fall 2018
Max Erler
Important (tentative) dates:

Quiz 1: 04-Oct-2018

Quiz 2: 09-Nov-2018

Term Project: 26-Nov-2018

Final Exam: 12-Dec-2018
Production Scheduling:
Air Canada
 About 10% of Air Canada’s flights are disrupted per year, half
because of weather
 The ripple effect throughout the system
 Cost is millions of dollars in lost revenue, overtime pay, food
and lodging vouchers
 The Operations Control Centre at Toronto’s Pearson Airport
adjusts to changes, notifies passengers, and keeps flights
flowing
 Mathematical programming to anticipate and react to potential
problems
Static programming
Dynamic programming (If – Then scenarios)
Short-Term Scheduling
Short-term schedules translate capacity decisions,
aggregate planning, and master schedules into job
sequences and specific assignments of personnel,
materials, and machinery
Figure 15.1
Scheduling Decisions
Importance of Short-Term Scheduling
 Effective and efficient scheduling can be a
competitive advantage
 Faster movement of goods through a facility
means better use of assets and lower costs
 Additional capacity resulting from faster
throughput improves customer service through
faster delivery
 Good schedules result in more dependable
deliveries
Scheduling Issues
 Scheduling deals with the timing of
operations
 The task is the allocation and prioritization
of demand
 Significant issues are
 The type of scheduling, forward or backward
 The criteria for priorities
Forward and Backward Scheduling
 Forward scheduling starts as soon as the
requirements are known
 Produces a feasible schedule though it
may not meet due dates
 Frequently results in
buildup of work-inprocess inventory
Now
Due
Date
Forward and Backward Scheduling
 Backward scheduling begins with the due
date and schedules the final operation
first
 Schedule is produced by working
backwards though the processes
 Resources may not
be available to
accomplish the
schedule
Now
Due
Date
Forward and Backward Scheduling
 Backward scheduling begins with
the due date and schedules the final
operation first
 Schedule is produced by working
backwards though the processes
 Resources may not
be available to
accomplish the
schedule
Now
Due
Date
Responsibilities of Production Control
Department
• Loading
– Allocate orders to workers and machines, worker
and machines to work centers etc.
• Sequencing
– Release work orders to shop & issue dispatch lists
for individual machines
• Monitoring
– Maintain progress reports on each job until it is
complete
Scheduling Criteria
1. Minimize completion time
2. Maximize utilization of facilities
3. Minimize work-in-process (WIP)
inventory
4. Minimize customer waiting time
Optimize the use of resources so
that production objectives are met
Scheduling
 Schedule incoming orders without
violating capacity constraints
 Check availability of tools and materials
before releasing an order
 Establish due dates for each job and
check progress
 Check work in progress
 Provide feedback
 Provide work efficiency statistics and
monitor times
Gantt Charts
 Load chart shows the loading and
idle times of departments,
machines, or facilities
 Displays relative workloads over
time
 Schedule chart monitors jobs in
process
 All Gantt charts need to be updated
frequently to account for changes
Gantt Load Chart Example
Day
Work
centre
Metalworks
Monday
Tuesday
Job 349
Job 349
Job 408
Painting
Processing
Thursday
Friday
Job 350
Mechanical
Electronics
Wednesday
Job 408
Job 349
Job 295
Job 408
Unscheduled
Job 349
centre not available
Figure 15.3
Gantt Schedule Chart Example
Job
Day
1
Day Day
2
3
Day Day Day Day Day
4
5
6
7
8
A
B
Start of an
activity
End of an
activity
Scheduled
activity time
allowed
Actual work
progress
Maintenance
Nonproduction
time
C
Point in time
when chart is
reviewed
Now
Figure 15.4
Assignment Method
 A special class of linear
programming models that assigns
tasks or jobs to resources
 Objective is to minimize cost or
time
 Only one job (or worker) is
assigned to one machine (or
project)
Assignment Method
 Build a table of costs or time
associated with particular
assignments
Job
R-34
A
$11
S-66
T-50
$ 8
$ 9
Typesetter
B
$14
$10
$12
C
$ 6
$11
$ 7
Assignment Method
1. Create zero opportunity costs by
repeatedly subtracting the lowest costs
from each row and column
2. Draw the minimum number of vertical
and horizontal lines necessary to cover
all the zeros in the table. If the number
of lines equals either the number of
rows or the number of columns,
proceed to step 4. Otherwise proceed to
step 3.
Assignment Method
3. Subtract the smallest number not
covered by a line from all other
uncovered numbers. Add the same
number to any number at the
intersection of two lines. Return to
step 2.
4. Optimal assignments are at zero
locations in the table. Select one, draw
lines through the row and column
involved, and continue to the next
assignment.
Assignment Example
Create zero
opportunity costs
by repeatedly
subtracting the
lowest costs from
each row and
column
Typesetter
Job
R-34
S-66
T-50
Step 1a - Rows
B
C
$11
$ 8
$ 9
$14
$10
$12
$ 6
$11
$ 7
Step 1b - Columns
Typesetter
Typesetter
A
Job
R-34
S-66
T-50
A
$ 5
$ 0
$ 2
B
$ 8
$ 2
$ 5
C
$ 0
$ 3
$ 0
Job
R-34
S-66
T-50
A
B
C
$ 5
$ 0
$ 2
$ 6
$ 0
$ 3
$ 0
$ 3
$ 0
Draw the minimum
number of vertical and
horizontal lines necessary
to cover all the zeros in
the table. If the number of
lines equals either the
number of rows or the
number of columns,
proceed to step 4.
Otherwise proceed to step
3.
Subtract the smallest
number not covered by a
line from all other
uncovered numbers.
Add the same number to
any number at the
intersection of two lines.
Return to step 2.
Step 2 - Lines
Typesetter
Job
R-34
S-66
T-50
A
B
C
$ 5
$ 0
$ 2
$ 6
$ 0
$ 3
$ 0
$ 3
$ 0
The smallest uncovered
number is 2 so this is
subtracted from all other
uncovered numbers and
added to numbers at the
intersection of lines
Step 3 - Subtraction
Typesetter
Because only two lines
are needed to cover all
the zeros, the solution
is not optimal
Job
R-34
S-66
T-50
A
B
C
$ 3
$ 0
$ 0
$ 4
$ 0
$ 1
$ 0
$ 5
$ 0
Optimal assignments are at
zero locations in the table.
Select one, draw lines through
the row and column involved,
and continue to the next
assignment.
Assignment Example
Step 2 - Lines
Typesetter
Job
R-34
S-66
T-50
A
B
C
$ 3
$ 0
$ 0
$ 4
$ 0
$ 1
$ 0
$ 5
$ 0
Because three lines are
needed, the solution is
optimal and
assignments can be
made
Start by assigning R-34 to
worker C as this is the only
possible assignment for
worker C. Job T-50 must
go to worker A as worker C
is already assigned. This
leaves S-66 for worker B.
Step 4 - Assignments
Typesetter
Job
R-34
S-66
T-50
A
B
C
$ 3
$ 0
$ 0
$ 4
$ 0
$ 1
$ 0
$ 5
$ 0
Assignment Example
Step 4 - Assignments
Typesetter
Typesetter
A
Job
R-34
S-66
T-50
$11
$ 8
$ 9
B
$14
$10
$12
C
$ 6
$11
$ 7
Job
R-34
S-66
T-50
A
B
C
$ 3
$ 0
$ 0
$ 4
$ 0
$ 1
$ 0
$ 5
$ 0
From the original cost table
Minimum cost = $6 + $10 + $9 = $25
Sequencing Jobs
 Specifies the order in which jobs
should be performed at work centres
 Priority rules are used to dispatch or
sequence jobs
 FCFS: First come, first served
 SPT: Shortest processing time
 EDD: Earliest due date
 LPT: Longest processing time
Comparison of
Sequencing Rules
 No one sequencing rule excels on all criteria
 SPT does well on minimizing flow time and
number of jobs in the system
 But SPT moves long jobs to the end which
may result in dissatisfied customers
 FCFS does not do especially well (or poorly)
on any criteria but is perceived as fair by
customers
 EDD minimizes maximum lateness
Critical Ratio (CR)
 An index number found by dividing the
time remaining until the due date by the
work time remaining on the job
 Jobs with low critical ratios are
scheduled ahead of jobs with higher
critical ratios
 Performs well on average job lateness
criteria
Time remaining
Due date – Today’s date
CR =
=
Workdays remaining
Work (lead) time remaining
Critical Ratio Technique
1. Helps determine the status of specific
jobs
2. Establishes relative priorities among
jobs on a common basis
3. Relates both stock and make-to-order
jobs on a common basis
4. Adjusts priorities automatically for
changes in both demand and job
progress
5. Dynamically tracks job progress
Example:

Machine shop has 5 unprocessed jobs (J1, J2, J3, J4, J5) numbers by
order they entered Bottleneck machines queue:
Job #
Process Time
Due Date
1
11
61
2
29
45
3
31
31
4
1
33
5
2
32
Using First Come First Serve (FCFS):
Sequence
Process
Time
Comp.
Time
D. Date
Tardiness
J1
11
11
61
0
J2
29
40
45
0
J3
31
71
31
40
J4
1
72
33
39
J5
2
74
32
42
Totals
268

Avg Tardiness: (121)/5 = 24.2

# Tardy Jobs: 3
121
Shortest Processing Time (SPT):
Sequence
Comp. Time
D. Date
Tardiness
J4
1
33
0
J5
3
32
0
J1
14
61
0
J2
43
45
0
J3
74
31
43
Totals
135

Avg Tardiness: (43)/5 = 8.6

# Tardy: 1
43
Earliest Due Date (EDD):
Sequence
Comp. Time
D. Date
Tardiness
J3
31
31
0
J5
33
32
1
J4
34
33
1
J2
63
45
18
J1
74
61
13
Totals
235

Avg Tardiness: (33)/5 = 6.6

# Tardy: 4
33
Critical Ratio (CR)

Set Current Time (sum of time of all
scheduled jobs so far)

Compute:
Due _ Date    Cur _ Time 

CR 
Pr._ Work _ Re maining

Model Starts with current time = 0

Current time updates after each selection
by adding scheduled Process Time to
current time
CR 
CR:
JOB
Pr.
Time
D.
Date
 Due _ Date    Cur _ Time 
CR
Pr._ Work _ Re maining
JOB
Pr.
Time
D.
Date
CR
Current Time = 31
Current Time = 0
1
11
61
5.546
1
11
61
2.727
2
29
45
1.552
2
29
45
.483
3
31
31
1.00
4
1
33
2
4
1
33
33
5
2
32
0.5
5
2
32
16
Continuing (CR)
JOB
Pr.
Time
D.
Date
CR
JOB
Proc.
Time
11
61
D. Date
Tardy
Summary
Current Time = 60
1
Comp.
Time
0.091
do last
3
31
31
31
0
2
29
60
45
15
4
1
33
-27*
4
1
61
31
30
5
2
32
-14**
5
2
63
33
30
1
11
74
32
42
*,** It is possible that the numerator will be negative
for some or all of the remaining jobs. When that
occurs it means that the job is late, and we will
assume that late jobs are automatically scheduled
next. If there is more than one late job, then the late
jobs are scheduled in SPT sequence.
Total
:
289
117
Summarizing from CR analysis:

Mean Tardiness: (117)/5 = 23.4

# Tardy: 4
Example
Taylor Machine Shop is open from 8:00 A.M. until 5:00 P.M. each weekday, plus
weekend hours as needed, the customer pickup times are measured in business
hours from the current time. Determine the schedule for the engine expert by
using
(a)
the EDD rule and
(b)
(b) the SPT rule.
For each rule, calculate the average flow time, average hours early, and average
hours past due. If average past due is most important, which rule should be
chosen?
Sequencing N Jobs on Two Machines:
Johnson’s Rule
 Works with two or more jobs that
pass through the same two
machines or work centers
 Minimizes total production time and
idle time
Johnson’s Rule
1. List all jobs and times for each work
center
2. Choose the job with the shortest activity
time. If that time is in the first work center,
schedule the job first. If it is in the second
work center, schedule the job last.
3. Once a job is scheduled, it is eliminated
from the list
4. Repeat steps 2 and 3 working toward the
center of the sequence
Johnson’s Rule Example
Job
Work centre 1
(drill press)
Work centre 2
(lathe)
A
5
2
B
3
6
C
8
4
D
10
7
E
7
12
Johnson’s Rule Example
Job
Work Centre 1
(drill press)
Work Centre 2
(lathe)
A
5
2
B
3
6
C
8
4
D
10
7
E
7
12
B E D C A
Johnson’s Rule Example
Job
Work Centre 1
(drill press)
Work Centre 2
(lathe)
A
5
2
B
3
6
C
8
4
D
10
7
E
7
12
Time
WC
1
WC
2
0
3
B
10
E
B E D C A
20
D
28
C
33
A
Johnson’s Rule Example
Job
Work Centre 1
(drill press)
Work Centre 2
(lathe)
A
5
2
B
3
6
C
8
4
D
10
7
E
7
12
Time
WC
1
0
3
10
B
E
WC
2
Time 0 1
20
5
28
D
B
3
B E D C A
C
E
7
9 10 11 12 13
B
33
A
D
17 19 21 22 2325
E
27
29
D
C
A
31
33 35
C A
Limitations of Rule-Based
Dispatching Systems
1. Scheduling is dynamic and rules
need to be revised to adjust to
changes
2. Rules do not look upstream or
downstream
3. Rules do not look beyond due
dates
Finite Capacity Scheduling
 Overcomes disadvantages of rule-based
systems by providing an interactive,
computer-based graphical system
 May include rules and expert systems or
simulation to allow real-time response to
system changes
 Initial data often from an MRP system
 FCS allows the balancing of delivery
needs and efficiency
Finite Capacity Scheduling
MRP Data
• Master
schedule
• BOM
• Inventory
Priority
rules
• Expert
systems
• Simulation
models
Interactive Finite Capacity Scheduling
• Routing files
• Work centre
information
Tooling
and other
resources
Setups and
run time
Figure 15.5
Scheduling Repetitive Facilities
 Level material use can help
repetitive facilities
 Better satisfy customer demand
 Lower inventory investment
 Reduce batch size
 Better utilize equipment and facilities
Scheduling Repetitive Facilities
 Advantages include:
1. Lower inventory levels
2. Faster product throughput
3. Improved component quality
4. Reduced floor-space requirements
5. Improved communications
6. Smoother production process
Scheduling Services
Service systems differ from manufacturing
Manufacturing
Schedules machines
and materials
Inventories used to
smooth demand
Machine-intensive and
demand may be smooth
Scheduling may be bound
by union contracts
Few social or behavioural
issues
Services
Schedule staff
Seldom maintain
inventories
Labour-intensive and
demand may be variable
Legal issues may constrain
flexible scheduling
Social and behavioural
issues may be quite
important
Scheduling Services
 Hospitals have complex scheduling
system to handle complex processes
and material requirements
 Banks use a cross-trained and flexible
workforce and part-time workers
 Retail stores use scheduling
optimization systems that track sales,
transactions, and customer traffic to
create work schedules in less time and
with improved customer satisfaction
Scheduling Services
 Airlines must meet complex FAA and
union regulations and often use linear
programming to develop optimal
schedules
 24/7 operations like police/fire
departments, emergency hot lines, and
mail order businesses use flexible
workers and variable schedules, often
created using computerized systems
Demand Management
 Appointment or reservation
systems
 FCFS sequencing rules
 Discounts or other promotional
schemes
 When demand management is not
feasible, managing capacity
through staffing flexibility may be
used
Scheduling Service Employees With
Cyclical Scheduling
 Objective is to meet staffing
requirements with the minimum
number of workers
 Schedules need to be smooth and
keep personnel happy
 Many techniques exist from simple
algorithms to complex linear
programming solutions