Chapter 14

© 2007 Pearson Education
SchedulingScheduling
Chapter 16Chapter 16

How Scheduling
fits the Operations Management
Philosophy
Operations As a Competitive
Weapon
Operations Strategy
Project Management Process Strategy
Process Analysis
Process Performance and Quality
Constraint Management
Process Layout
Lean Systems
Supply Chain Strategy
Location
Inventory Management
Forecasting
Sales and Operations Planning
Resource Planning
Scheduling

Air New Zealand
 Flight and crew scheduling is a complex process.
 Scheduling begins with a five-year market plan.
 This general plan is further refined to a three-year
plan, and put into an annual budget in which flight
segments have specific departure and arrival times.
 Crew availability must be matched to the flight
schedule. Two types of crews–pilots and
attendants–each comes with its own set of
constraints.
 Sophisticated optimization models are used to
design generic minimum-cost schedules.

Scheduling
 Scheduling: The allocation of resources over time
to accomplish specific tasks.
 Demand scheduling: A type of scheduling
whereby customers are assigned to a definite time
for order fulfillment.
 Workforce scheduling: A type of scheduling that
determines when employees work.
 Operations scheduling: A type of scheduling in
which jobs are assigned to workstations or
employees are assigned to jobs for specified time
periods.

Performance Measures
 Job flow time: The amount of time a job spends in the
service or manufacturing system. Also referred to as
throughput time or time spent in the system, including service.
 Makespan: The total amount of time required to complete a
group of jobs.
 Past due (Tardiness): The amount of time by which a job
missed its due date or the percentage of total jobs processed
over some period of time that missed their due dates.
 Work-in-process (WIP) inventory: Any job that is waiting
in line, moving from one operation to the next, being delayed,
being processed, or residing in a semi-finished state.
 Total inventory: The sum of scheduled receipts and on-
hand inventories.
 Utilization: The percentage of work time that is
productively spent by an employee or machine.

Gantt Charts
 Gantt chart: Used as a tool to monitor the
progress of work and to view the load on
workstations.
 The chart takes two basic forms: (1) the job or activity
progress chart, and (2) the workstation chart.
 The Gantt progress chart graphically displays the
current status of each job or activity relative to its
scheduled completion date.
 The Gantt workstation chart shows the load on
the workstations and the nonproductive time.

Gantt Progress ChartGantt Progress Chart
Plymouth
Ford
Pontiac
Job 4/20 4/22 4/23 4/24 4/25 4/264/214/17 4/18 4/19
CurrentCurrent
datedate
Scheduled activity time
Actual progress
Start activity
Finish activity
Nonproductive time
Gantt Progress Chart for an Auto Parts Company

Gantt Workstation ChartGantt Workstation Chart
Gantt Workstation Chart for Hospital Operating Rooms

Scheduling
Customer Demand
 Three methods are commonly used to schedule
customer demand:
(1) Appointments assign specific times for service
to customers.
(2) Reservations are used when the customer
actually occupies or uses facilities associated
with the service.
(3) Backlogs:
• The customer is given a due date for the
fulfillment a product order, or
• Allow a backlog to develop as customers arrive
at the system. Customers may never know
exactly when their orders will be fulfilled

Scheduling Employees
 Rotating schedule: A schedule that rotates
employees through a series of workdays or hours.
 Fixed schedule: A schedule that calls for each
employee to work the same days and hours each
week.
 Constraints: The technical constraints imposed on
the workforce schedule are the resources provided
by the staffing plan and the requirements placed on
the operating system.
 Other constraints, including legal and behavioral
considerations, also can be imposed.

DayDay MM TT WW ThTh FF SS SuSu
Number of employeesNumber of employees 66 44 88 99 1010 33 22
Required employeesRequired employees
The Amalgamated Parcel Service is open 7 days
a week. The schedule of requirements is:
The manager needs a workforce schedule that provides two
consecutive days off and minimizes the amount of total slack capacity.
To break ties in the selection of off days, the scheduler gives
preference to Saturday and Sunday if it is one of the tied pairs. If not,
she selects one of the tied pairs arbitrarily.
Workforce Scheduling
Example 16.1

Number of employeesNumber of employees 66 44 88 99 10*10* 33 22
EmployeeEmployee 11 XX XX XX XX XX
Example 16.1 Steps 1 & 2
Step 1. Find all the pairs of consecutive days that exclude the
maximum daily requirements. Select the unique pair that has the lowest
total requirements for the 2 days.
Friday contains the maximum requirements (10), and the pair S–Su has
the lowest total requirements. Therefore, Employee 1 is scheduled to
work Monday through Friday.
Step 2. If a tie occurs, choose one of the tied pairs or ask the employee
to make a choice.

Step 3. Subtract the requirements satisfied by the Employee 1 from the
net requirements for each day the employee is to work and repeat step
one.
Again the pair S–Su has the lowest total requirements. Therefore,
Employee 2 is scheduled to work Monday through Friday.
RequirementsRequirements 55 33 77 88 9*9* 33 22
Example 16.1 Step 3

RequirementRequirement 55 33 77 88 9*9* 33 22
Example 16.1 Step 4
Step 4. Repeat steps 1 through 3 until all the requirements have been
satisfied. After Employees 1, 2, and 3 have reduced the requirements,
the pair with the lowest requirements changes, and Employee 4 will be
scheduled for Wednesday through Sunday.

Example 16.1 Step 4 continued

EmployeeEmployee 11 XX XX XX XX XX offoff offoff
EmployeeEmployee 44 offoff offoff XX XX XX XX XX
EmployeeEmployee 99 offoff XX XX XX XX XX offoff
Final ScheduleFinal Schedule
Example 16.1

MM TT WW ThTh FF SS SuSu
EmployeeEmployee 99 offoff XX XX XX XX XX offoff
Example 16.1 Final Schedule
Capacity, C 7 8 10 10 10 3 2 50
Requirements, R 6 4 8 9 10 3 2 42
Slack, C – R 1 4 2 1 0 0 0 8
Total
Final ScheduleFinal Schedule

Operations Scheduling
 Operations schedules are short-term plans
designed to implement the master production
schedule.
 Operations scheduling focuses on how best to use
existing capacity.
 Often, several jobs must be processed at one or more
workstations. Typically, a variety of tasks can be
performed at each workstation.
 Job shop: A firm that specializes in low- to
medium-volume production and utilizes job or batch
processes.
 Flow shop: A firm that specializes in medium- to
high-volume production and utilizes line or
continuous processes.

ShippingDepartmentShippingDepartment
Manufacturing ProcessManufacturing Process
RawMaterialsRawMaterials
Legend:Legend:
Batch of partsBatch of parts
WorkstationWorkstation

Job Shop Dispatching
 Dispatching: A method of generating schedules in job
shops whereby the decision about which job to process next
is made using simple priority rules whenever the workstation
becomes available for further processing.
 Priority sequencing rules: The rules that specify the
job processing sequence when several jobs are waiting in line
at a workstation.
 Critical ratio (CR): A ratio that is calculated by dividing
the time remaining until a job’s due date by the total shop time
remaining for the job.
CR = (Due date – Today’s date)/Total shop time remaining(Due date – Today’s date)/Total shop time remaining
 Total Shop Time = Setup, processing, move, and expected
waiting times of all remaining operations, including the operation
being scheduled.

 Earliest due date (EDD): A priority sequencing
rule that specifies that the job with the earliest due
date is the next job to be processed.
 First-come, first-served (FCFS): A priority
sequencing rule that specifies that the job arriving
at the workstation first has the highest priority.
 Shortest processing time (SPT): A priority
sequencing rule that specifies that the job requiring
the shortest processing time is the next job to be
processed.

 Slack per remaining operations (S/RO): A
priority sequencing rule that determines
priority by dividing the slack by the number
of operations that remain, including the one
being scheduled.
S/RO = ((Due dateS/RO = ((Due date –– Today’s date) – Total shop time remaining)Today’s date) – Total shop time remaining)
Number of operations remainingNumber of operations remaining

 Single-dimension rules: A set of rules such as
FCFS, EDD, and SPT, that bases the priority of a
job on a single aspect of the job, such as arrival
time at the workstation, the due date, or the
processing time.
 Priority rules, such as CR and S/RO, incorporate
information about the remaining workstations at
which the job must be processed. We call these
rules multiple-dimension rules.
 Multiple-dimension rules: A set of rules that apply
to more than one aspect of a job.
Scheduling Jobs for
One Workstation

Five engine blocks are waiting for processing. The processing times
have been estimated. Expected completion times have been agreed.
The table shows the situation as of Monday morning. Customer
pickup times are measured in business hours from Monday morning.
Determine the schedule by using the EDD rule and then the SPT rule.
Calculate the average hours early, hours past due, WIP inventory, and
total inventory for each method.
If low job flow times and WIP inventories are critical, which rule should
be chosen?
Example 16.2Example 16.2
Single-Dimension Rule SequencingSingle-Dimension Rule Sequencing

8 + 14 + 17 + 32 + 448 + 14 + 17 + 32 + 44
4444
Average hours early = 0.6 hourAverage hours early = 0.6 hour
JobJob ScheduledScheduled ActualActual
EngineEngine ProcessingProcessing FlowFlow CustomerCustomer CustomerCustomer HoursHours
BlockBlock BeginBegin TimeTime TimeTime PickupPickup PickupPickup HoursHours PastPast
SequenceSequence WorkWork (hr)(hr) (hr)(hr) TimeTime TimeTime EarlyEarly DueDue
RangerRanger 88 1010
ExplorerExplorer 66 1212
Econoline 150Econoline 150 33 1818
BroncoBronco 1515 2020
ThunderbirdThunderbird 1212 2222
00 ++ == 88 1010 22
1717 ++ == 3232 3232 1212
88 ++ == 1414 1414 22
1414 ++ == 1717 1818 11
3232 ++ == 4444 4444 2222
Single-Dimension RuleSingle-Dimension Rule –– EDDEDD
Average job flow time = 23 hoursAverage job flow time = 23 hours
Average hours past due = 7.2 hoursAverage hours past due = 7.2 hours Average WIP = 2.61 blocksAverage WIP = 2.61 blocks
Average total inventory = 2.68 engine blocksAverage total inventory = 2.68 engine blocksAverage total inventory =Average total inventory =
10 + 14 + 18 + 32 + 4410 + 14 + 18 + 32 + 44
4444

3 + 9 + 17 + 29 + 443 + 9 + 17 + 29 + 44
4444
Average hours early = 3.6 hourAverage hours early = 3.6 hour
JobJob ScheduledScheduled ActualActual
EngineEngine ProcessingProcessing FlowFlow CustomerCustomer CustomerCustomer HoursHours
BlockBlock BeginBegin TimeTime TimeTime PickupPickup PickupPickup HoursHours PastPast
SequenceSequence WorkWork (hr)(hr) (hr)(hr) TimeTime TimeTime EarlyEarly DueDue
RangerRanger 88 1010
ExplorerExplorer 66 1212
Econoline 150Econoline 150 33 1818
BroncoBronco 1515 2020
ThunderbirdThunderbird 1212 2222
00 ++ == 33 1818 1515
1717 ++ == 2929 2929 77
88 ++ == 99 1212
1414 ++ == 1717 1717 33 77
2929 ++ == 4444 4444 2424
Single-Dimension RuleSingle-Dimension Rule –– SPTSPT
Average job flow time =Average job flow time = 20.4 hours20.4 hours
Average hours past due = 7.6 hoursAverage hours past due = 7.6 hours Average WIP = 2.32 blocksAverage WIP = 2.32 blocks
Average total inventory = 2.73 engine blocksAverage total inventory = 2.73 engine blocksAverage total inventory =Average total inventory =
18 + 12 + 17 + 20 + 4418 + 12 + 17 + 20 + 44
4444
Econoline 150
Explorer
Ranger
Thunderbird
Bronco
0
3
9
17
29
3
6
8
12
15
18
12
10
22
20

Comparing the
EDD and SPT Rules
EDD SPT
Average job flow time 23.00 20.40
Average hours early 0.60 3.60
Average hours past due 7.20 7.60
Average WIP 2.61 2.32
Average total inventory 2.68 2.73
Using the previous example, a comparison of the EDD and
SPT sequencing is shown below.
• The SPT schedule has a lower average job flow time and lower WIP inventory.
• The EDD schedule has better customer service, (average hours past due) and
lower maximum hours past due.
• EDD also has a lower total inventory because fewer hours were spent waiting
for customers to pick up their engine blocks after they had been completed.

Multiple-Dimension Rule –Multiple-Dimension Rule – CRCR
11 2.32.3 1515 1010 6.16.1 2.462.46
22 10.510.5 1010 22 7.87.8 1.281.28
33 6.26.2 2020 1212 14.514.5 1.381.38
44 15.615.6 88 55 10.210.2 .78.78
OperationOperation TimeTime
Time atTime at RemainingRemaining Number ofNumber of
EngineEngine to Due Dateto Due Date OperationsOperations Shop TimeShop Time
JobJob Lathe (hr)Lathe (hr) (Days)(Days) RemainingRemaining RemainingRemaining CRCR S/ROS/RO
CRCR ==
Time remaining to due dateTime remaining to due date
Shop time remainingShop time remaining

11 2.32.3 1515 1010 6.16.1 2.462.46 0.890.89
22 10.510.5 1010 22 7.87.8 1.281.28 1.101.10
33 6.26.2 2020 1212 14.514.5 1.381.38 0.460.46
44 15.615.6 88 55 10.210.2 .78.78 – 0.44– 0.44
S/ROS/RO ==
Time remaining to due dateTime remaining to due date –– Shop time remainingShop time remaining
Number of operations remainingNumber of operations remaining
Multiple-Dimension Rule –Multiple-Dimension Rule – S/ROS/RO

11 2.32.3 1515 1010 6.16.1 2.462.46 0.890.89
22 10.510.5 1010 22 7.87.8 1.281.28 1.101.10
33 6.26.2 2020 1212 14.514.5 1.381.38 0.460.46
44 15.615.6 88 55 10.210.2 .78.78 – 0.44– 0.44
CR SequenceCR Sequence = 4= 4 – 2 – 3 – 1– 2 – 3 – 1
S/RO SequenceS/RO Sequence = 4= 4 – 3 – 1 – 2– 3 – 1 – 2
CR SequenceCR Sequence ==
Comparing theComparing the
CRCR andand S/ROS/RO RulesRules

Priority Rule Summary
FCFS = 1 – 2 – 3 – 4
SPT = 1 – 3 – 2 – 4
EDD = 4 – 2 – 1 – 3
CR = 4 – 2 – 3 – 1
S/RO = 4 – 3 – 1 – 2
Avg Flow Time 17.175 16.100 26.175 27.150 24.025
Avg Early Time 3.425 6.050 0 0 0
Avg Past Due 7.350 8.900 12.925 13.900 10.775
Avg WIP 1.986 1.861 3.026 3.129 2.777
Avg Total Inv 2.382 2.561 3.026 3.129 2.777
Shortest Slack per
Processing Earliest Critical Remaining
FCFS Time Due Date Ratio Operation
• The S/RO rule is better than the EDD rule
and the CR rule but it is much worse than
the SPT rule and the FCFS rule for this
example.
• S/RO has the advantage of allowing
schedule changes when due dates
change. These results cannot be
generalized to other situations because
only four jobs are being processed.

Scheduling Jobs for
Multiple Workstations
 Priority sequencing rules can be used to schedule more than
one operation. Each operation is treated independently.
 Identifying the best priority rule to use at a particular operation
in a process is a complex problem because the output from one
process becomes the input for another.
 Computer simulation models are effective tools to determine
which priority rules work best in a given situation.
 When a workstation becomes idle, the priority rule is applied to
the jobs waiting for that operation, and the job with the highest
priority is selected.
 When that operation is finished, the job is moved to the next
operation in its routing, where it waits until it again has the
highest priority.

Johnson’s Rule
 Johnson’s rule: A procedure that minimizes makespan
when scheduling a group of jobs on two workstations.
 Step 1. Find the shortest processing time among the jobs not
yet scheduled. If two or more jobs are tied, choose one job
arbitrarily.
 Step 2. If the shortest processing time is on workstation 1,
schedule the corresponding job as early as possible. If the
shortest processing time is on workstation 2, schedule the
corresponding job as late as possible.
 Step 3. Eliminate the last job scheduled from further
consideration. Repeat steps 1 and 2 until all jobs have been
scheduled.

Eliminate M3 from consideration. The next shortest time
is M2 at Workstation 1, so schedule M2 first.
Eliminate M5 from consideration. The next shortest time is
M1 at workstation #1, so schedule M1 next.
Eliminate M1 and the only job remaining to be
scheduled is M4.
Example 16.5
Johnson’s RuleJohnson’s Rule at theat the Morris Machine Co.Morris Machine Co.
Time (hr)Time (hr)
MotorMotor Workstation 1Workstation 1 Workstation 2Workstation 2
M1M1 1212 2222
M2M2 44 55
M3M3 55 33
M4M4 1515 1616
M5M5 1010 88
Sequence =Sequence = M1M1M2M2 M3M3M4M4 M5M5
Shortest time is 3 hours at workstation 2, so
schedule job M3 last.
Eliminate M2 from consideration. The next shortest time is
M5 at workstation #2, so schedule M5 next to last.

Workstation
M2
(4)
M1
(12)
M4
(15)
M5
(10)
M3
(5)
Idle—available
for further work
0 5 10 15 20 25 30
Day
35 40 45 50 55 60 65
Idle2 M2
(5)
M1
(22)
M4
(16)
M5
(8)
M3
(3)Idle
1
Gantt Chart for the Morris Machine Company Repair Schedule
The schedule minimizes the idle time of workstation 2
and gives the fastest repair time for all five motors.
No other sequence will produce a lower makespan.
Example 16.5
Johnson’s RuleJohnson’s Rule at theat the Morris Machine Co.Morris Machine Co.

Labor-limited Environments
 The limiting resource thus far has been the number of
machines or workstations available. A more typical constraint
is the amount of labor available.
 Labor-limited environment: An environment in which
the resource constraint is the amount of labor available, not
the number of machines or workstations.
1. Assign personnel to the workstation with the job that has
been in the system longest.
2. Assign personnel to the workstation with the most jobs
waiting for processing.
3. Assign personnel to the workstation with the largest
standard work content.
4. Assign personnel to the workstation with the job that has
the earliest due date.

Linking Operations
Scheduling to the Supply Chain
 Advanced planning and scheduling (APS)
systems: Systems that seek to optimize resources across
the supply chain and align daily operations with strategic
goals. Four characteristics of these systems are:
1. Demand Planning. This capability enables companies in a
supply chain to share demand forecasts.
2. Supply Network Planning. Optimization models based on
linear programming can be used to make long-term decisions.
3. Available-to-Promise. Firms can use this capability to promise
delivery to customers by checking the availability of
components and materials at its suppliers.
4. Manufacturing Scheduling. This module attempts to
determine an optimal grouping and sequencing of
manufacturing orders based on detailed product attributes,
production line capacities, and material flows.

 The Food Bin grocery store operates 24 hours per day, 7
days per week. At the end of the month, they calculated the
average number of checkout registers that should be open
during the first shift each day. Results showed peak needs on
Saturdays and Sundays.
1. Develop a schedule that covers all requirements while giving two
consecutive days off to each clerk. How many clerks are needed?
2. Plans can be made to use the clerks for other duties if slack or idle
time resulting from this schedule can be determined. How much idle
time will result from this schedule, and on what days?
Solved Problem 1Solved Problem 1

 The Neptune’s Den Machine Shop specializes in overhauling outboard
marine engines. Currently, five engines with varying problems are
awaiting service. The best estimates for the labor times involved and
the promise dates (in number of days from today) are shown in the
following table. Customers usually do not pick up their engines early.
Develop separate schedules using SPT and then EDD rules. Compare them
using average job flow time, % of past due jobs, and maximum past due days.
Calculate average WIP inventory (in engines) and average total inventory.

Solved Problem 2
SPT
EDD

SPT EDD
Average job flow time 9.80 15.20
% of past due jobs 40% 60%
Maximum past due days 11 7
Average WIP inventory 2.13 3.30
Average total inventory 3.52 3.52
Solved Problem 2

Cleanup of chemical waste storage basins involves two
operations. Operation 1: Drain and dredge basin. Operation 2:
Incinerate materials. Management estimates that each
operation will require the following amounts of time (in days):
Find a schedule that minimizes the makespan. Calculate the
average job flow time of a storage basin through the two operations.
What is the total elapsed time for cleaning all 10 basins?

Dredge Incinerate
A 3 1
B 4 4
C 3 2
D 6 1
E 1 2
F 3 6
G 2 4
H 1 1
I 8 2
J 4 8
Four jobs are tied for the shortest process time: A, D, E, and H. (E and H
are tied for first place, while A and D are tied for last place.) We arbitrarily
choose to start with basin E
E H G F B J I C D A

Dredge E H G F B J I C D A
Incinerate E H G F B J I C D A
Storage basin
E H G F B J I C D A
The Gantt machine chart for this schedule

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