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Short-Term Scheduling

PowerPoint presentation to accompany

Heizer and Render

Operations Management, Eleventh Edition

Principles of Operations Management, Ninth Edition

PowerPoint slides by Jeff Heyl

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Outline

Global Company Profile:
Delta Air Lines

The Importance of Short-Term Scheduling
Scheduling Issues
Scheduling Process-Focused Facilities

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Outline - Continued

Loading Jobs

Scheduling Jobs

Finite Capacity Scheduling (FCS)

Scheduling Services

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Learning Objectives

When you complete this chapter you should be able to:

Explain the relationship between short-term scheduling, capacity planning, aggregate planning, and a master schedule
Draw Gantt loading and scheduling charts
Apply the assignment method for loading jobs

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When you complete this chapter you should be able to:

Learning Objectives

Name and describe each of the priority sequencing rules
Use Johnson’s rule
Define finite capacity scheduling
Use the cyclical scheduling technique

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Delta Airlines

About 10% of Delta’s flights are disrupted per year, half because of weather
Cost is $440 million in lost revenue, overtime pay, food and lodging vouchers
The $33 million Operations Control Center adjusts to changes and keeps flights flowing
Saves Delta $35 million per year

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Short-Term Scheduling

The objective of scheduling is to allocate and prioritize demand (generated by either forecasts or customer orders) to available facilities

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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

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Scheduling Issues

Scheduling deals with the timing of operations
The task is the allocation and prioritization of demand
Significant factors are

Forward or backward scheduling

Finite or infinite loading

The criteria for sequencing jobs

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Scheduling Decisions

TABLE 15.1	Scheduling Decisions
ORGANIZATION	MANAGERS SCHEDULE THE FOLLOWING
Delta Air Lines	Maintenance of aircraft Departure timetables Flight crews, catering, gate, ticketing personnel
Arnold Palmer Hospital	Operating room use Patient admissions Nursing, security, maintenance staffs Outpatient treatments
University of Alabama	Classrooms and audiovisual equipment Student and instructor schedules Graduate and undergraduate courses
Amway Center	Ushers, ticket takers, food servers, security personnel Delivery of fresh foods and meal preparation Orlando Magic games, concerts, arena football
Lockheed Martin Factory	Production of goods Purchases of materials Workers

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Figure 15.1

Scheduling Flow

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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-in-
process inventory

Due Date

Now

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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

Due Date

Now

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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

Forward and Backward Scheduling

Often these approaches are combined to develop a trade-off between capacity constraints and customer expectations

Due Date

Now

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Finite and Infinite Loading

Assigning jobs to work stations
Finite loading assigns work up to the capacity of the work station
All work gets done
Due dates may be pushed out
Infinite loading does not consider capacity
All due dates are met
Capacities may have to be adjusted

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Scheduling Criteria

Minimize completion time

Maximize utilization of facilities

Minimize work-in-process (WIP) inventory

Minimize customer waiting time

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Different Processes/
Different Approaches

TABLE 15.2	Different Processes Suggest Different Approaches to Scheduling
Process-focused facilities (job shops) Scheduling to customer orders where changes in both volume and variety of jobs/clients/patients are frequent Schedules are often due-date focused, with loading refined by finite loading techniques Examples: foundries, machine shops, cabinet shops, print shops, many restaurants, and the fashion industry
Repetitive facilities (assembly lines) Schedule module production and product assembly based on frequent forecasts Finite loading with a focus on generating a forward-looking schedule JIT techniques are used to schedule components that feed the assembly line Examples: assembly lines for washing machines at Whirlpool and automobiles at Ford.

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Different Processes/
Different Approaches

TABLE 15.2

Different Processes Suggest Different Approaches to Scheduling

Product-focused facilities (continuous) Schedule high volume finished products of limited variety to meet a reasonably stable demand within existing fixed capacity Finite loading with a focus on generating a forward-looking schedule that can meet known setup and run times for the limited range of products Examples: huge paper machines at International Paper, beer in a brewery at Anheuser-Busch, and potato chips at Frito-Lay

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Focus for Different
Process Strategies

Product-focused

(continuous)

Schedule finished product

Repetitive facilities (assemble lines)

Schedule modules

Process-focused

(job shops)

Schedule orders

Examples: Print shop Motorcycles Steel, Beer, Bread

Machine shop Autos, TVs Lightbulbs

Fine-dining restaurant Fast-food restaurant Paper

Typical focus of the master production schedule

Number of inputs

Number of end items

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Scheduling Process-Focused Facilities

High-variety, low volume
Production differ considerably
Schedule incoming orders without violating capacity constraints
Scheduling can be complex

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Loading Jobs

Assign jobs so that costs, idle time, or completion time are minimized
Two forms of loading
Capacity oriented
Assigning specific jobs to work centers

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Input-Output Control

Identifies overloading and underloading conditions
Prompts managerial action to resolve scheduling problems
Can be maintained using ConWIP cards that control the scheduling of batches

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Input-Output Control Example

Figure 15.2

Week Ending	6/6	6/13	6/20	6/27	7/4	7/11
Planned Input	280	280	280	280	280
Actual Input	270	250	280	285	280
Cumulative Deviation	–10	–40	–40	–35

Planned Output	320	320	320	320
Actual Output	270	270	270	270
Cumulative Deviation	–50	–100	–150	–200

Cumulative Change in Backlog

–20

–10

Work Center DNC Milling (in standard hours)

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Input-Output Control Example

Figure 15.2

Week Ending	6/6	6/13	6/20	6/27	7/4	7/11
Planned Input	280	280	280	280	280
Actual Input	270	250	280	285	280
Cumulative Deviation	–10	–40	–40	–35

Planned Output	320	320	320	320
Actual Output	270	270	270	270
Cumulative Deviation	–50	–100	–150	–200

Cumulative Change in Backlog

–20

–10

Work Center DNC Milling (in standard hours)

Explanation:

270 input,

270 output implies

0 change

Explanation:

250 input,

270 output implies

–20 change

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Input-Output Control Example

Options available to operations personnel include:

Correcting performances
Increasing capacity
Increasing or reducing input to the work center

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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

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Gantt Load Chart Example

Figure 15.3

Day

Monday

Tuesday

Wednesday

Thursday

Friday

Work Center

Metalworks

Mechanical

Electronics

Painting

Job 349

Job 408

Processing

Unscheduled

Center not available

Job 350

Job 349

Job 295

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Gantt Schedule Chart Example

Figure 15.4

Job	Day 1	Day 2	Day 3	Day 4	Day 5	Day 6	Day 7	Day 8
A
B
C

Now

Maintenance

Start of an activity

End of an activity

Scheduled activity time allowed

Actual work progress

Nonproduction time

Point in time when chart is reviewed

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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)

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Assignment Method

Build a table of costs or time associated with particular assignments

TYPESETTER
JOB	A	B	C
R-34	$11	$14	$ 6
S-66	$ 8	$10	$11
T-50	$ 9	$12	$ 7

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Assignment Method

Create zero opportunity costs by repeatedly subtracting the lowest costs from each row and column

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.

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Assignment Method

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.

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.

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Assignment Example

A B C

Job

R-34 $11 $14 $ 6

S-66 $ 8 $10 $11

T-50 $ 9 $12 $ 7

Typesetter

A B C

Job

R-34 $ 5 $ 8 $ 0

S-66 $ 0 $ 2 $ 3

T-50 $ 2 $ 5 $ 0

Typesetter

Step 1a - Rows

A B C

Job

R-34 $ 5 $ 6 $ 0

S-66 $ 0 $ 0 $ 3

T-50 $ 2 $ 3 $ 0

Typesetter

Step 1b - Columns

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Assignment Example

Because only two lines are needed to cover all the zeros, the solution is not optimal

The smallest uncovered number is 2 so this is subtracted from all other uncovered numbers and added to numbers at the intersection of lines

A B C

Job

R-34 $ 5 $ 6 $ 0

S-66 $ 0 $ 0 $ 3

T-50 $ 2 $ 3 $ 0

Typesetter

Step 2 - Lines

A B C

Job

R-34 $ 3 $ 4 $ 0

S-66 $ 0 $ 0 $ 5

T-50 $ 0 $ 1 $ 0

Typesetter

Step 3 - Subtraction

Smallest uncovered number

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Assignment Example

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.

A B C

Job

R-34 $ 3 $ 4 $ 0

S-66 $ 0 $ 0 $ 5

T-50 $ 0 $ 1 $ 0

Typesetter

Step 2 - Lines

A B C

Job

R-34 $ 3 $ 4 $ 0

S-66 $ 0 $ 0 $ 5

T-50 $ 0 $ 1 $ 0

Typesetter

Step 4 - Assignments

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Assignment Example

A B C

Job

R-34 $ 3 $ 4 $ 0

S-66 $ 0 $ 0 $ 5

T-50 $ 0 $ 1 $ 0

Typesetter

A B C

Job

R-34 $11 $14 $ 6

S-66 $ 8 $10 $11

T-50 $ 9 $12 $ 7

Typesetter

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Sequencing Jobs

Specifies the order in which jobs should be performed at work centers
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

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Sequencing Example

Apply the four popular sequencing rules to these five jobs

Job	Job Work (Processing) Time (Days)	Job Due Date (Days)
A	6	8
B	2	6
C	8	18
D	3	15
E	9	23

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Sequencing Example

FCFS: Sequence A-B-C-D-E

Job Sequence	Job Work (Processing) Time	Flow Time	Job Due Date	Job Lateness
A	6	6	8	0
B	2	8	6	2
C	8	16	18	0
D	3	19	15	4
E	9	28	23	5
28	77	11

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Sequencing Example

FCFS: Sequence A-B-C-D-E

Sum of total flow time

Number of jobs

Average completion time = = 77/5 = 15.4 days

Total job work time

Sum of total flow time

Utilization metric = = 28/77 = 36.4%

Sum of total flow time

Total job work time

Average number of jobs in the system

= = 77/28 = 2.75 jobs

Total late days

Number of jobs

Average job lateness = = 11/5 = 2.2 days

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Sequencing Example

SPT: Sequence B-D-A-C-E

Job Sequence	Job Work (Processing) Time	Flow Time	Job Due Date	Job Lateness
B	2	2	6	0
D	3	5	15	0
A	6	11	8	3
C	8	19	18	1
E	9	28	23	5
28	65	9

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Sequencing Example

SPT: Sequence B-D-A-C-E

Sum of total flow time

Number of jobs

Average completion time = = 65/5 = 13 days

Total job work time

Sum of total flow time

Utilization metric = = 28/65 = 43.1%

Sum of total flow time

Total job work time

Average number of jobs in the system

= = 65/28 = 2.32 jobs

Total late days

Number of jobs

Average job lateness = = 9/5 = 1.8 days

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Sequencing Example

EDD: Sequence B-A-D-C-E

Job Sequence	Job Work (Processing) Time	Flow Time	Job Due Date	Job Lateness
B	2	2	6	0
A	6	8	8	0
D	3	11	15	0
C	8	19	18	1
E	9	28	23	5
28	68	6

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Sequencing Example

EDD: Sequence B-A-D-C-E

Sum of total flow time

Number of jobs

Average completion time = = 68/5 = 13.6 days

Total job work time

Sum of total flow time

Utilization metric = = 28/68 = 41.2%

Sum of total flow time

Total job work time

Average number of jobs in the system

= = 68/28 = 2.43 jobs

Total late days

Number of jobs

Average job lateness = = 6/5 = 1.2 days

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Sequencing Example

LPT: Sequence E-C-A-D-B

Job Sequence	Job Work (Processing) Time	Flow Time	Job Due Date	Job Lateness
E	9	9	23	0
C	8	17	18	0
A	6	23	8	15
D	3	26	15	11
B	2	28	6	22
28	103	48

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Sequencing Example

LPT: Sequence E-C-A-D-B

Sum of total flow time

Number of jobs

Average completion time = = 103/5 = 20.6 days

Total job work time

Sum of total flow time

Utilization metric = = 28/103 = 27.2%

Sum of total flow time

Total job work time

Average number of jobs in the system

= = 103/28 = 3.68 jobs

Total late days

Number of jobs

Average job lateness = = 48/5 = 9.6 days

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Sequencing Example

Summary of Rules

Rule	Average Completion Time (Days)	Utilization Metric (%)	Average Number of Jobs in System	Average Lateness (Days)
FCFS	15.4	36.4	2.75	2.2
SPT	13.0	43.1	2.32	1.8
EDD	13.6	41.2	2.43	1.2
LPT	20.6	27.2	3.68	9.6

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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

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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

Due date – Today’s date

Work (lead) time remaining

Time remaining

Workdays remaining

CR = =

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Critical Ratio Example

Currently Day 25

With CR < 1, Job B is late. Job C is just on schedule and Job A has some slack time.

JOB	DUE DATE	WORKDAYS REMAINING
A	30	4
B	28	5
C	27	2

JOB	CRITICAL RATIO	PRIORITY ORDER
A	(30 - 25)/4 = 1.25	3
B	(28 - 25)/5 = .60	1
C	(27 - 25)/2 = 1.00	2

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Critical Ratio Technique

Helps determine the status of specific jobs

Establishes relative priorities among jobs on a common basis

Adjusts priorities automatically for changes in both demand and job progress

Dynamically tracks job progress

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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
An N/2 problem, N number of jobs through 2 workstations

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Johnson’s Rule

List all jobs and times for each work center

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.

Once a job is scheduled, it is eliminated from the list

Repeat steps 2 and 3 working toward the center of the sequence

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Johnson’s Rule Example

JOB	WORK CENTER 1 (DRILL PRESS)	WORK CENTER 2 (LATHE)
A	5	2
B	3	6
C	8	4
D	10	7
E	7	12

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Johnson’s Rule Example

JOB	WORK CENTER 1 (DRILL PRESS)	WORK CENTER 2 (LATHE)
A	5	2
B	3	6
C	8	4
D	10	7
E	7	12

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Johnson’s Rule Example

JOB	WORK CENTER 1 (DRILL PRESS)	WORK CENTER 2 (LATHE)
A	5	2
B	3	6
C	8	4
D	10	7
E	7	12

WC 1

WC 2

Time 0 3 10 20 28 33

Job completed

Idle

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Johnson’s Rule Example

Time 0 3 10 20 28 33

Time 0 1 3 5 7 9 10 11 12 13 17 19 21 22 23 25 27 29 31 33 35

JOB	WORK CENTER 1 (DRILL PRESS)	WORK CENTER 2 (LATHE)
A	5	2
B	3	6
C	8	4
D	10	7
E	7	12

WC 1

WC 2

Job completed

Idle

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Limitations of Rule-Based Dispatching Systems

Scheduling is dynamic and rules need to be revised to adjust to changes
Rules do not look upstream or downstream
Rules do not look beyond due dates

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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
FCS allows the balancing of delivery needs and efficiency

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Finite Capacity Scheduling

Figure 15.5

Interactive Finite Capacity Scheduling

Planning Data

Master schedule
BOM
Inventory

Priority rules

Expert systems
Simulation models

Routing files
Work center information

Tooling and other resources

Setups and run time

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Finite Capacity Scheduling

Figure 15.6

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Scheduling Services

Service systems differ from manufacturing

MANUFACTURING	SERVICES
Schedules machines and materials	Schedule staff
Inventories used to smooth demand	Seldom maintain inventories
Machine-intensive and demand may be smooth	Labor-intensive and demand may be variable
Scheduling may be bound by union contracts	Legal issues may constrain flexible scheduling
Few social or behavioral issues	Social and behavioral issues may be quite important

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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

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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

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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

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Cyclical Scheduling Example

Determine the staffing requirements
Identify two consecutive days with the lowest total requirements and assign these as days off
Make a new set of requirements subtracting the days worked by the first employee
Apply step 2 to the new row
Repeat steps 3 and 4 until all requirements have been met

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Employee 3	3	3	4	3	2	3	3
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Employee 3	3	3	4	3	2	3	3
Employee 4	2	2	3	2	2	3	2
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Employee 3	3	3	4	3	2	3	3
Employee 4	2	2	3	2	2	3	2
Employee 5	1	1	2	2	2	2	1
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Employee 3	3	3	4	3	2	3	3
Employee 4	2	2	3	2	2	3	2
Employee 5	1	1	2	2	2	2	1
Employee 6	1	1	1	1	1	1	0
Capacity (Employees)
Excess Capacity

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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Cyclical Scheduling Example

M	T	W	T	F	S	S
Employee 1	5	5	6	5	4	3	3
Employee 2	4	4	5	4	3	3	3
Employee 3	3	3	4	3	2	3	3
Employee 4	2	2	3	2	2	3	2
Employee 5	1	1	2	2	2	2	1
Employee 6	1	1	1	1	1	1	0
Employee 7	1
Capacity (Employees)	5	5	6	5	4	3	3
Excess Capacity	0	0	0	0	0	1	0

DAY	M	T	W	T	F	S	S
Staff required	5	5	6	5	4	3	3

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