© 2007 Pearson Education Scheduling Chapter 16. © 2007 Pearson Education How Scheduling fits the Operations Management Philosophy Operations As a Competitive

© 2007 Pearson Education

SchedulingScheduling

Chapter 16Chapter 16


How Scheduling fits the Operations Management

Philosophy

Operations As a Competitive Weapon

Operations StrategyProject Management Process Strategy

Process AnalysisProcess Performance and Quality

Constraint ManagementProcess LayoutLean Systems

Supply Chain StrategyLocation

Inventory ManagementForecasting

Sales and Operations PlanningResource 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

Current Current date date

Scheduled activity time

Actual progress

Start activity

Finish activity

Nonproductive time

Gantt Progress Chart for an Auto Parts Company


Gantt Workstation Chart Gantt 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 SchedulingExample 16.1




Number of employeesNumber of employees 66 44 88 99 10* 10* 33 22EmployeeEmployee 11 X X XX XX XX XX

Workforce SchedulingExample 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.


Number of employeesNumber of employees 66 44 88 99 10*10* 33 22EmployeeEmployee 11 XX XX XX XX XX

RequirementsRequirements 55 33 77 88 9*9* 33 22EmployeeEmployee 22 XX XX XX XX XX

Workforce SchedulingExample 16.1 Step 3





RequirementRequirement 55 33 77 88 9*9* 33 22EmployeeEmployee 22 XX XX XX XX XX


RequirementRequirement 33 11 55 66 7*7* 33 22

Workforce SchedulingExample 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.









Workforce SchedulingExample 16.1 Step 4 continued









Workforce SchedulingExample 16.1 Step 4 continued



EmployeeEmployee 11 XX XX XX XX XX offoff offoff



EmployeeEmployee 44 offoff offoff XX XX XX XX XXEmployeeEmployee 55 XX XX XX XX XX offoff offoff



EmployeeEmployee 99 offoff XX XX XX XX XX offoff


Final ScheduleFinal Schedule

Workforce SchedulingExample 16.1


MM TT WW ThTh FF SS SuSu







EmployeeEmployee 99 offoff XX XX XX XX XX offoff


Workforce SchedulingExample 16.1 Final Schedule

Capacity, C 7 8 10 10 10 3 2 50Requirements, R 6 4 8 9 10 3 2 42Slack, 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.


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Manufacturing ProcessManufacturing ProcessR

aw M

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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 date S/RO = ((Due date –– Today’s date) – Total shop time remaining) Today’s date) – Total shop time remaining)

Number of operations remaining Number 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 16.2Single-Dimension Rule SequencingSingle-Dimension Rule Sequencing


8 + 14 + 17 + 32 + 448 + 14 + 17 + 32 + 444444

Average hours early = 0.6 hourAverage hours early = 0.6 hour

JobJob ScheduledScheduled ActualActualEngineEngine ProcessingProcessing FlowFlow CustomerCustomer CustomerCustomer HoursHoursBlockBlock BeginBegin TimeTime TimeTime PickupPickup PickupPickup HoursHours PastPast

SequenceSequence WorkWork (hr)(hr) (hr)(hr) TimeTime TimeTime EarlyEarly DueDue

RangerRanger 88 1010ExplorerExplorer 66 1212Econoline 150Econoline 150 33 1818BroncoBronco 1515 2020ThunderbirdThunderbird 1212 2222

00 ++ == 88 1010 22

1717 ++ == 3232 3232 1212

88 ++ == 1414 1414 221414 ++ == 1717 1818 11

3232 ++ == 4444 4444 2222

Example 16.2Example 16.2Single-Dimension Rule Single-Dimension Rule –– EDD EDD

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 + 444444

Average hours early = 3.6 hourAverage hours early = 3.6 hour

JobJob ScheduledScheduled ActualActualEngineEngine ProcessingProcessing FlowFlow CustomerCustomer CustomerCustomer HoursHoursBlockBlock BeginBegin TimeTime TimeTime PickupPickup PickupPickup HoursHours PastPast

SequenceSequence WorkWork (hr)(hr) (hr)(hr) TimeTime TimeTime EarlyEarly DueDue

RangerRanger 88 1010ExplorerExplorer 66 1212Econoline 150Econoline 150 33 1818BroncoBronco 1515 2020ThunderbirdThunderbird 1212 2222

00 ++ == 33 1818 1515

1717 ++ == 2929 2929 77

88 ++ == 99 1212 1414 ++ == 1717 1717 33 77

2929 ++ == 4444 4444 2424

Example 16.2Example 16.2Single-Dimension Rule Single-Dimension Rule –– SPT SPT

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 20.40Average hours early 0.60 3.60Average hours past due 7.20 7.60Average WIP 2.61 2.32Average 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.


Example 16.3Example 16.3Multiple-Dimension Rule – Multiple-Dimension Rule – CRCR

11 2.32.3 1515 1010 6.16.1 2.462.4622 10.510.5 1010 22 7.87.8 1.281.2833 6.26.2 2020 1212 14.514.5 1.381.3844 15.615.6 88 55 10.210.2 .78.78

OperationOperation TimeTimeTime atTime at RemainingRemaining Number ofNumber ofEngineEngine 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 0.890.8922 10.510.5 1010 22 7.87.8 1.281.28 1.101.1033 6.26.2 2020 1212 14.514.5 1.381.38 0.460.4644 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

Example 16.3Example 16.3Multiple-Dimension Rule – Multiple-Dimension Rule – S/ROS/RO


11 2.32.3 1515 1010 6.16.1 2.462.46 0.890.8922 10.510.5 1010 22 7.87.8 1.281.28 1.101.1033 6.26.2 2020 1212 14.514.5 1.381.38 0.460.4644 15.615.6 88 55 10.210.2 .78.78 – 0.44– 0.44



CR SequenceCR Sequence = 4 = 4 – 2 – 3 – 1– 2 – 3 – 1S/RO SequenceS/RO Sequence = 4 = 4 – 3 – 1 – 2– 3 – 1 – 2CR SequenceCR Sequence ==

Comparing the Comparing the CRCR and and S/ROS/RO Rules Rules

© 2007 Pearson Education© 2007 Pearson Education

Priority Rule Summary

FCFS = 1 – 2 – 3 – 4SPT = 1 – 3 – 2 – 4EDD = 4 – 2 – 1 – 3CR = 4 – 2 – 3 – 1S/RO = 4 – 3 – 1 – 2

Avg Flow Time 17.175 16.100 26.175 27.150 24.025Avg Early Time 3.425 6.050 0 0 0Avg Past Due 7.350 8.900 12.925 13.900 10.775Avg WIP 1.986 1.861 3.026 3.129 2.777Avg Total Inv 2.382 2.561 3.026 3.129 2.777

Shortest Slack perProcessing 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 the at the Morris Machine Co.Morris Machine Co.

Time (hr)Time (hr)

MotorMotor Workstation 1Workstation 1 Workstation 2Workstation 2

M1M1 1212 2222M2M2 44 55M3M3 55 33M4M4 1515 1616M5M5 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 30Day

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 the at 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 2SPT

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

Documents

© 2007 Pearson Education Scheduling Chapter 16. © 2007 Pearson Education How Scheduling fits the Operations Management Philosophy Operations As a Competitive