15 to 16. Operations Scheduling and Control - Ud 19 August 2010

15 to 16. Operations Scheduling and Control

In

“OPERATIONS MANAGEMENT – I”

(WMP, Term I, Part B, July – Sep 2010) 2009)

By Prof. N. Narayanan

Reference: Ch 14: Short Term Scheduling (pp 563 – 601)

In: J. Heizer B. Render and J. Rajashekhar, Operations Management, 9th Edition, Pearson Education, 2009

Sessions Plan – Part B (Continued)

Sn. Nos.

Date Topic Text ; Exercise/ Case

15 – 16

14 Aug.(Sat)

21 Aug. (Sat)

Operations Scheduling & Control

Ch. 14: Short Term Scheduling (pp 563 – 601)

1.First Printing and Copy Centre – Assigning jobs to typesetters

•Problem No.: 14.6 (pp 597): Clair Consultants (Asgnmt. prob.)

2.Avanti Sethi Archtects: Sequencing Using Priority Rules (pp 576)

•Problem No. 14.11 (pp 598): Avianic Engine Repair Inc.)

(Single Machine Sequencing problem)

3.La Crosse, Wisconsin’s Tool and Die Shop: Johnson’s Rule Example (pp 580 -81)

•Problem No. 14.17 (pp 599): George Heinrich’s printing co. (Two m/c Flow Shop Seq. prob.)

4.Problem: Cyclical scheduling of service employees at Oncology Ward (pp 588)

5.Case: Scheduling Workers Who Fall Asleep is a Killer–Literally (pp 568)

6.Case: Scheduling Aircraft Turnaround (pp 586)

7.HBSP 9-699-154: The Patient Care Delivery Model at the Massachusetts General Hospital, 23pp.

Answers for the problems in ‘Operations Scheduling and Control’

• Problem No.: 14.6 (pp 597): Clair Consultants (Asgnmt. prob.)

The minimum-cost solution =

Chris Finance $120

Steve Marketing $20

Juana Human Resources $45

Rebecca Operations $25

$210

• Problem No. 14.11 (pp 598): Avianic Engine Repair Inc. (Single Machine Sequencing problem)

Jobs should be scheduled in the sequence 517, 103, 309, 205, 412, if scheduled by the critical ratio scheduling rule.

• Problem No. 14.17 (pp 599): George Heinrich’s printing co. (Two m/c Flow Shop Seq. prob.)

(a, c) The jobs should be processed in the sequence:

V–Y–U–Z–X–W–T, for a total time of 57.

(d) Binding is idle from 0 to 4 and from 51 to 54 for a total of 7 hours.

Answers for the problems in ‘Operations Scheduling and Control’

• Problem: Cyclical scheduling of service employees at Oncology Ward (pp 588)

• Case: Scheduling Workers Who Fall Asleep is a Killer–Literally (pp 568)

• Case: Scheduling Aircraft Turnaround (pp 586)

• HBSP 9-699-154: The Patient Care Delivery Model at the Massachusetts General Hospital, 23pp.

Overview: (Operations Scheduling and Control)

1. Introduction to Short Term Scheduling

Global Company Profile: Delta Airlines

2. Scheduling Approaches for Different Processes

3. Machine Loading Methods (OMIT)

3a. Assignment Method

3b. Input-Output Control

3c. Gantt Load Chart

[Continued]

Overview: (Operations Scheduling and Control)

4. Sequencing for Scheduling

4a. Use of ‘Priority Dispatching Rules”

4b. Sequencing for 2-Machine Flow Shop, using Johnson’s Rule

5. Cyclical Scheduling for Service Employees

6. Problems/ Cases in Operations Scheduling

1. Introduction toShort Term Scheduling

Global Company Profile:Delta Airlines

(p 564 – 565)

Global Company Profile: Global Company Profile:

Delta Airlines Delta Airlines (p 564)(p 564)

1.1. About 10% of Delta’s flights are About 10% of Delta’s flights are disrupted per year, half because of disrupted per year, half because of weather.weather.

2.2. Cost is $440 million in lost revenue, Cost is $440 million in lost revenue, overtime pay, food and lodging overtime pay, food and lodging vouchers.vouchers.

3.3. The $33 million Operations Control The $33 million Operations Control Center Center adjusts to changes adjusts to changes responsively, responsively, and keeps flights flowing.and keeps flights flowing.

Global Company Profile: Global Company Profile:

Delta Airlines Delta Airlines (p 564)(p 564)(Continued)(Continued)

4.4. It must adjust to the changes continually It must adjust to the changes continually by by

– – Maintaining valid a Maintaining valid a tentative scheduletentative schedule, , byby

– – Having a ‘Having a ‘rapid rescheduling capabilityrapid rescheduling capability ’ ’ and byand by

– – Taking specific ‘Taking specific ‘dispatchingdispatching11’ decisions at ’ decisions at various points in time, on the immediate various points in time, on the immediate actions to be taken.actions to be taken.

5.5. Saves Delta $35 million per year.Saves Delta $35 million per year.

“Dispatching” in Operations Scheduling and Control

• ‘Dispatching’ is a decision made just ahead of an intended action, with an explicit purpose to execute the decision through the intended action, immediately.

• The dispatching decision is generally a part of a larger plan or schedule, over a planning/ scheduling horizon ahead, that has recently been updated.

• Dispatching as a process allows a supervisor or manager to utilize scheduling as a way to develop a perspective at various points in time, but actually confine his immediate commitment to just the single decision that enables his immediate action.

• Further actions in the future would again be subject to similar dispatching process.

The Role of Short Term Scheduling in The Role of Short Term Scheduling in the Integrated OPCthe Integrated OPC

Examples of Scheduling Decisions in Different CompaniesExamples of Scheduling Decisions in Different Companies

OrganizationOrganization Managers Must Schedule the FollowingManagers Must Schedule the Following

Arnold Palmer Arnold Palmer HospitalHospital

Operating room useOperating room usePatient admissionsPatient admissionsNursing, security, maintenance staffsNursing, security, maintenance staffsOutpatient treatmentsOutpatient treatments

University of University of MissouriMissouri

Classrooms and audiovisual equipmentClassrooms and audiovisual equipmentStudent and instructor schedulesStudent and instructor schedulesGraduate and undergraduate coursesGraduate and undergraduate courses

Lockheed-Martin Lockheed-Martin factoryfactory

Production of goodsProduction of goodsPurchases of materialsPurchases of materialsWorkersWorkers

Hard Rock CafeHard Rock Cafe Chef, waiters, bartendersChef, waiters, bartendersDelivery of fresh foodsDelivery of fresh foodsEntertainersEntertainersOpening of dining areasOpening of dining areas

Delta AirlinesDelta Airlines Maintenance of aircraftMaintenance of aircraftDeparture timetablesDeparture timetablesFlight crews, catering, gate, ticketing personnelFlight crews, catering, gate, ticketing personnel

Strategic Importance of Short-Term SchedulingStrategic Importance of Short-Term Scheduling

Effective and efficient scheduling can be a Effective and efficient scheduling can be a competitive advantagecompetitive advantage

Faster movement of goods through a facility Faster movement of goods through a facility means better use of assets and lower costsmeans better use of assets and lower costs

Additional capacity resulting from faster Additional capacity resulting from faster throughput improves customer service through throughput improves customer service through faster deliveryfaster delivery

Good schedules result in more reliable Good schedules result in more reliable deliveriesdeliveries

The detailed ‘Operations Scheduling’ serves as The detailed ‘Operations Scheduling’ serves as the vital link from the higher level plans to the vital link from the higher level plans to ‘execution’.‘execution’.

Scheduling IssuesScheduling Issues

Scheduling deals with the timing of Scheduling deals with the timing of operationsoperations

The task is the allocation and The task is the allocation and prioritization of demands—from the prioritization of demands—from the higher level planshigher level plans

Significant issues areSignificant issues are The type of scheduling, forward or The type of scheduling, forward or

backwardbackward

The criteria for prioritiesThe criteria for priorities

Forward and Backward SchedulingForward and Backward Scheduling

Forward scheduling starts as soon as Forward scheduling starts as soon as the requirements are knownthe requirements are known

Produces a feasible schedule though it Produces a feasible schedule though it may not meet due datesmay not meet due dates

Frequently results in Frequently results in excessive work-in-excessive work-in-process inventoryprocess inventory Due Due

DateDate11NowNow

1 The ‘Due dates’ may have been determined by higher level planning, such as the ‘Material Requirements Planning’

‘MRP’ itself is a result of the backward scheduling logic, applied from the ‘Master Production Schedules’.

Forward Scheduling (Looks from ‘Resources’ Point of View):

Forward and Backward Scheduling Forward and Backward Scheduling (Continued)(Continued)

Backward scheduling begins with the Backward scheduling begins with the due date and schedules the final due date and schedules the final operation firstoperation first

Schedule is produced by working Schedule is produced by working backwards though the processesbackwards though the processes

Resources may not Resources may not be available to be available to accomplish the accomplish the scheduleschedule

Due Due DateDateNowNow

Backward Scheduling (Looks from ‘Requirements’ Point of View):

1 The ‘Due dates’ may have been determined by higher level planning, such as the ‘Material Requirements Planning’

2. Scheduling Approaches for Different Processes

Scheduling Approaches for Different ProcessesScheduling Approaches for Different Processes

1.1. Process-Process-focused focused facilitiesfacilities

Forward-looking schedulesForward-looking schedulesMRP due datesMRP due datesFinite capacity forward schedulingFinite capacity forward scheduling

2.2. Work cellsWork cells Forward-looking schedulesForward-looking schedulesMRP due datesMRP due datesDetailed schedule done using work cell priority Detailed schedule done using work cell priority rulesrules

3.3. Repetitive Repetitive facilitiesfacilities

Forward-looking schedule with a balanced lineForward-looking schedule with a balanced linePull techniques for scheduling, to meet the Pull techniques for scheduling, to meet the requirements of the next stage ‘customer’.requirements of the next stage ‘customer’.

4.4. Product-Product-focused focused facilitiesfacilities

Forward-looking schedule with stable demand Forward-looking schedule with stable demand and fixed capacityand fixed capacityCapacity, set-up, and run times knownCapacity, set-up, and run times knownCapacity limited by long-term capital investmentCapacity limited by long-term capital investment

Scheduling Process-Focused FacilitiesScheduling Process-Focused Facilities

Maximum of complexity in short term scheduling of Maximum of complexity in short term scheduling of operations is involved in the case ‘Process Focused operations is involved in the case ‘Process Focused Facilities’. Toward simplifying the problem, following Facilities’. Toward simplifying the problem, following broad policies are generally employed:broad policies are generally employed:

1.1.Schedule incoming orders without violating capacity Schedule incoming orders without violating capacity constraintsconstraints

2.2.Check availability of tools and materials before Check availability of tools and materials before releasing an orderreleasing an order

3.3.Establish due dates for each job and check progressEstablish due dates for each job and check progress

4.4.Check work in progressCheck work in progress

5.5.Provide feedbackProvide feedback

6.6.Provide work efficiency statistics and monitor timesProvide work efficiency statistics and monitor times

Production Database: Production Database: Planning and Control FilesPlanning and Control Files

For Scheduling Process-Focused FacilitiesFor Scheduling Process-Focused Facilities

1.1. An item master file contains information about each An item master file contains information about each componentcomponent

2.2. A routing file indicates each component’s flow A routing file indicates each component’s flow through the shopthrough the shop

3.3. A work-center master file contains information A work-center master file contains information about the work centerabout the work center

Planning FilesPlanning Files

Control FilesControl Files

Track the actual progress made against the planTrack the actual progress made against the plan

3. Machine Loading Methods

3a. Assignment Method



– OMIT

Loading JobsLoading Jobs

Assignment of jobs to work or processing Assignment of jobs to work or processing centers, so that costs, idle time, or centers, so that costs, idle time, or completion time are minimizedcompletion time are minimized

Two forms of loadingTwo forms of loading

Assigning specific jobs to work centers Assigning specific jobs to work centers (based on relative efficiencies of different (based on relative efficiencies of different machines for a job) – This can be a machines for a job) – This can be a long-to-long-to-medium termmedium term decision. decision.

Capacity oriented – This is generally a Capacity oriented – This is generally a medium-to-short termmedium-to-short term decision. decision.

3a. Assignment Method(P 573 – 575)

Assignment MethodAssignment Method(Employed when routing a job through(Employed when routing a job through

different alternative machines is possible)different alternative machines is possible)

A special class of linear programming A special class of linear programming models that assign tasks or jobs to models that assign tasks or jobs to resourcesresources

Objective is to minimize cost or timeObjective is to minimize cost or time

Only one job (or worker) is assigned Only one job (or worker) is assigned to one machine (or project)to one machine (or project)

Assignment MethodAssignment Method

Build a table of costs or time associated Build a table of costs or time associated with particular assignments.with particular assignments.

TypesetterTypesetter

JobJob A A B B C C

R-34R-34 $11 $11 $14 $ 6 $14 $ 6

S-66S-66 $ 8 $ 8 $10 $10 $ 11 $ 11

T-50T-50 $ 9 $ 9 $12 $12 $ 7 $ 7

1.

Assignment MethodAssignment Method

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

2.2. Draw the minimum number of vertical Draw the minimum number of vertical and horizontal lines necessary to cover and horizontal lines necessary to cover all the zeros in the table. If the number all the zeros in the table. If the number of lines equals either the number of rows of lines equals either the number of rows or the number of columns, proceed to or the number of columns, proceed to step 4. Otherwise proceed to step 3.step 4. Otherwise proceed to step 3.

Assignment MethodAssignment Method (Continued) (Continued)

3.3. Subtract the smallest number not covered Subtract the smallest number not covered by a line from all other uncovered by a line from all other uncovered numbers. Add the same number to any numbers. Add the same number to any number at the intersection of two lines. number at the intersection of two lines. Return to step 2.Return to step 2.

4.4. Optimal assignments are at zero locations Optimal assignments are at zero locations in the table. Select one, draw lines through in the table. Select one, draw lines through the row and column involved, and continue the row and column involved, and continue to the next assignment.to the next assignment.

Assignment ExampleAssignment Example

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 8$ 8 $ 0$ 0

S-66S-66 $ 0$ 0 $ 2$ 2 $ 3$ 3

T-50T-50 $ 2$ 2 $ 5$ 5 $ 0$ 0


Step 1a: Subtract smallest from rowsStep 1a: Subtract smallest from rows

AA BB CCJobJob

R-34R-34 $11$11 $14$14 $ 6$ 6

S-66S-66 $ 8$ 8 $10$10 $11$11

T-50T-50 $ 9$ 9 $12$12 $ 7$ 7


The Problem:The Problem:

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 6$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 3$ 3

T-50T-50 $ 2$ 2 $ 3$ 3 $ 0$ 0


Step 1b: Subtract smallest from columnsStep 1b: Subtract smallest from columns


Step 2: Draw minimum number of Step 2: Draw minimum number of vertical and horizontal lines to cover vertical and horizontal lines to cover all zerosall zeros

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 6$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 3$ 3

T-50T-50 $ 2$ 2 $ 3$ 3 $ 0$ 0


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

Step 3: Subtraction: The smallest Step 3: Subtraction: The smallest uncovered number is 2 so this is uncovered number is 2 so this is subtracted from all other uncovered subtracted from all other uncovered numbers and added to numbers at the numbers and added to numbers at the intersection of linesintersection of lines

AA BB CCJobJob

R-34R-34 $ 3$ 3 $ 4$ 4 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 5$ 5

T-50T-50 $ 0$ 0 $ 1$ 1 $ 0$ 0



Because three lines are needed, the Because three lines are needed, the solution is optimal and assignments solution is optimal and assignments can be madecan be made

Return to Step 2: Draw the lines - LinesReturn to Step 2: Draw the lines - Lines

AA BB CCJobJob

R-34R-34 $ 3$ 3 $ 4$ 4 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 5$ 5

T-50T-50 $ 0$ 0 $ 1$ 1 $ 0$ 0


Step 4: Assignments:Step 4: Assignments:

Start by assigning R-34 to worker C Start by assigning R-34 to worker C as this is the only possible as this is the only possible assignment for worker C. assignment for worker C.

Job T-50 must go to worker A as Job T-50 must go to worker A as worker C is already assigned. worker C is already assigned.

This leaves S-66 for worker BThis leaves S-66 for worker B

AA BB CCJobJobR-34 $ 3$ 3 $ 4$ 4 $ 0S-66 $ 0$ 0 $ 0 $ 5$ 5T-50 $ 0 $ 1$ 1 $ 0$ 0



Step 4 - AssignmentsStep 4 - Assignments

AA BB CCJobJobR-34 $ 3$ 3 $ 4$ 4 $ 0S-66 $ 0$ 0 $ 0 $ 5$ 5T-50 $ 0 $ 1$ 1 $ 0$ 0

TypesetterTypesetterAA BB CC

JobJob

R-34R-34 $11$11 $14$14 $ 6$ 6

S-66S-66 $ 8$ 8 $10$10 $11$11

T-50T-50 $ 9$ 9 $12$12 $ 7$ 7


The Problem:The Problem:

Problem No. 14.6 (p 597)

Claire Consultants:

The Assignment Problem

Problem No. 14.6: Claire Consultants (pp 597)

Marketing

Finance Operatio

nsHR

Chris 80 120 125 140

Steve 20 115 145 160

Juana 40 100 85 45

Rebecca 65 35 25 75

Time Taken (minutes):

Marketing

Finance Operatio

nsHR

Chris 0 40 45 60

Steve 0 95 125 140

Juana 0 60 45 5

Rebecca 40 10 0 50

After deducting smallest number from each row:

Marketing

Finance Operatio

nsHR

Chris 0 30 45 55

Steve 0 85 125 135

Juana 0 50 45 0

Rebecca 40 0 0 45

After deducting smallest number from each col.:

Marketing

Finance Operatio

nsHR

Chris 0 0 15 25

Steve 0 55 95 105

Juana 30 50 45 0

Rebecca 70 0 0 45

Three red lines, which is less than the smaller of the number of rows and columns.

After subtracting the smallest number from all uncovered numbers, adding the same to the numbers at the intersections.

Claire Consultants (pp 597)(Continued)

The minimum-cost solution is

• ChrisFinance $120

• SteveMarketing $20

• Juana Human Resources $45

• Rebecca Operations $25

Total $210

Input-Output ControlInput-Output Control

Identifies overloading and under-Identifies overloading and under-loading conditionsloading conditions

Prompts managerial action to resolve Prompts managerial action to resolve scheduling problemsscheduling problems

Can be maintained using ConWIP Can be maintained using ConWIP cards that control the scheduling of cards that control the scheduling of batchesbatches

Input-Output Control ExampleInput-Output Control Example– Figure 14.2 (pp 571)– Figure 14.2 (pp 571)

Week Ending 6/6 6/13 6/20 6/27 7/4 7/11

Planned Input1 280 280 280 280 280

Actual Input 270 250 280 285 280

Cumulative Deviation

–10 –40 –40 –36

Planned Output1 320 320 320 320

Actual Output 270 270 270 270


–50 –100 –150 –200

Cumulative Change in Backlog

0 –20 –10 +5

Work Center DNC Milling (in standard hours)

1 The ‘Inputs’ to the Work Centers can arise from either the ‘Order Point Inventory Control Systems’, or from the ‘Material Requirements Planning Systems’.

Input-Output Control ExampleInput-Output Control Example

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


–10 –40 –40 –36

Planned Output 320 320 320 320

Actual Output 270 270 270 270


–50 –100 –150 –200

Cumulative Change in Backlog

0 –20 –10 +5

Work Center DNC Milling (in standard hours)

Explanation:270 input, 270 output implies 0 change

Explanation: 250 input,270 output implies –20 change

Input-Output Control ExampleInput-Output Control Example (Continued) (Continued)

Options available to operations Options available to operations personnel include:personnel include:

1.1. Correcting performancesCorrecting performances

2.2. Increasing capacityIncreasing capacity

3.3. Increasing or reducing input to Increasing or reducing input to the work centerthe work center

Gantt ChartsGantt Charts

Load chart shows the loading and idle Load chart shows the loading and idle times of departments, machines, or times of departments, machines, or facilitiesfacilities

Displays relative workloads over timeDisplays relative workloads over time

Schedule chart monitors jobs in Schedule chart monitors jobs in processprocess

All Gantt charts need to be updated All Gantt charts need to be updated frequentlyfrequently

Gantt Load Chart ExampleGantt Load Chart Example

Day Monday Tuesday Wednesday Thursday FridayWork Center

Metalworks

Mechanical

Electronics

Painting

Job 349

Job 349

Job 349

Job 408

Job 408

Job 408

ProcessingProcessing UnscheduledUnscheduled Center not availableCenter not available

Job 350

Job 349

Job 295

Gantt Schedule Chart ExampleGantt Schedule Chart Example

Job Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

A

B

C

NowNow

Maintenance

Start of an Start of an activityactivity

End of an End of an activityactivity

Scheduled Scheduled activity time activity time allowedallowed

Actual work Actual work progressprogress

Nonproduction Nonproduction timetime

Point in time Point in time when chart is when chart is reviewedreviewed

4. Sequencing for Scheduling


4b. Sequencing for 2-Machine Flow Shop, using Johnson’s Rule

Using Priority Dispatching Rules – An ExampleUsing Priority Dispatching Rules – An ExampleConsider 5 Jobs, A, B, C, D and E, arrived at the shop in that order:Consider 5 Jobs, A, B, C, D and E, arrived at the shop in that order:

Job

Proc.Time(days)

Due Date(Days Hence)

SPT

Seq.

EDD

Seq.

A

B

C

D

E

3 5

6 8

2 6

4 4

1 2 1 1

3 3

2

2

4

4

5 5

FCFS

Seq.

1

2

4

5

3

Critical Ratio

CR Seq.

2/1

1

3

4

5/3

8/6

6/2

2

5

4/4

A ‘Bar Chart’ can now be drawn, using the above job sequences, and the ‘schedule performances’ achieved can accordingly be determined.

Scheduling CriteriaScheduling Criteria

1.1. Minimize ‘completion time’ or ‘flow time’.Minimize ‘completion time’ or ‘flow time’.

2.2. Maximize utilization of facilitiesMaximize utilization of facilities

3.3. Minimize work-in-process (WIP) inventory Minimize work-in-process (WIP) inventory (e.g., “Number of jobs in the system”)(e.g., “Number of jobs in the system”)

4.4. Minimize customer waiting timeMinimize customer waiting time

Optimize the use of resources so that Optimize the use of resources so that production objectives are metproduction objectives are met


– In ‘Sequencing’ and Scheduling’

(and Evaluations of ‘Schedule Performance’ arising from Using the Priority Rules)

Average completion time = Total flow timeNumber of jobs

Utilization = Total job work time

Total flow time

Average number of jobs in the system =

Total flow timeTotal job work time

Average job lateness = Total late daysNumber of jobs

Sequencing JobsSequencing Jobs

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

Priority rules are used to dispatch or Priority rules are used to dispatch or sequence jobssequence jobs FCFS: First come, first servedFCFS: First come, first served

SPT: Shortest processing timeSPT: Shortest processing time

EDD: Earliest due dateEDD: Earliest due date

LPT: Longest processing timeLPT: Longest processing time

Example 5 (pp 576): Avanti Sethi Associates

Sequencing Using Priority Rules

(pp 576 - 579)

2.

Sequencing Example Sequencing Example (pp 576)(pp 576)

JobJob

Job Work (Processing) Job Work (Processing) TimeTime

(Days)(Days)Job Due DateJob Due Date

(Days)(Days)

AA 66 88

BB 22 66

CC 88 1818

DD 33 1515

EE 99 2323

Apply the four popular sequencing rules Apply the four popular sequencing rules to these five jobsto these five jobs

Sequencing ExampleSequencing Example

Job Job SequenceSequence

Job Work Job Work (Processing) Time(Processing) Time

Flow Flow TimeTime

Job Due Job Due DateDate

Job Job LatenessLateness

AA 66 66 88 00

BB 22 88 66 22

CC 88 1616 1818 00

DD 33 1919 1515 44

EE 99 2828 2323 55

2828 7777 1111

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



Job Work Job Work (Processing) (Processing)

TimeTimeFlow Flow TimeTime



AA 66 66 88 00

BB 22 88 66 22

CC 88 1616 1818 00

DD 33 1919 1515 44

EE 99 2828 2323 55

2828 7777 1111

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

Average completion time = = 77/5 = 15.4 daysTotal flow timeNumber of jobs

Utilization = = 28/77 = 36.4%Total job work time

Total flow time

Average number of jobs in the system = = 77/28 = 2.75 jobs


Average job lateness = = 11/5 = 2.2 daysTotal late daysNumber of jobs




Flow Flow TimeTime



BB 22 22 66 00

DD 33 55 1515 00

AA 66 1111 88 33

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6565 99

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

Note:Job Tardiness for job i = Ti = Max {0, Li}, where Li = Lateness of job i can also be computed.







BB 22 22 66 00

DD 33 55 1515 00

AA 66 1111 88 33

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6565 99

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

Average completion time = = 65/5 = 13 daysTotal flow timeNumber of jobs


Total flow time




Note:As another measure of schedule performance,

Job Tardiness for job i = Ti = Max {0, Li}, where Li = Lateness of job i,

and accordingly, ‘Average Job Tardiness’ = T, can also be computed.







BB 22 22 66 00

AA 66 88 88 00

DD 33 1111 1515 00

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6868 66

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







BB 22 22 66 00

AA 66 88 88 00

DD 33 1111 1515 00

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6868 66

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



Total flow time







Flow Flow TimeTime



EE 99 99 2323 00

CC 88 1717 1818 00

AA 66 2323 88 1515

DD 33 2626 1515 1111

BB 22 2828 66 2222

2828 103103 4848

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







EE 99 99 2323 00

CC 88 1717 1818 00

AA 66 2323 88 1515

DD 33 2626 1515 1111

BB 22 2828 66 2222

2828 103103 4848

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



Total flow time





RuleRule

Average Average Completion Completion Time (Days)Time (Days)

Utilization Utilization (%)(%)

Average Number of Average Number of Jobs in SystemJobs in System

(a measure of WIP)(a measure of WIP)

Average Average Lateness Lateness

(Days)(Days)

Desired kind of Desired kind of performanceperformance LOWLOW HIGHHIGH LOWLOW LOWLOW

FCFSFCFS 15.415.4 36.436.4 2.752.75 2.22.2

SPTSPT 13.013.0 43.143.1 2.322.32 1.81.8

EDDEDD 13.613.6 41.241.2 2.432.43 1.21.2

LPTLPT 20.620.6 27.227.2 3.683.68 9.69.6

Summary of Performance Under the Various Priority Rules:Summary of Performance Under the Various Priority Rules:

Note:As another measure of schedule performance,

Job Tardiness for job i = Ti = Max {0, Li}, where Li = Lateness of job i,

and accordingly, ‘Average Job Tardiness’ = T, can also be computed.

Conclusion: SPT rule has performed best on the first three measures, and is reasonably good on the fourth measure also.

Comparison of Priority Sequencing RulesComparison of Priority Sequencing Rules

No one sequencing rule excels on all criteriaNo one sequencing rule excels on all criteria

SPT does well on minimizing flow time and SPT does well on minimizing flow time and number of jobs in the systemnumber of jobs in the system

But SPT moves long jobs to the end which But SPT moves long jobs to the end which may result in dissatisfied customersmay result in dissatisfied customers

FCFS does not do especially well (or poorly) FCFS does not do especially well (or poorly) on any criteria but is perceived as fair by on any criteria but is perceived as fair by customerscustomers

EDD minimizes latenessEDD minimizes lateness

Another Priority Dispatching Rule:Another Priority Dispatching Rule:Critical Ratio (CR) RuleCritical Ratio (CR) Rule

An index number found by dividing the time An index number found by dividing the time remaining until the due date by the work time remaining until the due date by the work time remaining on the jobremaining on the job

Jobs with low critical ratios are scheduled Jobs with low critical ratios are scheduled ahead of jobs with higher critical ratiosahead of jobs with higher critical ratios

Performs well on average job lateness Performs well on average job lateness criteriacriteria

CR = =CR = = Due date - Today’s dateDue date - Today’s date

Work (lead) time remainingWork (lead) time remaining

Time remainingTime remaining

Workdays remainingWorkdays remaining

Critical Ratio ExampleCritical Ratio Example

JobJobDue Due DateDate

Workdays Workdays RemainingRemaining Critical RatioCritical Ratio

Priority Priority OrderOrder

AA 3030 44 (30 - 25)/4 = 1.25(30 - 25)/4 = 1.25 33

BB 2828 55 (28 - 25)/5 = .60(28 - 25)/5 = .60 11

CC 2727 22 (27 - 25)/2 = 1.00(27 - 25)/2 = 1.00 22

Currently Day 25Currently Day 25

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

Critical Ratio TechniqueCritical Ratio Technique

1.1. Helps determine the status of specific jobsHelps determine the status of specific jobs

2.2. Establishes relative priorities among jobs Establishes relative priorities among jobs on a common basison a common basis

3.3. Relates both stock and make-to-order Relates both stock and make-to-order jobs on a common basisjobs on a common basis

4.4. Adjusts priorities automatically for Adjusts priorities automatically for changes in both demand and job progresschanges in both demand and job progress

5.5. Dynamically tracks job progressDynamically tracks job progress

4b. Sequencing for a 2-Machine Flow Shop,

using Johnson’s Rule

– A ‘Sequencing Algorithm’ for Scheduling

3.

Sequencing N Jobs on Two Machines: Sequencing N Jobs on Two Machines: Johnson’s RuleJohnson’s Rule

Works with two or more jobs that pass Works with two or more jobs that pass through the same two machines or work through the same two machines or work centerscenters

MinimizesMinimizes total production time total production time (also often (also often called the ‘called the ‘makespanmakespan’) and’) and idle time idle time..

It is based a property of a 2-machine flow It is based a property of a 2-machine flow shop problem that, for the criterion of shop problem that, for the criterion of minimizing ‘minimizing ‘makespanmakespan’, that, for the optimal ’, that, for the optimal solution, the sequence of jobs will be the solution, the sequence of jobs will be the same on both the machines.same on both the machines.

Johnson’s RuleJohnson’s Rule1.1. List all jobs and times for each work List all jobs and times for each work

centercenter

2.2. Choose the job with the shortest activity Choose the job with the shortest activity time. If that time is in the first work center, time. If that time is in the first work center, schedule the job first. If it is in the second schedule the job first. If it is in the second work center, schedule the job last.work center, schedule the job last.

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

4.4. Repeat steps 2 and 3 working toward the Repeat steps 2 and 3 working toward the center of the sequencecenter of the sequence

La Crosse, Wisconsin’s Tool and Die ShopLa Crosse, Wisconsin’s Tool and Die ShopJohnson’s Rule Example Johnson’s Rule Example (pp 580 -81)(pp 580 -81)

JobJobWork Center 1 Work Center 1

(Drill Press)(Drill Press)Work Center 2 Work Center 2

(Lathe)(Lathe)

AA 55 22

BB 33 66

CC 88 44

DD 1010 77

EE 77 1212

Johnson’s Rule ExampleJohnson’s Rule Example



(Lathe)(Lathe)

AA 55 22

BB 33 66

CC 88 44

DD 1010 77

EE 77 1212

DD AABB CCEE

Johnson’s Rule ExampleJohnson’s Rule Example



(Lathe)(Lathe)

AA 55 22

BB 33 66

CC 88 44

DD 1010 77

EE 77 1212

BB AACCDDEE

TimeTime 00 33 1010 2020 2828 3333

B ACDEWC 1

WC 2

Johnson’s Rule Example Johnson’s Rule Example (p 580 – 81)(p 580 – 81)



(Lathe)(Lathe)

AA 55 22

BB 33 66

CC 88 44

DD 1010 77

EE 77 1212

BB AACCDDEE

Sequence as determined by Johnson’s Rule:

TimeTime 00 33 1010 2020 2828 3333

TimeTime 0 0 11 33 55 77 99 1010 1111 1212 1313 1717 1919 21 22 2321 22 23 2525 2727 29 29 3131 3333 3535

B ACDE

B ACDE

WC 1

WC 2

BB EE DD CC AA

‘Bar Chart’ drawn for the Johnson’s Sequence for the ‘Two Machine Flow Shop’:

: Job completed

Legend:

The ‘Makespan’ realized with the above schedule = 35 hours

One More Example -- Johnson’s Rule – 5 JobsOne More Example -- Johnson’s Rule – 5 Jobs

Job

Proc. Time(days)

A

B

C

D

E

5 3

6 8

3 6

4 5

1 2

Seq.

5

4

3

1

2

WC1 WC2

A ‘Bar chart’ can be drawn for this sequence, and the minimum ‘makespan’ determined.

Limitations of Priority Rules-Based Limitations of Priority Rules-Based Dispatching Systems Dispatching Systems (p 582)(p 582)

1.1. Scheduling in practice needs to be dynamic, Scheduling in practice needs to be dynamic, and so the scheduling rules need to be and so the scheduling rules need to be revised to adjust to changes.revised to adjust to changes.

2.2. The Rules are based on local information at The Rules are based on local information at a work centre, and do not look upstream or a work centre, and do not look upstream or downstream, to consider information from downstream, to consider information from other work centers.other work centers.

3.3. Rules do not look beyond ‘due dates’, etc., Rules do not look beyond ‘due dates’, etc., to consider other intangible information that to consider other intangible information that may be available.may be available.

5. Cyclical Scheduling for Service Employees

(p 587 – 589)

4.

Development of Weekly Staffing Plan at Oncology Ward of Doris Laughlin’s Hospital (p 588)

• Staffing requirements for the Oncology Ward vary over the week. (Doctors tend to work early during the week, and patients tend to peak on Wednesday, and then taper off.)

• Staffing to be with the standard 5-days work week, with two consecutive days off for every employee, while meeting the needed staffing requirements for all the 7 days of the week.

• Also, need to minimize the total staff employed.

Development of Weekly Staffing Plan at Oncology Ward of Doris Laughlin’s Hospital (p 588)

Day Mon Tue Wed Thu Fri Sat Sun

Staff Requirement

5 5 6 5 4 3 3

Staffing Requirement:

Staff Requirement before assigning ‘work days’ and ‘off-days’ for an employee:

The ward requires 6 full time employees, and also one employee to work on Saturday:

One employee may work overtime on Saturday, or a part-time employee may be hired for Saturday.

Cyclical Scheduling – Some Observations

1. The ‘weekly cyclical scheduling’ takes advantage of the fixed length of a week (7 days).

2. There can also be ‘daily cyclical scheduling’ in terms of scheduling staffs in different ways during

a. Each of the ‘2-Production shifts’, or the ‘3-Production shifts’, operations for the operations staff,

b. The ‘General shift’ for the office staff, and

c. The ‘Maintenance shifts’ for the maintenance staff, and so on,

with appropriate planned roles and interactions between the staffs working in the various shifts.

Cyclical Scheduling – Some Observations(Continued)

3. ‘Cyclical scheduling’, as a practice, enables setting/ development of a rhythmic pattern in work, which can be

– Highly acceptable and enjoyable to people because of the simplicity and predictability that they provide, and

– Improved, through ‘continual improvements’ over time, to make an operation ‘uniformly highly efficient operation’.

4. In ‘Lean Operations’, the concept of ‘cyclical scheduling’ is often taken to further detailed levels, of

a. Hourly cycles of production schedules over the day, and

b. Takt time, ‘τ’, that becomes the common target cycle time for all operations throughout the organization.

Cyclical Scheduling – Some Observations(Continued)

5. In general, ‘order’ is characterized by simplicity, which is further characterized by periodicity’ or ‘cyclicity’ present in the associated processes. On the other hand ‘chaos’ is characterized by absence of such patterns of simplicity.

6. Thus, in scheduling, every effort should be made, wherever possible, to introduce cyclicity in scheduling.

7. ‘Lean’ is about a. First making cyclicity possible (through introduction of

‘leveled production’, etc., through process improvements), and then accordingly, also

b. Introduce the cyclicity (in terms of ‘Takt time’, τ) in scheduling.

6. Cases in ‘Operations Scheduling

1. Problem No.: 14.6 (pp 597): Clair Consultants (Assignmnt. prob.) 2. Problem No. 14.11 (pp 598): Avianic Engine Repair Inc.) (Single Machine Sequencing problem) 3. Problem No. 14.17 (pp 599): George Heinrich’s printing co. (Two m/c Flow Shop Seq. prob.) 4. Problem: Cyclical scheduling of service employees at Oncology

Ward (pp 588)5. Case: Scheduling Workers Who Fall Asleep is a Killer–Literally

(pp 568) 6. Case: Scheduling Aircraft Turnaround (pp 586) 7. HBSP 9-699-154: The Patient Care Delivery Model at the

Massachusetts General Hospital, 23pp.

1. Problem:

Problem No.: 14.6 (pp 597): Clair Consultants (Assignment

Problem)

2. Problem:

Problem No. 14.11 (pp 598): Avianic Engine Repair Inc.) (Single Machine

Sequencing problem)

3. Problem:

Problem No. 14.17 (pp 599): George Heinrich’s printing co.

(Two m/c Flow Shop Seq. prob.)

4. Problem:

Problem: Cyclical scheduling of service employees at Oncology

Ward (pp 588)

Assignment xCase: Scheduling at Hard Rock Café (pp 600)

•At Hard Rock, the ‘weekly cyclical scheduling’ process starts by “examining the last year’s sales at the café for the same day of the week.” •However, there may also be some observable seasonal pattern over a year (from the sales data), in addition to the weekly sales pattern. This may point to a need also for a cyclical scheduling process that covers a whole year.

Answer the four discussion questions at the end of the case, taking the above points into consideration.

(Submission date: x August 2010)

5. Case:

Scheduling Workers Who Fall Asleep is a Killer—Literally (pp

568)

5.

Case:

Scheduling Workers Who Fall Asleep is a Killer—Literally (pp 568)

1. Three case histories: Nuclear plants at (a) Three Miles Island, Pennsylvania, (b) Chernobyl, Russia, and the disaster at (c) Union Carbide, Bhopal—all occurred between midnight and 4.00 AM.

2. Similar case histories, of pilots involved in air crashes, and of workers in the night shifts.

3. Firms with 24/7 operations have a major problem.

4. Motorola, Dow Chemicals, Detroit Edison, Pennzoil, and Exxon give workers several days off between shift changes.

5. Shift work can be made less dangerous, with shifts that a. Do not exceed 12 hours,

b. Encourage 8 hours of sleep each day, and

c. Have extended time off between shift changes.

6. Case:

Scheduling Aircraft Turnaround (pp 586)

6.

Case:

Scheduling Aircraft Turnaround (pp 586)

1. The importance of efficient scheduling of ground turnaround activities for flights.

2. ‘Scheduling turnarounds in 20 minutes’ has been standard policy for years, for low-cost, point-to-point carriers like Southwest Airlines.

3. However, for others like Continental, United, and US Airways, the approach is new.

4. US Airways have been able to increase the average number of trips for an aircraft from six to seven, by cutting the turnaround time from 45 minutes to 20 minutes, using an improved six step approach

7. Case:

HBSP Case: 9-699-154: The Patient Care Delivery Model

at the Massachusetts General Hospital, 23pp.

7.

Case: ‘The Patient Care Delivery Model’at the Massachusetts General Hospital, 23pp.

1. What are the goals of the ‘Patient Care Delivery Model’ at MGH, as proposed by the consulting firm, and how is it supposed to accomplish them? What are the potential risks of the model?

2. Is the PCDM working? If not, what evidence do you have to prove it? How would you evaluate the results of the PCDM thus far?

3. What do you recommend that Jeanette Ives Erickson do next?

The End

Any Questions?

15 to 16. Operations Scheduling and Control - Ud 19 August 2010

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