scheduling of operations

8/8/2019 Scheduling of Operations

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Terminologies(cont)

Administration related termsDispatching: Administrative process of authorizingprocessing of jobs by resources in the operating system, asidentified by the scheduling system. Authorization could bein the form of shop order or information communicatedelectronically.Expediting: Administrative process of reviewing the progressof the job in the operating system and ensuring that it travelsthrough various stages of the process as indicated inrouting, without harming the performance measures. If there

are deviations and delays, it calls for pushing the job forwardthrough the system.


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LoadingLoading

Process of assigning work to limited resourcesProcess of assigning work to limited resourcesPerform work on most efficient resourcesPerform work on most efficient resourcesUse assignment method of linear programmingUse assignment method of linear programmingto determine allocationto determine allocation


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Assignment Method: ExampleAssignment Method: Example

Row reductionRow reduction Column reductionColumn reduction Cover all zerosCover all zeros

55 00 11 55 33 00 11 44 33 0 1 44

44 00 22 44 22 00 22 33 22 0 2 3322 11 00 11 00 11 00 00 0 1 0 055 11 00 66 33 11 00 55 33 1 0 55

Number linesNumber lines number of rows so modify matrixnumber of rows so modify matrix

Initial PROJECTInitial PROJECTMatrixMatrix 11 2 2 33 44

BryanBryan 1010 55 66 1010KariKari 66 22 44 66

NoahNoah 77 66 55 66ChrisChris 99 55 44 1010


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Assignment Method: Example (cont.)Assignment Method: Example (cont.)

Modify matrixModify matrix Cover all zerosCover all zeros11 00 11 22 1 0 1 200 00 22 11 0 0 2 100 33 22 00 0 3 2 011 11 00 33 1 1 0 3

Number of lines = number of rows so at optimal solutionNumber of lines = number of rows so at optimal solution

11 2 2 33 44

BryanBryan 11 00 11 22

KariKari 00 00 22 11NoahNoah 00 33 22 00ChrisChris 11 11 00 33

PROJECTPROJECT11 2 2 33 44

BryanBryan 1010 5 66 1010

KariKari 6 22 44 66NoahNoah 77 66 55 6ChrisChris 99 55 4 1010

PROJECTPROJECT

Project Cost = 5 + 6 + 6 + 4 = 21Project Cost = 5 + 6 + 6 + 4 = 21


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Scheduling ContextScheduling Context

The following parameters adequately describeThe following parameters adequately describethe scheduling problem.the scheduling problem.

Number of machines/resourcesNumber of machines/resourcesNumber of jobsNumber of jobsShop configuration: the manner in which machinesShop configuration: the manner in which machinesare organized on the shop floor and the flow patternare organized on the shop floor and the flow patternof the jobs utilizing the machines.of the jobs utilizing the machines.

Flow shop resources are organized one after other in theFlow shop resources are organized one after other in theorder the jobs are processes. If there areorder the jobs are processes. If there are n n jobs, there are jobs, there aren n ! ways in which one can draw up alternative schedule.! ways in which one can draw up alternative schedule.Job shop machines are not organized in processingJob shop machines are not organized in processingorder, rather similar type of resources is grouped together.order, rather similar type of resources is grouped together.If there areIf there are n n jobs and jobs and m m machines, there are (machines, there are ( n n !)!)m m ways inways inwhich one can draw up alternative schedule.which one can draw up alternative schedule.


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Scheduling RulesScheduling Rules

SPT - shortest processing timeSPT - shortest processing timeLPT - longest processing timeLPT - longest processing timeEDD - Earliest Due DateEDD - Earliest Due DateCR - critical ratioCR - critical ratio

Considers both processing time and due date information.Considers both processing time and due date information.CR estimates the criticality of the job asCR estimates the criticality of the job as

CR = Remaining time / Remaining workCR = Remaining time / Remaining work= (Due date Current date) / Remaining processing time= (Due date Current date) / Remaining processing time

Smaller the value of CR indicates the job is more critical.Smaller the value of CR indicates the job is more critical.If CR < 1, indicates the available time is not sufficient and the job is alreadyIf CR < 1, indicates the available time is not sufficient and the job is alreadyrunning late and if CR > 1, indicates some slack is available for the job.running late and if CR > 1, indicates some slack is available for the job.

FCFS - first-come, first-servedFCFS - first-come, first-served

LCFS - last come, first servedLCFS - last come, first servedRAN Random orderRAN Random orderCUSTPR - highest customer priorityCUSTPR - highest customer prioritySETUP - similar required setupsSETUP - similar required setups


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Job No Processing time

Orderof

arrival

Due by

1 12 1 23

2 9 2 243 22 3 30

4 11 4 20

CR Order

1.917 3

2.667 41.364 1

1.818 2

SPT LPT EDD FCFS

3 2 2 1

1 4 3 24 1 4 3

2 3 1 4

Random No RAN

0.8403 3

0.9930 4

0.6439 2

0.4418 1

Current time = 0

EXAMPLE


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Performance criterionPerformance criterion

Completion-based measuresCompletion-based measuresAssessment of the processing time is done.Assessment of the processing time is done.Frequently used measures:Frequently used measures:

Flow Time the elapsed time between releasing a job into theFlow Time the elapsed time between releasing a job into the

shop and the time of completion of processing of the job. It isshop and the time of completion of processing of the job. It isequal to the sum of processing time of all operations of the jobequal to the sum of processing time of all operations of the joband other non-productive time including waiting and moving time.and other non-productive time including waiting and moving time.

Release time of the job be RRelease time of the job be R ii, Completion time of the job be C, Completion time of the job be C ii, then, thenFlow time FFlow time F ii = R= R ii C C ii

Make span the time taken to complete all the jobs released intoMake span the time taken to complete all the jobs released intothe shop for processing. It is the completion time of the last job inthe shop for processing. It is the completion time of the last job inthe shop.the shop.

Make span (maximum completion time) CMake span (maximum completion time) C maxmax = max { C= max { C ii }}


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Due date-based measuresDue date-based measuresEfficacy of the scheduling rule is evaluated with reference to theEfficacy of the scheduling rule is evaluated with reference to thedue date of the jobs.due date of the jobs.Measures:Measures:

Lateness: The difference between completion time and due date.Lateness: The difference between completion time and due date.If the due date is denoted as DIf the due date is denoted as D ii, then lateness L, then lateness L ii = C= C ii D D ii

Tardiness: Captures information of only those jobs that are late.Tardiness: Captures information of only those jobs that are late.Negative values of lateness are considered to be 0.Negative values of lateness are considered to be 0.

Tardiness TTardiness T ii = max(0, L= max(0, L ii))

Number of tardy jobs nNumber of tardy jobs n TT

Utilization-based measuresUtilization-based measuresBased on actual inventory build up in the shop or utilization of the shopBased on actual inventory build up in the shop or utilization of the shopresources.resources.Measures include the mean number of jobs waiting, mean number ofMeasures include the mean number of jobs waiting, mean number offinished jobs,finished jobs,Simulation models are typically used such scheduling problems.Simulation models are typically used such scheduling problems.

Performance criterion (cont)Performance criterion (cont)


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PROCESSINGPROCESSING DUEDUEJOBJOB TIMETIME DATEDATE

AA 55 1010BB 1010 1515CC 22 55DD 88 1212EE 66 88

Example


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Sequencing Rules: FCFSSequencing Rules: FCFS

AA 00 55 55 1010 00BB 55 1010 1515 1515 00CC 1515 22 1717 55 1212DD 1717 88 2525 1212 1313

EE

2525

66

3131

88

2323

FCFSFCFS STARTSTART PROCESSINGPROCESSING COMPLETIONCOMPLETION DUEDUESEQUENCESEQUENCE TIMETIME TIMETIME TIMETIME DATEDATE TARDINESSTARDINESS


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Sequencing Rules: EDDSequencing Rules: EDD

CC 00 22 22 55 00EE 22 66 88 88 00AA 88 55 1313 1010 33DD 1313 88 2121 1212 99BB 2121 1010 3131 1515 1616

EDDEDD STARTSTART PROCESSINGPROCESSING COMPLETIONCOMPLETION DUEDUESEQUENCESEQUENCE TIMETIME TIMETIME TIMETIME DATEDATE TARDINESSTARDINESS


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A(10-0) 5 = 5B(15-0) - 10 = 5C(5-0) 2 = 3D(12-0) 8 = 4E(8-0) 6 = 2

Sequencing Rules:Sequencing Rules:

SLACK SLACK

EE 00 66 66 88 00

CC 66 22 88 55 33DD 88 88 1616 1212 44AA 1616 55 2121 1010 1111BB 2121 1010 3131 1515 1616

SLACKSLACK STARTSTART PROCESSINGPROCESSING COMPLETIONCOMPLETION DUEDUESEQUENCESEQUENCE TIMETIME TIMETIME TIMETIME DATEDATE TARDINESSTARDINESS


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A(10)/5 = 2.00B(15)/10 = 1.50

C (5)/2 = 2.50D(12)/8 = 1.50E (8)/6 = 1.33

Sequencing Rules: CRSequencing Rules: CR

EE 00 66 66 88 00DD 66 88 1414 1212 22BB 1414 1010 2424 1515 99AA 2424 55 2929 1010 1919

CC 2929 22 3131 55 2626

CRCR STARTSTART PROCESSINGPROCESSING COMPLETIONCOMPLETION DUEDUE

SEQUENCESEQUENCE TIMETIME TIMETIME TIMETIME DATEDATE TARDINESSTARDINESS


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Sequencing Rules: SPTSequencing Rules: SPT

CC 00 22 22 55 00AA 22 55 77 1010 00EE 77 66 1313 88 55DD 1313 88 2121 1212 99BB 2121 1010 3131 1515 1616

SPTSPT STARTSTART PROCESSINGPROCESSING COMPLETIONCOMPLETION DUEDUESEQUENCESEQUENCE TIMETIME TIMETIME TIMETIME DATEDATE TARDINESSTARDINESS


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Sequencing Rules: SummarySequencing Rules: Summary

FCFSFCFS 18.6018.60 9.69.6 3 2323DDATEDDATE 15.0015.00 5.6 3 16SLACKSLACK 16.4016.40 6.86.8 44 1616CRCR 20.8020.80 11.211.2 44 2626SPTSPT 14.80 6.06.0 3 16

AVERAGEAVERAGE AVERAGEAVERAGE NO. OFNO. OF MAXIMUMMAXIMUMRULERULE COMPLETION TIMECOMPLETION TIME TARDINESSTARDINESS JOBS TARDYJOBS TARDY TARDINESSTARDINESS


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A manufacturer is in the process of assessing theA manufacturer is in the process of assessing theusefulness of SPT and EDD rules for the purpose of usefulness of SPT and EDD rules for the purpose of scheduling four jobs on a machine. The tablescheduling four jobs on a machine. The tablebelow gives the related information. Computebelow gives the related information. Computerelevant performance measures and comment.relevant performance measures and comment.

Job No Job No Process timeProcess time Due byDue by11 44 6622 77 9933 22 191944 88 1717


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A flow process with two machines andA flow process with two machines andnn number of jobs to be scheduled.number of jobs to be scheduled.

Johnsons RuleJohnsons RuleList time required to process each job at each machine.List time required to process each job at each machine.Set up a one-dimensional matrix to represent desired sequenceSet up a one-dimensional matrix to represent desired sequencewith number of slots equal to number of jobs.with number of slots equal to number of jobs.Select smallest processing time at either machine.Select smallest processing time at either machine.If that time is on machine 1, put the job as near to beginning ofIf that time is on machine 1, put the job as near to beginning ofsequence as possible.sequence as possible.If smallest time occurs on machine 2, put the job as near to theIf smallest time occurs on machine 2, put the job as near to theend of the sequence as possible.end of the sequence as possible.Remove job from list.Remove job from list.Repeat until all slots in matrix are filled and all jobs are sequenced.Repeat until all slots in matrix are filled and all jobs are sequenced.

The resulting sequence of the jobs is the best schedule to minimizeThe resulting sequence of the jobs is the best schedule to minimizethe make span of the jobs.the make span of the jobs.


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EXAMPLE: Using Johnsons RuleEXAMPLE: Using Johnsons Rule

JOBJOB PROCESS 1PROCESS 1 PROCESS 2PROCESS 2

AA 66 88BB 1111 66CC 77 33DD 99 77EE 55 1010

CE A BD


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Johnsons Rule (cont.) Johnsons Rule (cont.)

A B CDE

E A D B C Process 1Process 1(sanding)(sanding)

55 1111 2020 3131 3838

E A D B C Process 2Process 2

(painting)(painting)

55 1515 2323 3030 3737 4141

Idle timeIdle time

Completion time = 41Idle time = 5+1+1+3=10


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Guidelines for Selecting a SequencingGuidelines for Selecting a SequencingRuleRule

1.1. SPT most useful when shop is highly congestedSPT most useful when shop is highly congested2.2. Use SLACK for periods of normal activityUse SLACK for periods of normal activity3.3. Use EDD when only small tardiness values can beUse EDD when only small tardiness values can be

toleratedtolerated4.4. Use LPT if subcontracting is anticipatedUse LPT if subcontracting is anticipated5.5. Use FCFS when operating at low-capacity levelsUse FCFS when operating at low-capacity levels6.6. Do not use SPT to sequence jobs that have to beDo not use SPT to sequence jobs that have to be

assembled with other jobs at a later dateassembled with other jobs at a later date


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MonitoringMonitoring

Work packageWork packageShop paperwork that travels with a jobShop paperwork that travels with a job

Gantt ChartGantt ChartShows both planned and completed activities against aShows both planned and completed activities against atime scaletime scale

Input/Output ControlInput/Output ControlMonitors the input and output from each work centerMonitors the input and output from each work center


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11 22 33 44 55 66 88 99 1010 1111 1212 DaysDays

11

22

33

Todays DateTodays Date

Job 32BJob 32B

Job 23CJob 23C

Job 11CJob 11C Job 12AJob 12A

F a c

i l i t y

F a c

i l i t y

Key:Key: Planned activityPlanned activityCompleted activityCompleted activity

Behind scheduleBehind schedule

Ahead of scheduleAhead of schedule

On scheduleOn schedule

Gantt ChartGantt Chart


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Input/Output ControlInput/Output Control

Input/Output ReportInput/Output Report

Planned inputPlanned input 6060 6565 7070 7575Actual inputActual input 6060 6060 6565 6565DeviationDeviation

Planned outputPlanned output 7575 7575 7575 7575Actual outputActual output 7070 8080 7070 6565DeviationDeviation

BacklogBacklog 3030

PERIODPERIOD 11 22 33 44 TOTALTOTAL


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Input/Output ReportInput/Output Report

Planned inputPlanned input 6060 6565 7070 7575 270270Actual inputActual input 6060 6060 6565 6565 250250DeviationDeviation 00 -5-5 -5-5 -10-10 -20-20

Planned outputPlanned output 7575 7575 7575 7575 300300Actual outputActual output 7070 8080 7070 6565 270270DeviationDeviation -5-5 55 -5-5 -10-10 -30-30

BacklogBacklog 3030 3535 3535 4545 6565

PERIODPERIOD 11 22 33 44 TOTALTOTAL

Input/Output Control (cont.)Input/Output Control (cont.)


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Employee SchedulingEmployee Scheduling

Labor is very flexible resourceLabor is very flexible resourceScheduling workforce is complicated repetitive taskScheduling workforce is complicated repetitive taskAssignment method can be usedAssignment method can be usedHeuristics are commonly usedHeuristics are commonly used


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Employee Scheduling HeuristicEmployee Scheduling Heuristic

1.1. LetLet N = no. of workers availableN = no. of workers availableDi = demand for workers on day iDi = demand for workers on day iX = day workingX = day workingO = day offO = day off

2.2. Assign the first N - D1 workers day 1 off. Assign the next N -Assign the first N - D1 workers day 1 off. Assign the next N -D2 workers day 2 off. Continue in a similar manner until allD2 workers day 2 off. Continue in a similar manner until alldays are have been scheduleddays are have been scheduled

3.3. If number of workdays for full time employee < 5, assignIf number of workdays for full time employee < 5, assignremaining workdays so consecutive days off are possibleremaining workdays so consecutive days off are possible

4.4. Assign any remaining work to part-time employeesAssign any remaining work to part-time employees5.5. If consecutive days off are desired, consider switchingIf consecutive days off are desired, consider switching

schedules among days with the same demand requirementsschedules among days with the same demand requirements


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DAY OF WEEKDAY OF WEEK MM TT WW THTH FF SASA SUSUMIN NO. OFMIN NO. OF

WORKERS REQUIREDWORKERS REQUIRED 33 33 44 33 44 55 33

Taylor Taylor

SmithSmithSimpsonSimpsonAllenAllenDickersonDickerson

Employee SchedulingEmployee Scheduling


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Taylor Taylor OO XX XX OO XX XX XX

SmithSmith OO XX XX OO XX XX XXSimpsonSimpson XX OO XX XX OO XX XXAllenAllen XX OO XX XX XX XX OODickersonDickerson XX XX OO XX XX XX OO

Completed schedule satisfies requirements but has noCompleted schedule satisfies requirements but has noconsecutive days off consecutive days off

Employee Scheduling (cont.)Employee Scheduling (cont.)


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Employee Scheduling (cont.)Employee Scheduling (cont.)



Taylor Taylor OO OO XX XX XX XX XX

SmithSmith OO OO XX XX XX XX XXSimpsonSimpson XX XX OO OO XX XX XXAllenAllen XX XX XX OO XX XX OODickersonDickerson XX XX XX XX OO XX OO

Revised schedule satisfies requirements with consecutiveRevised schedule satisfies requirements with consecutivedays off for most employeesdays off for most employees

scheduling of operations

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