Copyright 2006 John Wiley & Sons, Copyright 2006 John Wiley & Sons, Inc. Inc. Beni Asllani Beni Asllani University of Tennessee at University of Tennessee at Chattanooga Chattanooga Scheduling Scheduling Operations Management - 5 th Edition Chapter 16 Chapter 16 Roberta Russell & Bernard W. Taylor, III Roberta Russell & Bernard W. Taylor, III
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Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.Beni AsllaniBeni Asllani
University of Tennessee at ChattanoogaUniversity of Tennessee at Chattanooga
Roberta Russell & Bernard W. Taylor, IIIRoberta Russell & Bernard W. Taylor, III
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. 16-16-22
Lecture OutlineLecture Outline
Objectives in Scheduling Loading Sequencing Monitoring Advanced Planning and Scheduling Systems Theory of Constraints Employee Scheduling
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John Deere Case : Page 718 John Deere Case : Page 718
Scheduling ProblemScheduling Problem Genetic Algorithms (GA)Genetic Algorithms (GA)
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What is Scheduling?What is Scheduling?
Last stage of planning before production Last stage of planning before production occursoccurs
Specifies Specifies whenwhen labor, equipment, labor, equipment, facilities are needed to produce a facilities are needed to produce a product or provide a serviceproduct or provide a service
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Scheduling function differs Scheduling function differs based on type of operation .based on type of operation .
Process industriesProcess industries Mass ProductionMass Production ProjectsProjects Batch or Job Shop productionBatch or Job Shop production
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type of operationtype of operation
Projects one-of-a-kind production of a product to customer order
Batch production systems process many different jobs through the system in
groups or batches Mass production
produces large volumes of a standard product for a mass market
Continuous production (Process Industries) used for very-high volume commodity products
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Scheduled OperationsScheduled Operations
Process IndustryProcess Industry Linear programmingLinear programming EOQ with non-instantaneous EOQ with non-instantaneous
replenishmentreplenishment Mass ProductionMass Production
Assembly line balancingAssembly line balancing ProjectProject
Batch or Job shop Batch or Job shop ProductionProduction Aggregate planningAggregate planning Master schedulingMaster scheduling Material requirements Material requirements
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This chapter concentrates onThis chapter concentrates on
Batch or Job shop SchedulingBatch or Job shop Scheduling Is also known asIs also known as
Shop Floor control (SFC) orShop Floor control (SFC) or Production controlProduction control Production Activities Control (PAC)Production Activities Control (PAC)
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Shop Floor ControlShop Floor Control
Loading Loading [ [ จ่�ายงานให้เครื่ �องจ่�กรื่แต่�ละเครื่ �องจ่�ายงานให้เครื่ �องจ่�กรื่แต่�ละเครื่ �อง ]] Check availability of material, machines and laborCheck availability of material, machines and labor
Release work orders to shop and issue dispatch lists Release work orders to shop and issue dispatch lists for individual machinesfor individual machines
Monitoring Monitoring [ [ ต่�ดต่ามความกาวห้นาของแต่�ละงานต่�ดต่ามความกาวห้นาของแต่�ละงาน ]] Maintain progress reports on each job until it is Maintain progress reports on each job until it is
completecomplete
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LoadingLoading
Process of assigning work to limited resources
If there is enough capacity, perform work If there is enough capacity, perform work on most efficient resourceson most efficient resources
Use assignment method of linear Use assignment method of linear programming to determine allocationprogramming to determine allocation
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Assignment MethodAssignment Method
1.1. Perform row reductionsPerform row reductions subtract minimum value in each subtract minimum value in each
row from all other row valuesrow from all other row values
2.2. Perform column reductionsPerform column reductions subtract minimum value in each subtract minimum value in each
column from all other column column from all other column valuesvalues
3.3. Cross out all zeros in matrixCross out all zeros in matrix use minimum number of use minimum number of
horizontal and vertical lineshorizontal and vertical lines
4.4. If number of lines equals number of If number of lines equals number of rows in matrix then orows in matrix then optimum solution ptimum solution has been found. Make assignments has been found. Make assignments where zeros appearwhere zeros appear
5.5. Else modify matrixElse modify matrix subtract minimum uncrossed value subtract minimum uncrossed value
from all uncrossed valuesfrom all uncrossed values add it to all cells where two lines add it to all cells where two lines
intersectintersect other values in matrix remain other values in matrix remain
unchangedunchanged
6.6. Repeat steps 3 through 5 until Repeat steps 3 through 5 until optimum solution is reachedoptimum solution is reached
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Assignment Method: ExampleAssignment Method: Example
Row reductionRow reduction Column reduction Column reduction Cover all zeros Cover all zeros
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SequencingSequencing
Prioritize jobs assigned to a resourcePrioritize jobs assigned to a resource If no order specified use first-come If no order specified use first-come
first-served (FCFS)first-served (FCFS) Many other sequencing rules existMany other sequencing rules exist Each attempts to achieve to an Each attempts to achieve to an
objectiveobjective
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Sequencing RulesSequencing Rules
FCFS - first-come, first-servedFCFS - first-come, first-served LCFS - last come, first servedLCFS - last come, first served DDATE - earliest due dateDDATE - earliest due date CUSTPR - highest customer priorityCUSTPR - highest customer priority SETUP - similar required setupsSETUP - similar required setups SLACK - smallest slackSLACK - smallest slack
Slack = (due date – today’s date) – processing timeSlack = (due date – today’s date) – processing time CR - critical ratioCR - critical ratio SPT - shortest processing timeSPT - shortest processing time LPT - longest processing timeLPT - longest processing time
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Single Machine Scheduling ModelSingle Machine Scheduling Model
a queue of jobs at one machine.a queue of jobs at one machine. No new jobs arrive during the analysis.No new jobs arrive during the analysis. processing times and due dates are fixed.processing times and due dates are fixed. Setup times is considered negligible.(Setup times is considered negligible.( เวลาเวลา
AVERAGEAVERAGE AVERAGEAVERAGE NO. OFNO. OF MAXIMUMMAXIMUMRULERULE COMPLETION TIMECOMPLETION TIME TARDINESSTARDINESS JOBS TARDYJOBS TARDY TARDINESSTARDINESS
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Sequencing Jobs Through Two Sequencing Jobs Through Two Serial ProcessSerial Process
Flow ShopFlow Shop
…
m machines
n jobs
…..
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Flow ShopFlow Shop ม#ส่ถึาน#ผล�ต่ ม#ส่ถึาน#ผล�ต่ m m ส่ถึาน# ม#งาน ส่ถึาน# ม#งาน n n งานงาน งานแต่�ละงานต่องผ�านส่ถึาน#ผล�ต่ที่+กส่ถึาน#ไปัต่ามล�าด�บที่#�เห้ม อนงานแต่�ละงานต่องผ�านส่ถึาน#ผล�ต่ที่+กส่ถึาน#ไปัต่ามล�าด�บที่#�เห้ม อน
1.1. List time required to process each job at each List time required to process each job at each machine. Set up a one-dimensional matrix to machine. Set up a one-dimensional matrix to represent desired sequence with # of slots equal to represent desired sequence with # of slots equal to # of jobs.# of jobs.
2.2. 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 If that time is on machine 1, put the job as near to beginning of sequence as possible.beginning of sequence as possible.
3.3. If smallest time occurs on machine 2, put the job as If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible.near to the end of the sequence as possible.
4.4. Remove job from list.Remove job from list.5.5. Repeat steps 2-4 until all slots in matrix are filled Repeat steps 2-4 until all slots in matrix are filled
and all jobs are sequenced.and all jobs are sequenced.
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Johnson’s RuleJohnson’s 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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Johnson’s Rule (cont.)Johnson’s 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 Guidelines for Selecting a Sequencing RuleSequencing Rule
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 DDATE when only small tardiness values can Use DDATE when only small tardiness values can
be toleratedbe tolerated4.4. 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 be Do 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 package Shop paperwork that travels with a jobShop paperwork that travels with a job
Gantt ChartGantt Chart Shows both planned and completed Shows both planned and completed
activities against a time scaleactivities against a time scale Input/Output ControlInput/Output Control
Monitors the input and output from each Monitors the input and output from each work centerwork center
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11 22 33 44 55 66 88 99 1010 1111 1212 DaysDays
11
22
33
Today’s DateToday’s Date
Job 32BJob 32B
Job 23CJob 23C
Job 11CJob 11C Job 12AJob 12A
Fac
ility
Fac
ility
Key:Key: Planned activityPlanned activity
Completed 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 6565 6565 7070 7575
Actual inputActual input 6060 6060 6565 6565
DeviationDeviation
Planned outputPlanned output 7575 7575 7575 7575
Actual outputActual output 7070 7070 6565 6565
DeviationDeviation
BacklogBacklog 3030
PERIODPERIOD 11 22 33 44 TOTALTOTAL
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Actual outputActual output 7070 7070 6565 6565 270270
DeviationDeviation -5-5 -5-5 -10-10 -10-10 -30-30
BacklogBacklog 3030 2020 1010 1010 1010
PERIODPERIOD 11 22 33 44 TOTALTOTAL
Input/Output Control (cont.)Input/Output Control (cont.)
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Advanced Planning and Advanced Planning and Scheduling SystemsScheduling Systems
Infinite - assumes infinite capacityInfinite - assumes infinite capacity Loads without regard to capacityLoads without regard to capacity Then levels the load and sequences jobsThen levels the load and sequences jobs
Finite - assumes finite (limited) capacityFinite - assumes finite (limited) capacity Sequences jobs as part of the loading Sequences jobs as part of the loading
decisiondecision Resources are never loaded beyond Resources are never loaded beyond
capacitycapacity
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Advanced Planning and Advanced Planning and Scheduling Systems (cont.)Scheduling Systems (cont.)
Advanced planning and scheduling (APS)Advanced planning and scheduling (APS) Add-ins to ERP systemsAdd-ins to ERP systems Constraint-based programming (CBP) identifies a Constraint-based programming (CBP) identifies a
solution space and evaluates alternativessolution space and evaluates alternatives Genetic algorithms based on natural selection Genetic algorithms based on natural selection
properties of geneticsproperties of genetics Manufacturing execution system (MES) monitors Manufacturing execution system (MES) monitors
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Theory of ConstraintsTheory of Constraints
Not all resources are used evenlyNot all resources are used evenly Concentrate on the” bottleneck” Concentrate on the” bottleneck”
resourceresource Synchronize flow through the Synchronize flow through the
bottleneckbottleneck Use process and transfer batch sizes Use process and transfer batch sizes
to move product through facilityto move product through facility
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Drum-Buffer-Rope
DrumDrum Bottleneck, beating to set the pace of production for Bottleneck, beating to set the pace of production for
the rest of the systemthe rest of the system Buffer Buffer
Inventory, placed in front of the bottleneck to ensure Inventory, placed in front of the bottleneck to ensure it is always kept busyit is always kept busy
Determines output or throughput of the systemDetermines output or throughput of the system RopeRope
Communication signal, tells processes upstream Communication signal, tells processes upstream when they should begin productionwhen they should begin production
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TOC Scheduling Procedure
Identify bottleneck Schedule job first whose lead time to the
bottleneck is less than or equal bottleneck processing time
Forward schedule the bottleneck machine Backward schedule the other machines to
sustain the bottleneck schedule Transfer in batch sizes smaller than the
process batch size
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Operation Operation jj of item of item ii performed at performed at machine center machine center kk takes takes ll minutes minutes to processto process
Item Item iiKey:Key: i
ij ij k l l
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1.1. Let Let N = no. of workers availableN = no. of workers availableDDii = demand for workers on day i = demand for workers on day i
X = day workingX = day workingO = day offO = day off
2.2. Assign the first N - DAssign the first N - D11 workers day 1 off. Assign the next N - D workers day 1 off. Assign the next N - D22
workers day 2 off. Continue in a similar manner until all days are workers day 2 off. Continue in a similar manner until all days are have been scheduledhave been scheduled
3.3. If number of workdays for full time employee < 5, assign If number of workdays for full time employee < 5, assign remaining 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 employees
5.5. If consecutive days off are desired, consider switching schedules If consecutive days off are desired, consider switching schedules among days with the same demand requirementsamong days with the same demand requirements
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Revised schedule satisfies requirements with consecutive Revised schedule satisfies requirements with consecutive days off for most employeesdays off for most employees
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Automated Scheduling Systems
Staff Scheduling Schedule Bidding Schedule
Optimization
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