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C17 C17 Presentation Transcript

  • Chapter 17Scheduling
  • Lecture Outline• Objectives in Scheduling• Loading• Sequencing• Monitoring• Advanced Planning and Scheduling Systems• Theory of Constraints• Employee SchedulingCopyright 2011 John Wiley & Sons, Inc. 17-2
  • What is Scheduling?• Last stage of planning before production occurs• Specifies when labor, equipment, and facilitiesare needed to produce a product or provide aserviceCopyright 2011 John Wiley & Sons, Inc. 17-3
  • Scheduled Operations• Process Industry– Linear programming– EOQ with non-instantaneousreplenishment• Mass Production– Assembly line balancing• Project– Project -schedulingtechniques (PERT, CPM)• Batch Production– Aggregate planning– Master scheduling– Material requirementsplanning (MRP)– Capacity requirementsplanning (CRP)Copyright 2011 John Wiley & Sons, Inc. 17-4
  • Objectives in Scheduling• Meet customer due dates• Minimize job lateness• Minimize response time• Minimize completion time• Minimize time in thesystem• Minimize overtime• Maximize machine orlabor utilization• Minimize idle time• Minimize work-in-processinventoryCopyright 2011 John Wiley & Sons, Inc. 17-5
  • Shop Floor Control (SFC)• Schedule and monitor day-to-day job shopproduction• Also called production control and productionactivity control (PAC)• Performed by production control department• Loading - check availability of material, machines,and labor• Sequencing - release work orders to shop and issuedispatch lists for individual machines• Monitoring - maintain progress reports on each jobuntil it is completeCopyright 2011 John Wiley & Sons, Inc. 17-6
  • Loading• Process of assigning work to limited resources• Perform work with most efficient resources• Use assignment method of linear programmingto determine allocationCopyright 2011 John Wiley & Sons, Inc. 17-7
  • Assignment Method1. Perform row reductions– subtract minimum value in eachrow from all other row values2. Perform column reductions– subtract minimum value in eachcolumn from all other columnvalues3. Cross out all zeros in matrix– use minimum number ofhorizontal and vertical lines4. If number of lines equals numberof rows in matrix, then optimumsolution has been found. Makeassignments where zeros appear‾ Else modify matrix:‾ subtract minimum uncrossedvalue from all uncrossed values‾ add it to all cells where two linesintersect‾ other values in matrix remainunchanged5. Repeat steps 3 and 4 untiloptimum solution is reachedCopyright 2011 John Wiley & Sons, Inc. 17-8
  • Assignment MethodCopyright 2011 John Wiley & Sons, Inc. 17-9Initial PROJECTMatrix 1 2 3 4Bryan 10 5 6 10Kari 6 2 4 6Noah 7 6 5 6Chris 9 5 4 10Row reduction Column reduction Cover all zeros5 0 1 5 3 0 1 4 3 0 1 44 0 2 4 2 0 2 3 2 0 2 32 1 0 1 0 1 0 0 0 1 0 05 1 0 6 3 1 0 5 3 1 0 5Number lines number of rows so modify matrix
  • Copyright 2011 John Wiley & Sons, Inc. 17-101 2 3 4Bryan 1 0 1 2Kari 0 0 2 1Noah 0 3 2 0Chris 1 1 0 3PROJECT1 2 3 4Bryan 10 5 6 10Kari 6 2 4 6Noah 7 6 5 6Chris 9 5 4 10PROJECTProject Cost = (5 + 6 + 4 + 6) X $100 = $2,100Modify matrix Cover all zeros1 0 1 2 1 0 1 20 0 2 1 0 0 2 10 3 2 0 0 3 2 01 1 0 3 1 1 0 3Number of lines = number of rows so at optimal solutionAssignment Method
  • Assignment Method - SetupCopyright 2011 John Wiley & Sons, Inc. 17-11Solution goes hereOnly 1 leader canbe assigned toeach projectClick “Solve” forsolutionSum of all rows andcolumns = 1
  • Assignment Method - SolutionCopyright 2011 John Wiley & Sons, Inc. 17-12Assignments indicated by 1Cost of solution
  • Sequencing• Prioritize jobs assigned to a resource• If no order specified use first-come first-served (FCFS)• Other Sequencing Rules• FCFS - first-come, first-served• LCFS - last come, first served• DDATE - earliest due date• CUSTPR - highest customer priority• SETUP - similar required setups• SLACK - smallest slack• CR - smallest critical ratio• SPT - shortest processing time• LPT - longest processing timeCopyright 2011 John Wiley & Sons, Inc. 17-13
  • Minimum Slack & Smallest Critical Ratio• SLACK considers both work and time remaining• CR recalculates sequence as processingcontinues and arranges information in ratio formCopyright 2011 John Wiley & Sons, Inc. 17-14CR = =If CR > 1, job ahead of scheduleIf CR < 1, job behind scheduleIf CR = 1, job on scheduletime remaining due date - today’s datework remaining remaining processing timeSLACK = (due date – today’s date) – (processing time)
  • Sequencing Jobs Through One Process• Flow time (completion time)• Time for a job to flow through system• Makespan• Time for a group of jobs to be completed• Tardiness• Difference between a late job’s due date and itscompletion timeCopyright 2011 John Wiley & Sons, Inc. 17-15
  • Simple Sequencing RulesCopyright 2011 John Wiley & Sons, Inc. 17-16PROCESSING DUEJOB TIME DATEA 5 10B 10 15C 2 5D 8 12E 6 8
  • Simple Sequencing Rules: FCFSCopyright 2011 John Wiley & Sons, Inc. 17-17A 0 5 5 10 0B 5 10 15 15 0C 15 2 17 5 12D 17 8 25 12 13E 25 6 31 8 23Total 93 48Average 93/5 = 18.60 48/5 = 9.6FCFS START PROCESSING COMPLETION DUESEQUENCE TIME TIME TIME DATE TARDINESS
  • Simple Sequencing Rules: DDATECopyright 2011 John Wiley & Sons, Inc. 17-18C 0 2 2 5 0E 2 6 8 8 0A 8 5 13 10 3D 13 8 21 12 9B 21 10 31 15 16Total 75 28Average 75/5 = 15.00 28/5 = 5.6DDATE START PROCESSING COMPLETION DUESEQUENCE TIME TIME TIME DATE TARDINESS
  • Simple SequencingRules: SLACKCopyright 2011 John Wiley & Sons, Inc. 17-19A(10-0) – 5 = 5B(15-0) – 10 = 5C(5-0) – 2 = 3D(12-0) – 8 = 4E(8-0) – 6 = 2E 0 6 6 8 0C 6 2 8 5 3D 8 8 16 12 4A 16 5 21 10 11B 21 10 31 15 16Total 82 34Average 82/5 = 16.40 34/5 = 6.8SLACK START PROCESSING COMPLETION DUESEQUENCE TIME TIME TIME DATE TARDINESS
  • Simple Sequencing Rules: SPTCopyright 2011 John Wiley & Sons, Inc. 17-20C 0 2 2 5 0A 2 5 7 10 0E 7 6 13 8 5D 13 8 21 12 9B 21 10 31 15 16Total 74 30Average 74/5 = 14.80 30/5 = 6SPT START PROCESSING COMPLETION DUESEQUENCE TIME TIME TIME DATE TARDINESS
  • Simple Sequencing Rules: SummaryCopyright 2011 John Wiley & Sons, Inc. 17-21FCFS 18.60 9.6 3 23DDATE 15.00 5.6 3 16SLACK 16.40 6.8 4 16SPT 14.80 6.0 3 16AVERAGE AVERAGE NO. OF MAXIMUMRULE COMPLETION TIME TARDINESS JOBS TARDY TARDINESSBest values
  • Sequencing Jobs ThroughTwo Serial ProcessCopyright 2011 John Wiley & Sons, Inc. 17-22Johnson’s Rule1. List time required to process each job at each process. Set upa one-dimensional matrix to represent desired sequence with# of slots equal to # of jobs.2. Select smallest processing time at either process. If that timeis on process 1, put the job as near to beginning of sequenceas possible.3. If smallest time occurs on process 2, put the job as near to theend of the sequence as possible.4. Remove job from list.5. Repeat steps 2-4 until all slots in matrix are filled and all jobsare sequenced.
  • SequencingWithExcelCopyright 2011 John Wiley & Sons, Inc. 17-23
  • Johnson’s RuleCopyright 2011 John Wiley & Sons, Inc. 17-24JOB PROCESS 1 PROCESS 2A 6 8B 11 6C 7 3D 9 7E 5 10CE A BD
  • Johnson’s RuleCopyright 2011 John Wiley & Sons, Inc. 17-25A B CDEE A D B C Process 1(sanding)5 11 20 31 38E A D B C Process 2(painting)5 15 23 30 37 41Idle timeCompletion time = 41Idle time = 5+1+1+3=10
  • Excel for Johnson’s RuleCopyright 2011 John Wiley & Sons, Inc. 17-26User inputs processingtimes and sequenceExcel calculatescompletion timesand makespanWhen the set ofjobs is completed
  • Guidelines for Selecting aSequencing Rule• SPT most useful when shop is highly congested• Use SLACK for periods of normal activity• Use DDATE when only small tardiness values can betolerated• Use LPT if subcontracting is anticipated• Use FCFS when operating at low-capacity levels• Do not use SPT to sequence jobs that have to beassembled with other jobs at a later dateCopyright 2011 John Wiley & Sons, Inc. 17-27
  • Monitoring• Work package• Shop paperwork that travels with a job• Gantt Chart• Shows both planned and completed activities againsta time scale• Input/Output Control• Monitors the input and output from each work centerCopyright 2011 John Wiley & Sons, Inc. 17-28
  • Gantt ChartCopyright 2011 John Wiley & Sons, Inc. 17-291 2 3 4 5 6 8 9 10 11 12 Days123Today’s DateJob 32BJob 23CJob 11C Job 12AFacilityKey: Planned activityCompleted activityBehind scheduleAhead of scheduleOn schedule
  • Input/Output ControlCopyright 2011 John Wiley & Sons, Inc. 17-30Planned input 65 65 70 70 270Actual input 0Deviation 0Planned output 75 75 75 75 300Actual output 0Deviation 0Backlog 30PERIOD 1 2 3 4 TOTAL20 10 5 0
  • Input/Output ControlCopyright 2011 John Wiley & Sons, Inc. 17-31Planned input 65 65 70 70 270Actual input 60 60 65 65 250Deviation -5 -5 -5 -5 -20Planned output 75 75 75 75 300Actual output 75 75 65 65 280Deviation -0 -0 -10 -10 -20Backlog 30 15 0 0 0PERIOD 1 2 3 4 TOTAL
  • Excel for Input/Output ControlCopyright 2011 John Wiley & Sons, Inc. 17-32User inputsplanned andactual valuesExcel calculates deviationsand backlog
  • Advanced Planning and SchedulingSystems• Infinite scheduling - assumes infinite capacity• Loads without regard to capacity• Then levels the load and sequences jobs• Finite scheduling - assumes finite (limited)capacity• Sequences jobs as part of the loading decision• Resources are never loaded beyond capacityCopyright 2011 John Wiley & Sons, Inc. 17-33
  • Advanced Planning and SchedulingSystems• Advanced planning and scheduling (APS)• Add-ins to ERP systems• Constraint-based programming (CBP) identifies asolution space and evaluates alternatives• Genetic algorithms based on natural selectionproperties of genetics• Manufacturing execution system (MES) monitorsstatus, usage, availability, qualityCopyright 2011 John Wiley & Sons, Inc. 17-34
  • Advanced Planning and SchedulingCopyright 2011 John Wiley & Sons, Inc. 17-35
  • Theory of Constraints• Not all resources are used evenly• Finite scheduling approach• Concentrate on the” bottleneck” resource• Synchronize flow through the bottleneck• Use process and transfer batch sizes to moveproduct through facilityCopyright 2011 John Wiley & Sons, Inc. 17-36
  • Drum-Buffer-Rope• Drum• Bottleneck, beating to set the pace of production forthe rest of the system• Buffer• Inventory placed in front of the bottleneck to ensure itis always kept busy• Determines output or throughput of the system• Rope• Communication signal; tells processes upstreamwhen they should begin productionCopyright 2011 John Wiley & Sons, Inc. 17-37
  • TOC Scheduling Procedure• Identify bottleneck• Schedule job first whose lead time to bottleneckis less than or equal to bottleneck processingtime• Forward schedule bottleneck machine• Backward schedule other machines to sustainbottleneck schedule• Transfer in batch sizes smaller than processbatch sizeCopyright 2011 John Wiley & Sons, Inc. 17-38
  • Synchronous ManufacturingCopyright 2011 John Wiley & Sons, Inc. 17-39BAC DB1 1 5B2 2 3B3 1 7C1 3 2C2 1 10C3 2 15D1 3 10D2 2 8D3 3 5Item iKey: iIj k lOperation j of item i performed atmachine center k takes l minutesto process
  • Copyright 2011 John Wiley & Sons, Inc. 17-40Synchronous ManufacturingDemand = 100 A’sMachine setup time = 60 minutesMACHINE 1 MACHINE 2 MACHINE 3B1 5 B2 3 C1 2B3 7 C3 15 D3 5C2 10 D2 8 D1 10Sum 22 26* 17* Bottleneck
  • Synchronous ManufacturingCopyright 2011 John Wiley & Sons, Inc. 17-41Machine 1Machine 3SetupCompletiontime1002 232212 27320 200 1260 19402737C2 B1 B3C3 B2 D2C1 D1 D3IdleSetupSetupSetupSetup15621512 1872SetupMachine 2Idle2
  • Copyright 2011 John Wiley & Sons, Inc.Employee Scheduling• Labor is very flexible resource• Scheduling workforce is complicated, repetitivetask• Assignment method can be used• Heuristics are commonly used17-42Copyright 2011 John Wiley & Sons, Inc.
  • Employee Scheduling HeuristicCopyright 2011 John Wiley & Sons, Inc. 17-431. Let N = no. of workers availableDi = demand for workers on day iX = day workingO = day off2. Assign the first N - D1 workers day 1 off. Assign the next N - D2workers day 2 off. Continue in a similar manner until all days arehave been scheduled3. If number of workdays for full time employee < 5, assignremaining workdays so consecutive days off are possible4. Assign any remaining work to part-time employees5. If consecutive days off are desired, consider switching schedulesamong days with the same demand requirements
  • Employee SchedulingCopyright 2011 John Wiley & Sons, Inc. 17-44DAY OF WEEK M T W TH F SA SUMIN NO. OFWORKERS REQUIRED 3 3 4 3 4 5 3TaylorSmithSimpsonAllenDickerson
  • Employee SchedulingCopyright 2011 John Wiley & Sons, Inc. 17-45DAY OF WEEK M T W TH F SA SUMIN NO. OFWORKERS REQUIRED 3 3 4 3 4 5 3Taylor O X X O X X XSmith O X X O X X XSimpson X O X X O X XAllen X O X X X X ODickerson X X O X X X OCompleted schedule satisfies requirements but has noconsecutive days off
  • Copyright 2011 John Wiley & Sons, Inc. 17-46DAY OF WEEK M T W TH F SA SUMIN NO. OFWORKERS REQUIRED 3 3 4 3 4 5 3Taylor O O X X X X XSmith O O X X X X XSimpson X X O O X X XAllen X X X O X X ODickerson X X X X O X ORevised schedule satisfies requirements with consecutivedays off for most employeesEmployee Scheduling
  • Automated Scheduling Systems• Staff Scheduling• Assign workers to standardize shift patterns• Schedule Bidding• Workers bid for certain shift positions or schedules• Schedule Optimization• Creates demand-driven forecast of labor needs• Assigns workers to variable schedules• Uses mathematical programming and artificialintelligence techniquesCopyright 2011 John Wiley & Sons, Inc. 17-47
  • Copyright 2011 John Wiley & Sons, Inc. 17-48Copyright 2011 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation of thiswork beyond that permitted in section 117 of the 1976United States Copyright Act without express permissionof the copyright owner is unlawful. Request for furtherinformation should be addressed to the PermissionDepartment, John Wiley & Sons, Inc. The purchasermay make back-up copies for his/her own use only andnot for distribution or resale. The Publisher assumes noresponsibility for errors, omissions, or damages causedby the use of these programs or from the use of theinformation herein.