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Scheduling Çizelgeleme
Chapter 16 Scheduling Çizelgeleme Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III Beni Asllani University of Tennessee at Chattanooga Copyright 2006 John Wiley & Sons, Inc.
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Lecture Outline Objectives in Scheduling Loading Sequencing Monitoring
Advanced Planning and Scheduling Systems Theory of Constraints Employee Scheduling Copyright 2006 John Wiley & Sons, Inc.
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What is Scheduling? Çizelgeleme Nedir?)
Last stage of planning before production occurs (üretimin gerçekleşmesinden önceki son aşama Specifies when labor, equipment, facilities are needed to produce a product or provide a service (bir ürün ya da hizmet sağlamak için işgücü, donanım, tesislere ne zaman ihtiyaç duyulacağını belirler) Copyright 2006 John Wiley & Sons, Inc.
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Scheduled Operations Process Industry Mass Production Project
Linear programming EOQ with non-instantaneous replenishment Mass Production Assembly line balancing Project Project -scheduling techniques (PERT, CPM) Batch Production Aggregate planning Master scheduling Material requirements planning (MRP) Capacity requirements planning (CRP) Copyright 2006 John Wiley & Sons, Inc.
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Objectives in Scheduling Çizelgelemenin Amaçları
Meet customer due dates (müşteriye teslim tarihlerinin karşılanması) Minimize job lateness (gecikmelerin minimize edilmesi) Minimize response time (tepki sürelerinin minimize edilmesi) Minimize completion time (tamamlanma sürelerinin minimize edilmesi) Minimize time in the system (sistemde geçirilen sürenin minimize edilmesi Minimize overtime (fazla mesainin minimize edilmesi) Maximize machine or labor utilization (Makine ve işgücü kullanım oranlarının maksimize edilmesi) Minimize idle time (boş zamanın minimize edilmesi) Minimize work-in-process inventory (işlenmekte olan parça stokunun minimize edilmesi) Copyright 2006 John Wiley & Sons, Inc.
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Shop Floor Control (Atöyle Denetimi
Loading (İş yükleme) Check availability of material, machines and labor Malzeme, makine ve işgücünün mevcudiyetinin kontrol edilmesi Sequencing (İş sıralama) Release work orders to shop and issue dispatch lists for individual machines Atölyeye, bireysel makineler için iş emirlerinin gönderilmesi Monitoring (izleme) Maintain progress reports on each job until it is complete Her iş(sipariş) tamamlanıncaya kadar ilerleme raporlarının hazırlanması Copyright 2006 John Wiley & Sons, Inc.
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Loading İş yükleme Process of assigning work to limited resources Sınırlı kaynaklara işlerin tahsis edilmesi süreci Perform work on most efficient resources Et etkin kaynaklar üzerinde işin yapılması Use assignment method of linear programming to determine allocation Tahsis için DP’nin tahsis yönteminin kullanılması Copyright 2006 John Wiley & Sons, Inc.
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Assignment Method Perform row reductions Perform column reductions
subtract minimum value in each row from all other row values Perform column reductions subtract minimum value in each column from all other column values Cross out all zeros in matrix use minimum number of horizontal and vertical lines If number of lines equals number of rows in matrix then optimum solution has been found. Make assignments where zeros appear Else modify matrix subtract minimum uncrossed value from all uncrossed values add it to all cells where two lines intersect other values in matrix remain unchanged Repeat steps 3 through 5 until optimum solution is reached Copyright 2006 John Wiley & Sons, Inc.
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Assignment Method: Example
Initial PROJECT Matrix Bryan Kari Noah Chris Row reduction Column reduction Cover all zeros Number lines number of rows so modify matrix Copyright 2006 John Wiley & Sons, Inc. 12
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Assignment Method: Example (cont.)
Modify matrix Cover all zeros Number of lines = number of rows so at optimal solution Bryan Kari Noah Chris PROJECT Bryan Kari Noah Chris Project Cost = ( ) X $100 = $2,100 Copyright 2006 John Wiley & Sons, Inc. 12
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Sequencing Prioritize jobs assigned to a resource
If no order specified use first-come first-served (FCFS) Many other sequencing rules exist Each attempts to achieve to an objective Copyright 2006 John Wiley & Sons, Inc.
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Sequencing Rules Sıralama Kuralları)
FCFS - first-come, first-served (İl gelene ilk hizmet) LCFS - last come, first served (Son gelene ilk hizmet) DDATE - earliest due date (en erken teslim tarihi) CUSTPR - highest customer priority (en yüksek müşteri önceliği) SETUP - similar required setups (benzer makine hazırlık gerektiren) SLACK - smallest slack (boşluğu en küçük olan) CR - critical ratio (kritik oran SPT - shortest processing time (en düşük işleme süresi) LPT - longest processing time (en uzun işleme süresi) Copyright 2006 John Wiley & Sons, Inc.
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Critical Ratio Rule CR considers both time and work remaining Hem
süreyi hem de kalan süreyi ele alır CR = = If CR > 1, job ahead of schedule (iş, planın ilerisindedir) If CR < 1, job behind schedule (iş, planın gerisindedir) If CR = 1, job on schedule (iş, planlandığı gibi gitmektedir) time remaining kalan süre) due date - today’s date work remaining(kalan iş) remaining processing time Copyright 2006 John Wiley & Sons, Inc.
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Sequencing Jobs Through One Process
Flowtime (completion time) Akış süresi (tamamlanma zamanı) Time for a job to flow through the system (bir işin sistemde akış süresi) Makespan (üretim süresi Time for a group of jobs to be completed (bir grup işin tamamlanma süresi) Tardiness (Gecikme) Difference between a late job’s due date and its completion time (işin teslim tarihi ile tamamlanma tarihi arasındaki fark) Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules
PROCESSING DUE JOB TIME DATE A 5 10 B 10 15 C 2 5 D 8 12 E 6 8 Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: FCFS
A B C D E FCFS START PROCESSING COMPLETION DUE SEQUENCE TIME TIME TIME DATE TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: DDATE
B DDATE START PROCESSING COMPLETION DUE SEQUENCE TIME TIME TIME DATE TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: SLACK
B (15-0) - 10 = 5 C (5-0) – 2 = 3 D (12-0) – 8 = 4 E (8-0) – 6 = 2 Simple Sequencing Rules: SLACK E C D A B SLACK START PROCESSING COMPLETION DUE SEQUENCE TIME TIME TIME DATE TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: CR
A (10)/5 = 2.00 B (15)/10 = 1.50 C (5)/2 = 2.50 D (12)/8 = 1.50 E (8)/6 = 1.33 Simple Sequencing Rules: CR E D B A C CR START PROCESSING COMPLETION DUE SEQUENCE TIME TIME TIME DATE TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: SPT
A E D B SPT START PROCESSING COMPLETION DUE SEQUENCE TIME TIME TIME DATE TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Simple Sequencing Rules: Summary
FCFS DDATE SLACK CR SPT AVERAGE AVERAGE NO. OF MAXIMUM RULE COMPLETION TIME TARDINESS JOBS TARDY TARDINESS Copyright 2006 John Wiley & Sons, Inc.
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Sequencing Jobs Through Two Serial Process
Johnson’s Rule List time required to process each job at each machine. Set up a one-dimensional matrix to represent desired sequence with # of slots equal to # of jobs. Select smallest processing time at either machine. If that time is on machine 1, put the job as near to beginning of sequence as possible. If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible. Remove job from list. Repeat steps 2-4 until all slots in matrix are filled and all jobs are sequenced. Copyright 2006 John Wiley & Sons, Inc.
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Johnson’s Rule A B C D E JOB PROCESS 1 PROCESS 2 A 6 8 B 11 6 C 7 3
Copyright 2006 John Wiley & Sons, Inc.
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Johnson’s Rule (cont.) E A D B C Completion time = 41
Process 1 (sanding) 5 11 20 31 38 Process 2 (painting) 15 23 30 37 41 Idle time Completion time = 41 Idle time = =10 Copyright 2006 John Wiley & Sons, Inc.
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Guidelines for Selecting a Sequencing Rule
SPT most useful when shop is highly congested Use SLACK for periods of normal activity Use DDATE when only small tardiness values can be tolerated Use LPT if subcontracting is anticipated Use FCFS when operating at low-capacity levels Do not use SPT to sequence jobs that have to be assembled with other jobs at a later date Copyright 2006 John Wiley & Sons, Inc.
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Monitoring Work package Gantt Chart Input/Output Control
Shop paperwork that travels with a job Gantt Chart Shows both planned and completed activities against a time scale Input/Output Control Monitors the input and output from each work center Copyright 2006 John Wiley & Sons, Inc.
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Gantt Chart 1 2 3 4 5 6 8 9 10 11 12 Days Today’s Date Job 32B Job 23C
Job 12A Facility Key: Planned activity Completed activity Behind schedule Ahead of schedule On schedule Copyright 2006 John Wiley & Sons, Inc.
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Input/Output Control Input/Output Report PERIOD 1 2 3 4 TOTAL
Planned input Actual input Deviation Planned output Actual output Backlog 30 PERIOD TOTAL Copyright 2006 John Wiley & Sons, Inc.
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Input/Output Control (cont.)
Input/Output Report Planned input Actual input Deviation Planned output Actual output Deviation Backlog PERIOD TOTAL Copyright 2006 John Wiley & Sons, Inc.
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Advanced Planning and Scheduling Systems
Infinite - assumes infinite capacity Loads without regard to capacity Then levels the load and sequences jobs Finite - assumes finite (limited) capacity Sequences jobs as part of the loading decision Resources are never loaded beyond capacity Copyright 2006 John Wiley & Sons, Inc.
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Advanced Planning and Scheduling Systems (cont.)
Advanced planning and scheduling (APS) Add-ins to ERP systems Constraint-based programming (CBP) identifies a solution space and evaluates alternatives Genetic algorithms based on natural selection properties of genetics Manufacturing execution system (MES) monitors status, usage, availability, quality Copyright 2006 John Wiley & Sons, Inc.
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Theory of Constraints Not all resources are used evenly
Concentrate on the” bottleneck” resource Synchronize flow through the bottleneck Use process and transfer batch sizes to move product through facility Copyright 2006 John Wiley & Sons, Inc.
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Drum-Buffer-Rope Drum Buffer Rope
Bottleneck, beating to set the pace of production for the rest of the system Buffer Inventory, placed in front of the bottleneck to ensure it is always kept busy Determines output or throughput of the system Rope Communication signal, tells processes upstream when they should begin production Copyright 2006 John Wiley & Sons, Inc.
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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 Copyright 2006 John Wiley & Sons, Inc.
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Synchronous Manufacturing
B A C D B B B C C C D D D Operation j of item i performed at machine center k takes l minutes to process Item i Key: i ij k l Synchronous Manufacturing Copyright 2006 John Wiley & Sons, Inc.
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Synchronous Manufacturing (cont.)
Demand = 100 A’s Machine setup time = 60 minutes MACHINE 1 MACHINE 2 MACHINE 3 B1 5 B2 3 C1 2 B3 7 C3 15 D3 5 C2 10 D2 8 D1 10 Sum * 17 * Bottleneck Copyright 2006 John Wiley & Sons, Inc.
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Synchronous Manufacturing (cont.)
Machine 1 Machine 3 Setup Completion time 1002 2322 12 2732 200 1260 1940 2737 C2 B1 B3 C3 B2 D2 C1 D1 D3 Idle 1562 1512 1872 Machine 2 2 Copyright 2006 John Wiley & Sons, Inc.
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Employee Scheduling Labor is very flexible resource
Scheduling workforce is complicated repetitive task Assignment method can be used Heuristics are commonly used Copyright 2006 John Wiley & Sons, Inc.
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Employee Scheduling Heuristic
Let N = no. of workers available Di = demand for workers on day i X = day working O = day off Assign the first N - D1 workers day 1 off. Assign the next N - D2 workers day 2 off. Continue in a similar manner until all days are have been scheduled If number of workdays for full time employee < 5, assign remaining workdays so consecutive days off are possible Assign any remaining work to part-time employees If consecutive days off are desired, consider switching schedules among days with the same demand requirements Copyright 2006 John Wiley & Sons, Inc.
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Employee Scheduling DAY OF WEEK M T W TH F SA SU MIN NO. OF
WORKERS REQUIRED Taylor Smith Simpson Allen Dickerson Copyright 2006 John Wiley & Sons, Inc.
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Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU MIN NO. OF WORKERS REQUIRED Taylor O X X O X X X Smith O X X O X X X Simpson X O X X O X X Allen X O X X X X O Dickerson X X O X X X O Completed schedule satisfies requirements but has no consecutive days off Copyright 2006 John Wiley & Sons, Inc.
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Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU MIN NO. OF WORKERS REQUIRED Taylor O O X X X X X Smith O O X X X X X Simpson X X O O X X X Allen X X X O X X O Dickerson X X X X O X O Revised schedule satisfies requirements with consecutive days off for most employees Copyright 2006 John Wiley & Sons, Inc.
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Automated Scheduling Systems
Staff Scheduling Schedule Bidding Schedule Optimization Copyright 2006 John Wiley & Sons, Inc.
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Copyright 2006 John Wiley & Sons, Inc. All rights reserved
Copyright 2006 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. Copyright 2006 John Wiley & Sons, Inc.
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