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© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chapter 16 Scheduling

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Scheduling Specifies when labor, equipment, facilities are needed to produce a product or provide a service Last stage of planning before production occurs

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Scheduling Function By Process Type Process Industry –linear programming –EOQ with noninstantaneous replenishment Mass Production –assembly line balancing Project –project -scheduling techniques (PERT, CPM)

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Batch Production –many planning steps aggregate planning master scheduling material requirements planning (MRP) capacity requirements planning (CRP) Scheduling determines –machine/worker/job assignments –resource/requirement matchings Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Scheduling Batch/Job Shop Operations

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Difficulties Of Job Shop Scheduling Variety of jobs (customers) processed Distinctive routing and processing requirements of each job/customer Number of different orders in the facility at any one time Competition for common resources

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e This Variety Necessitates Planning for the production of each job as it arrives Scheduling its use of limited resources Monitoring its progress through the system

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Objectives in Scheduling Meet customer due dates Minimize job lateness Minimize response time Minimize completion time Minimize time in the system Minimize overtime Maximize machine or labor utilization Minimize idle time Minimize work-in-process inventory

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Responsibilities of Production Control Department 1. Loading - Check availability of material, machines & labor 2. Sequencing - Release work orders to shop & issue dispatch lists for individual machines 3. Monitoring - Maintain progress reports on each job until it is complete

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Loading Allocate work to machines (resources) Perform work on most efficient resources Use assignment method of linear programming to determine allocation

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Assignment Method 1. Perform row reductions –subtract minimum value in each row from all other row values 2. Perform column reductions –subtract minimum value in each column from all other column values 3. Result is an opportunity cost matrix –cross out all zeros in matrix using minimum number of horizontal & vertical lines

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 2/e 4. If number of lines equals number of rows in matrix, optimum solution has been found. Make assignments where zeros appear. Otherwise modify matrix by subtracting minimum uncrossed value from all uncrossed values & adding it to all cells where two lines intersect. All other values in matrix remain unchanged. 5. Repeat steps 3 & 4 until optimum solution reached

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© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Assignment Example Cooker Food Beans Peaches6246 Tomatoes7656 Corn95410 Row reduction Column reduction Cover all zeros Number lines <> number of rows so modify matrix

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Cooker Food1234 Beans Peaches6246 Tomatoes7656 Corn95410 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Assignment Example Cooker Food1234 Beans1012 Peaches0021 Tom0320 Corn1103 Modify matrix Cover all zeros # lines = # rows so at optimal solution Orders completed in 6 hours

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 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

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sequencing Rules FCFS - first-come, first-served LCFS - last come, first served SPT - shortest processing time DDATE - earliest due date SLACK - smallest slack –(due date - today’s date) - (remaining processing time) RWK - remaining work on all operations

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Critical Ratio Rule CR = time remaining / work remaining If CR > 1, job ahead of schedule If CR < 1, job behind schedule If CR = 1, job on schedule due date - today’s date remaining processing time =

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Flowtime (completion time) –time for a job to flow through the system Makespan –time for a group of jobs to be completed Tardiness –difference between a late job’s due date and its completion time Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sequencing Jobs Through One Process

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sequencing Rule Example A5 10 (10-1) - 5 = 4 (10-1)/5 = 1.80 B1015 (15-1)-10 = 4 (15-1)/10 = 1.40 C2 5 (5-1)-2 = 2 (5-1)/2 = 2.00 D812 (12-1)-8 = 3 (12-1)/8 = 1.37 E68 (8-1)-6 = 1 (8-1)/6 = possible sequences for 5 jobs ProcessingDue Critical JobTimeDateSlackRatio

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e First-Come First-Served A B C D E Average Start Processing Completion Due Sequence Time Time Time Date Tardiness

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Earliest Due Date C E A D E Average Start Processing Completion Due Sequence Time Time Time Date Tardiness

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Slack E C D A B Average Start Processing Completion Due Sequence Time Time Time Date Tardiness Slack for each job A - 4, B - 4, C - 2, D - 3, E - 1

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Critical Ratio E D B A C Average Start Processing Completion Due Sequence Time Time Time Date Tardiness CR for each job A , B , C , D , E

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Shortest Processing Time C A E D B Average Start Processing Completion Due Sequence Time Time Time Date Tardiness

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Summary FCFS DDATE SLACK CR SPT * best values Average Average No. of Maximum Rule Completion Time TardinessJobs TardyTardiness * ** * * * * *

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sequencing Jobs Through Two Serial Process 1. 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. 2. 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. 3. If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible. 4. Remove job from list. 5. Repeat steps 2-4 until all slots in matrix are filled & all jobs are sequenced.

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Johnson’s Rule Example A68 B116 C73 D97 E510 MachineMachine JobCenter 1Center 2 E A D B C

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sequencing Jobs Through Many Machines / Processes Facility is dynamic, new jobs added Develop global sequencing rules –first-in-system, first-served (FISFS) –work-in-next-queue (WINQ) –fewest # remaining operations (NOPN) –slack per remaining operation (S/OPN) –remaining work (RWK) Study system via simulation

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Guidelines for Selecting a Sequencing Rule 1. SPT most useful when shop is highly congested 2. Use SLACK or S/OPN for periods of normal activity 3. Use DDATE when only small tardiness values can be tolerated 4. Use LPT if subcontracting is anticipated 5. Use FCFS when operating at low-capacity levels 6. Do not use SPT to sequence jobs that have to be assembled with other jobs at a later date

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Gantt Chart –shows both planned and completed activities against a time scale Input / Output Control –monitors the input and output from each work center Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Monitoring

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Gantt Chart Days Today’s Date Job 32B Job 23C Job 11CJob 12A Facility Key: Planned Activity Completed Activity Behind schedule Ahead of schedule On schedule

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Input/Output Report Planned input Actual input Deviation Planned output Actual output Deviation Backlog Period Total

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Infinite/Finite Scheduling Infinite - assumes infinite capacity –loads without regard to capacity –then levels the load and sequence jobs Finite - assumes finite (limited) capacity –sequences jobs as part of the loading decision –resources are never loaded beyond capacity

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Synchronous Manufacturing 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

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Synchronous Mfg Example i B1 B2 B3 B A C C1 C2 C3 D D1 D2 D3 k ijl Operation j of item i performed at machine center k takes l minutes to process Item i Key: Demand = 100 As One B, C & D used to make an A Each item processed at 3 workcenters Machine setup time = 60 minutes

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Solution Method 1. Identify bottleneck machine - sum process time of all operations to be performed on machine 2. Schedule first item whose lead time to the bottleneck is <= bottleneck processing time 3. Forward schedule the bottleneck machine 4. Backward schedule other machines to sustain bottleneck schedule 5. Recall that transfer batch size does not have to equal process batch size

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Bottleneck Identification B1 5 B2 3 C1 2 B3 7 C3 15 D3 5 C2 10 D2 8 D Machine 1 Machine 2 Machine 3 *

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Gantt Chart Solution

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Employee Scheduling Labor is very flexible resource Scheduling workforce is complicated repetitive task Assignment method can be used Heuristics are commonly used

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Employee Scheduling Heuristic 1. Let N = # of workers available D i = demand for workers on day i X = day working O = day off 2. Assign the first N - D 1 workers day 1 off. Assign the next N - D 2 workers day 2 off. Continue until all days are have been scheduled 3.If # of workdays for full time employee < 5, assign remaining workdays so consecutive days off are possible 4. Assign any remaining work to part-time employees 5. If consecutive days off are desired, consider switching schedules among days with the same demand requirements.

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Employee Scheduling Example Day of weekMTWThFSaSu Min # workers TaylorOXX0XXX SmithOXX0XXX SimpsonXOXXOXX AllenXOXXXXO DickersonXXOXXXO IMPROVED SCHEDULE Day of weekMTWThFSaSu Min # workers TaylorOOXXXXX SmithOOXX XXX SimpsonXXOOXXX AllenXXXOXXO DickersonXXXXOXO

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Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e DSS For Scheduling Generate scheduling pattern to follow cyclically throughout the year Determine whether 40-hr or 80-hr base for overtime is more cost-effective Examine effect of alternate-days-off patterns Determine appropriate full-time/part-time mix Justify use of additional staff Determine benefit of cross training employees

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