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dr hab. inż., prof. nadzw. PWR Dorota Kuchta Operations Scheduling and Production – Activity Control

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Job Shop Scheduling JOB PROCESSING TIME (HOURS) JOB PROCESSING TIME (HOURS) = = = = = 33

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Common Scheduling Criteria CRITERIADEFINITIONOBJECTIVES 1. MakespanTime to process a set of jobsMinimize makespan 2. FlowtimeTime a job spends in the shopMinimize average flowtime 3. TardinessThe amount by which completionMinimize number of tardy jobs time exceeds the due date of a jobMinimize the maximum tardiness

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Scheduling with Due Dates JOB PROCESSING TIME DUE DATE JOBFLOWTIMETARDINESS = = = = 2213 average JOBDUE DATE LATEST START The optimal sequence is JOBFLOWTIMEDUE DATETARDINESS = = = = 22211

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Minimalizacja liczby opóźnionych elementów 1.Wstawić 1. zadanie do ciągu S 2.Jeśli koniec wykonania ciągu przypada po terminie wykonania jego ostatniego elementu, wyrzucić najdłuższy element ciągu poza ciąg 3. Jeśli jeszcze są zadania nie ustawione, wstawić kolejne zadanie do ciągu, krok 2. W przeciwnym przypadku stop Proc due356678

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Two – Machine Flowshop Problem JOBSHEARPUNCH

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Two – Machine Flowshop Problem JOBFLOWTIME

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Two – Machine Flowshop Problem (Johnsons Rule) JOBSHEARPUNCH Since the minimum time is on the second machine, job 2 is scheduled last: __ __ __ __ 2 Next, we pick the second – smallest processing time. This is 2, which corresponds to job 5 on machine 1. Therefore, job 5 is scheduled first: 5 __ __ ___ 2 In the next step, we have a tie between job 1 on the shear and job 3 on the punch press. When ties occur, either job can be chosen. If we pick job 1, we then have 5 1 __ __ 2 Continuing with Johnsons rule, the last two steps yield: 5 1 __

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Two – Machine Flowshop Problem (Johnsons Rule) Since the minimum time is on the second machine, job 2 is scheduled last: __ __ __ __ 2 Next, we pick the second – smallest processing time. This is 2, which corresponds to job 5 on machine 1. Therefore, job 5 is scheduled first: 5 __ __ ___ 2 In the next step, we have a tie between job 1 on the shear and job 3 on the punch press. When ties occur, either job can be chosen. If we pick job 1, we then have 5 1 __ __ 2 Continuing with Johnsons rule, the last two steps yield: 5 1 __

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Job Data for Lynwoods Job Shop JOB ARRIVAL TIME PROCESSING SEQUENCE (PROCESSING TIME) 10L(10) - D(20) - G(35) 20D(25) - L(20) - G(30) - M(15) 320D(10) - M(10) 430L(15) - G(10) - M(20)

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Shop Status at Time T

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Open shop dla dwóch maszyn Wyznaczyć najkrótszy czas i odpowiedni element umieścić na tej maszynie, gdzie ten czas jest dłuższy (na tej drugiej) Uzupełnić szeregi na każdej maszynie w tej samej kolejności, co poprzednie

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Priority Dispatching Rules for Job Shops LP.RULETYPEDESCRIPTION 1Earliest release dateStaticTime job is released to the shop 2Shortest processing timeStaticProcessing time of operation for which job is waiting 3Total workStaticSum of all processing times 4Earliest due dateStaticDue date of job 5Least work remainingStatic Sum of all processing times for oparations not yet performed 6 Fewest operations remainingStaticNumber of operations yet to be performed 7Work in next queueDynamic Amount of work awaiting the next machine in a job's processing time 8Slack timeDynamic Time remaining until due date minus remaining processing time 9Slack/ remaining operationsDynamicSlack time divided by the number of operations remaining 10Critical ratioDynamic Time remaining until due date divided by days required to complete job

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Simulation of Dispatching Rules (lwr)

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Simulation of Dispatching Rules

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Simulation of Lynwood Manufacturing Problem

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Bar Chart for Lynwoods Job Shop

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Simulation Results Using Least Work Remaining for Lynwoods Job Shop JOBWAITING TIMECOMPLETION TIMEMACHINEIDLE TIME (MAKESPAN - PROCESSING TIME) Lathe Drill Grind Mill75

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Scheduling Consecutive Days Off MTWTFSS EMPLOYEE NO.MTWTFSS MTWTFSS MTWTFSS

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Scheduling Consecutive Days Off MTWTFSS EMPLOYEE NO.MTWTFSS MTWTFSS

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Scheduling Consecutive Days Off EMPLOYEE NO.MTWTFSS

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Scheduling Consecutive Days Off EMPLOYEEMTWTFSS 1xxxxx 2xxxxx 3x xxxx 4xxxxx 5xx xxx 6xxxxx 7 xxxxx 8xx xxx 9 xxxxx 10x xxxx Total

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Vehicle Scheduling Customer

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Vehicle Scheduling

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Vehicle Scheduling ROUTETIME The total time required is reduced to 358 minutes, or about 6 hours, a savings of about 3.8 hours over the original schedule.

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