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IE 573 PAPER PRESENTATION by Ersin K rpeoglu

Agenda. IntroductionProblem Definition and NotationPrevious WorkImproving Robustness and FlexibilityThe Scheduling SystemBreakdowns and Rescheduling MethodsExperimentsDiscussion and conclusion. Introduction. Traditional scheduling focuses on minimizing a performance measure and gives static

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IE 573 PAPER PRESENTATION by Ersin K rpeoglu

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    1. IE 573 PAPER PRESENTATION by Ersin Krpeoglu Improving robustness and flexibility of tardiness and total flow-time job shops using robustness measures

    2. Agenda Introduction Problem Definition and Notation Previous Work Improving Robustness and Flexibility The Scheduling System Breakdowns and Rescheduling Methods Experiments Discussion and conclusion

    3. Introduction Traditional scheduling focuses on minimizing a performance measure and gives static results. In practice, some deficiencies in the system is inevitable. Most common deficiencies are machine breakdowns, so breakdown term will be used for deficiencies. The initial solution is no longer valid after a breakdown.

    4. Introduction Delaying all processes by the amount of breakdown is called right shifting. Changing the schedule of the jobs that are not processed when a break down occurs is called rescheduling using search. After a break down, a preschedule which tends to perform better when schedule is right shifted is termed robust, a preschedule which tends to perform better when jobs are rescheduled is termed flexible.

    5. Problem Definition N jobs, M machines, a job needs a sequence of operations and each operation is processed on a specific machine with a time . A job has at most one operation on each machine. The processing order is in the sequence . A machine can process one job at a time, no preemption, and denotes the end of processing time of job j. The objectives considered are , , , and .

    6. Previous Work Kouvalis and Yu first introduced the robust scheduling Wu et. al. Produced more flexible solutions for weighted tardiness problem Al-Harkan proposed that job shop scheduling based on pesimistic estimates of the processing times is superior to scheduling based on processing time averages. Hart et. al. Conjectured that artificial immune system (AIS) produced robust results. Leon et. al. Treated machine breakdown with a robustness measure based on slack makespan job shop problems. Jensen proposed that robust schedules performed better in case of break downs for job shop makespan problem.

    7. Improving Robustness and Flexibility Minimizing Lmax instead of Tmax increases schedule robustness and flexibility if the problem is loose, i.e no tardy jobs. Using total lateness instead of total tardiness is also suggested and experimented.

    8. Improving Robustness and Flexibility Neighbourhood-based robustness measures The idea is as follows:

    9. Improving Robustness and Flexibility A neighbourhood of schedule s is defined as: All schedules that can be achieved by interchanging two consequtive operations on the same machine. is the robustness measure where

    10. The Scheduling System Genetic Algorithm(GA) is used to come up with schedules. Encoding: A sequence is represented by a sequence of job numbers describing the operation processing order: The schedule shown is encoded as: 1-3-2-2-1-2-3-1-3

    11. The Scheduling System After encoding the schedule, a generational GA is used with a population size of 100. Algorithm was run for 100 generations, with a tournament size of 2. Mutation probability is taken as 0.1. The general order crossover (GOX) and position based mutation (PBM) operations are used. Elitism is not used. Decoding: Two different types are used.

    12. The Scheduling System A special version of Giffler-Thompson (GT) algorithm was used for total flowtime experiments. This algorithm creates active schedules with a bias towards non-delay schedules and is not problem specific. For summed and maximum tardiness, a problem specific decoder is used. It uses a semi-active decoding of the gene, followed by a hillclimber. Two versions of hillclimbers are used. One minimized Lmax, the other RLmax.

    13. The Scheduling System After a schedule is created via GA, the solution is improved via hillclimbing approach. The hillclimber searches the neighbourhood and choses the best solution. This way, the preschedule is obtained.

    14. Breakdowns and Rescheduling Machine breakdowns are generated randomly and downtimes are assumed to be deterministic. Breakdown creation algoritm: 1. Preschedule s is generated 2. An operation ox is selected randomly. 3. The start time of ox is chosen as breaktime. 4. All operations that have start time at breakdown or later in s are included in the resceduling problem. 5. Release dates and initial setup times are added accordingly

    15. Breakdowns and Rescheduling Example for breakdown creation:

    16. Breakdowns and Rescheduling Example for breakdown creation:

    17. Breakdowns and Rescheduling Example for breakdown creation:

    18. Breakdowns and Rescheduling Example for breakdown creation:

    19. Breakdowns and Rescheduling Example for breakdown creation:

    20. Breakdowns and Rescheduling Example for breakdown creation:

    21. Breakdowns and Rescheduling Example for breakdown creation:

    22. Breakdowns and Rescheduling 5 techniques are used for rescheduling after breakdown: Right shifting: simply shift the schedule by the amount of breakdown based rescheduling: Search neighbourhood of the preschudule to find the best among them Hillclimbing rescheduling: Finds a local optimum by neighbourhood search. Only usable for Tmax, Lmax and Rlmax. Reduced rescheduling Complete rescheduling In reduced and complete rescheduling GA is used.

    23. Breakdowns and Rescheduling 5 techniques are used for rescheduling after breakdown: Reduced rescheduling: The ones with orange outline. Complete rescheduling: Orange + blue outline.

    24. Experiments Average Tmax

    25. Experiments

    26. Experiments Number of Best Results

    27. Experiments Loose Problems

    28. Experiments Tight Problems

    29. Experiments Given maximum tardiness value, probability having a performance of that or better if there is right shifting. RLmax performs significantly better in terms of probability.

    30. Experiments Given maximum tardiness value, the same probability if there is complete rescheduling. RLmax performs better in terms of probability.

    31. Experiments Average Summed T

    32. Experiments Loose Problems

    33. Experiments Tight Problems

    34. Experiments Total Flowtime

    35. Discussion and Conclusion The robustness and flexibility of tardiness and total flow-time job shob schedules facing breakdowns have been investigated. For loose problems, minimizing lateness instead of tardines increases the robustness and flexibility. Neighbourhood-based robustness measures generally improves robustness of the problem and often improves the flexibility. The cases that the neighbourhood-based robustness does not increase flexibility are mainly problems with many critical points.

    36. THANK YOU FOR YOU ATTENTION QUESTIONS?

    37. References Jensen, M.T., "Improving Robustness and Flexibility of Tardiness and Total Flow-Time Job Shops Using Robustness Measures", Applied Soft Computing, 1, 35-52, 2001.

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