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Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm

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Abstract

This paper is devoted to ponder a joint production and maintenance problem. For solving the problem, a genetic algorithm named similarity-based subpopulation genetic algorithm (SBSPGA) is introduced. SBSPGA is presented based on a well-known evolutionary algorithm, the subpopulation genetic algorithm II (SPGA-II). Compared with the SPGA-II, the innovation of the SBSPGA could be divided into two parts: (1) using a similarity model for the elitism strategy and (2) performing the algorithm in just one stage. To tackle the maintenance aspect, reliability models are employed in this paper. The aim of this paper was to optimize two objectives: minimization of the makespan for the production part and minimization of the system unavailability for the maintenance part. To execute our proposed problem, two decisions must be made at the same time: achieving the best assignment of n jobs on m machines to minimize the makespan and determining the time at which the preventive maintenance activities must be performed to minimize the system unavailability. The maintenance activity numbers and the maintenance intervals are not fixed in advanced. Promising the acquired results, a benchmark with tremendous number of test instances (more than 5,000) is employed.

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References

  1. 1.

    Adzapka KP, Adjallah KH, Yalaoui F (2004) On-line maintenance job scheduling and assignment to resources in distributed systems by heuristic-based optimization. J Intell Manuf 15:131–140

  2. 2.

    Aghezzaf EH, Jamali MA, Ait-Kadi D (2007) An integrated production and preventive maintenance planning model. Eur J Oper Res 181(2):679–685

  3. 3.

    Barichard V (2005) Hybrid approaches for multiobjective problems. PhD thesis, Doctoral School of Angers, France (in French)

  4. 4.

    Basseur M (2005) Design of cooperative algorithms for multi-objective optimization: application to flow-shop scheduling problems. PhD thesis, University of Sciences and Technologies of Lille, France (in French)

  5. 5.

    Berrichi A, Amodeo L, Yalaoui F, Châtelet E, Mezghiche M (2008) Bi-objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem. J Intell Manuf 20:389–400. doi:10.1007/s10845-008-0113-5

  6. 6.

    Cassady CR, Kutanoglu E (2003) Minimizing job tardiness using integrated preventive maintenance planning and production scheduling. IEEE Trans 35(6):503–513

  7. 7.

    Cassady CR, Kutanoglu E (2005) Integrating preventive maintenance planning and production scheduling for a single machine. IEEE Trans Reliab 54(2):304–309

  8. 8.

    Chang PC, Chen SH (2009) The development of a sub-population genetic algorithm II (SPGA II) for multi-objective combinatorial problems. Applied Soft Computing 9:173–181

  9. 9.

    Chelbi A, Ait-Kadi D (2004) Analysis of a production/inventory system with randomly failing production unit submitted to regular preventive maintenance. Eur J Oper Res 156(3):712–718

  10. 10.

    Ebeling CE (1997) An introduction to reliability and maintainability engineering. McGraw-Hill, USA

  11. 11.

    Fleischer M (2003) The measure of Pareto optima, applications to the multi-objective metaheuristics. Lect Notes Comput Sci, Springer (EMO’03) 2632:519–533

  12. 12.

    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco

  13. 13.

    Gharbi A, Kenne JP (2005) Maintenance scheduling and production control of multiple-machine manufacturing systems. Comput Ind Eng 48(4):693–707

  14. 14.

    Jain AS, Meeran S (1999) Deterministic job-shop scheduling: past, present and future. Eur J Oper Res 113(2):390–434

  15. 15.

    Kaabi J, Varnier C, Zerhouni N (2002) Heuristics for scheduling maintenance and production on a single machine. IEEE Conference on Systems, Man and Cybernetics, October 6–9, Hammamet, Tunisia

  16. 16.

    Kaabi J, Varnier C, Zerhouni N (2003) Genetic algorithm for scheduling production and maintenance in a flow-shop. Laboratory of Automatic of Besançon, France (in French)

  17. 17.

    Kenne JP, Gharbi A, Beit M (2007) Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale. Eur J Oper Res 178(2):408–420

  18. 18.

    Lee C-Y (1996) Machine scheduling with an availability constraint. J Glob Optim 9:395–416

  19. 19.

    Lee CY, Chen ZL (2000) Scheduling jobs and maintenance activities on parallel machines. Nav Res Logist 47(2):145–165

  20. 20.

    McCall JJ (1965) Maintenance policies for stochastically failing equipment: a survey. Manage Sci 11:493–524

  21. 21.

    Mellouli R, Sadfi C, Kacem I, Chu C (2006) Scheduling on parallel machines with availability constraints. Sixth International Francophone Conference of Modeling and Simulation, Mosim ‘06, Marocco (in French)

  22. 22.

    Pham H, Wang HZ (1996) Imperfect maintenance. Eur J Oper Res 94(3):425–438

  23. 23.

    Pinedo M (1995) Scheduling theory, algorithms and systems, 1st edn. Prentice Hall, Englewood Cliffs

  24. 24.

    Pinedo M (2002) Scheduling theory, algorithms, and systems, Chapter 2. Prentice-Hall, Englewood Cliffs

  25. 25.

    Qi X, Chen T, Tu F (1999) Scheduling the maintenance on single machine. J Oper Res Soc 50(10):1071–1078

  26. 26.

    Ruiz R, García-Diaz JC, Maroto C (2007) Considering scheduling and preventive maintenance in the flow-shop sequencing problem. Comput Oper Res 34(11):3314–3330

  27. 27.

    Schmidt G (2000) Scheduling with limited machine availability. Eur J Oper Res 121:1–15

  28. 28.

    Sherif YS, Smith ML (1981) Optimal maintenance models for systems subject to failure—a review. Nav Res Logist 28(1):47–74

  29. 29.

    Villemeur A (1991) Reliability, availability, maintainability and safety assessment. Wiley, USA

  30. 30.

    Wang HZ (2002) A survey of maintenance policies of deteriorating systems. Eur J Oper Res 139(3):469–489

  31. 31.

    Weinstein L, Chung CH (1999) Integrated maintenance and production decisions in hierarchical production planning environment. Comput Oper Res 26:1059–1074

  32. 32.

    Xu D, Sun K, Li H (2008) Parallel machine scheduling with almost periodic non-preemptive maintenance and jobs to minimize makespan. Comput Oper Res 35:1344–1349

  33. 33.

    Zitzler E (1999) Evolutionary algorithms for multi-objective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, Zurich

  34. 34.

    Zydallis JB (2003) Explicit building-block multi-objective genetic algorithms: theory, analysis, and development. PhD dissertation, Air Force Institute of Technology, Ohio

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Correspondence to M. Zandieh.

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Moradi, E., Zandieh, M. Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm. Int J Adv Manuf Technol 51, 829–840 (2010). https://doi.org/10.1007/s00170-010-2666-7

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Keywords

  • Bi-objective scheduling
  • Preventive maintenance
  • Reliability
  • Unavailability
  • Evolutionary algorithm