Advertisement

β-Robust Solutions for the Fuzzy Open Shop Scheduling

  • Juan José Palacios
  • Inés González-Rodríguez
  • Camino R. Vela
  • Jorge Puente Peinador
Part of the Communications in Computer and Information Science book series (CCIS, volume 442)

Abstract

We consider the open shop scheduling problem with uncertain durations modelled as fuzzy numbers. We define the concepts of necessary and possible β-robustness of schedules and set as our goal to maximise them. Additionally, we propose to assess solution robustness by means of Monte Carlo simulations. Experimental results using a genetic algorithm illustrate the proposals.

Keywords

Completion Time Fuzzy Number Open Shop Fuzzy Interval Stochastic Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pinedo, M.L.: Scheduling. Theory, Algorithms, and Systems, 3rd edn. Springer (2008)Google Scholar
  2. 2.
    Sha, D.Y., Cheng-Yu, H.: A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research 35, 3243–3261 (2008)zbMATHCrossRefGoogle Scholar
  3. 3.
    Herroelen, W., Leus, R.: Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research 165, 289–306 (2005)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dubois, D., Fargier, H., Fortemps, P.: Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge. European Journal of Operational Research 147, 231–252 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Van de Vonder, S., Demeulemeester, E., Herroelen, W.: Proactive heuristic procedures for robust project scheduling: An experimental analysis. European Journal of Operational Research 189, 723–733 (2008)zbMATHCrossRefGoogle Scholar
  6. 6.
    Aissi, H., Bazgan, C., Vanderpooten, D.: Min-max and min-max regret versions of combinatorial optimization problems: A survey. European Journal of Operational Research 197, 427–438 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, J.: A fuzzy robust scheduling approach for product development projects. European Journal of Operational Research 152, 180–194 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Kasperski, A., Kule, M.: Choosing robust solutions in discrete optimization problems with fuzzy costs. Fuzzy Sets and Systems 160, 667–682 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Daniels, R.L., Carrillo, J.E.: β-robust scheduling for single-machine systems with uncertain processing times. IIE Transactions 29, 977–985 (1997)Google Scholar
  10. 10.
    Aiche, F., Abbas, M., Dubois, D.: Chance-constrained programming with fuzzy stochastic coefficients. Fuzzy Optimization and Decision Making 12, 125–152 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fortemps, P.: Jobshop scheduling with imprecise durations: a fuzzy approach. IEEE Transactions of Fuzzy Systems 7, 557–569 (1997)CrossRefGoogle Scholar
  12. 12.
    Sakawa, M., Kubota, R.: Fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms. European Journal of Operational Research 120, 393–407 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    González Rodríguez, I., Puente, J., Vela, C.R., Varela, R.: Semantics of schedules for the fuzzy job shop problem. IEEE Transactions on Systems, Man and Cybernetics, Part A 38(3), 655–666 (2008)CrossRefGoogle Scholar
  14. 14.
    Puente, J., Vela, C.R., González-Rodríguez, I.: Fast local search for fuzzy job shop scheduling. In: Proc. of ECAI 2010, pp. 739–744. IOS Press (2010)Google Scholar
  15. 15.
    Alcaide, D., Rodriguez-Gonzalez, A., Sicilia, J.: A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures. International Journal of Flexible Manufacturing Systems 17, 201–226 (2006)zbMATHCrossRefGoogle Scholar
  16. 16.
    González-Rodríguez, I., Palacios, J.J., Vela, C.R., Puente, J.: Heuristic local search for fuzzy open shop scheduling. In: Proc. FUZZ-IEEE 2010, pp. 1858–1865. IEEE (2010)Google Scholar
  17. 17.
    Noori-Darvish, S., Mahdavi, I., Mahdavi-Amiri, N.: A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due-dates. Applied Soft Computing 12, 1399–1416 (2012)CrossRefGoogle Scholar
  18. 18.
    Palacios, J.J., González-Rodríguez, I., Vela, C.R., Puente, J.: Swarm lexicographic goal programming for fuzzy open shop scheduling. Journal of Intelligent Manufacturing (2013)Google Scholar
  19. 19.
    Palacios, J.J., Puente, J., Vela, C.R., González-Rodríguez, I.: A genetic algorithm for the open shop problem with uncertain durations. In: Mira, J., Ferrández, J.M., Álvarez, J.R., de la Paz, F., Toledo, F.J. (eds.) IWINAC 2009, Part I. LNCS, vol. 5601, pp. 255–264. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1986)Google Scholar
  21. 21.
    Niu, Q., Jiao, B., Gu, X.: Particle swarm optimization combined with genetic operators for job shop scheduling problem with fuzzy processing time. Applied Mathematics and Computation 205, 148–158 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Wu, C.W., Brown, K.N., Beck, J.C.: Scheduling with uncertain durations: Modeling β-robust scheduling with constraints. Computers & Operations Research 36, 2348–2356 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  24. 24.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)zbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    Graham, R., Lawler, E., Lenstra, J., Rinnooy Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 4, 287–326 (1979)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Juan José Palacios
    • 1
  • Inés González-Rodríguez
    • 2
  • Camino R. Vela
    • 1
  • Jorge Puente Peinador
    • 1
  1. 1.Department of Computer ScienceUniversity of OviedoSpain
  2. 2.Department of Mathematics, Statistics and ComputingUniversity of CantabriaSpain

Personalised recommendations