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.
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References
Pinedo, M.L.: Scheduling. Theory, Algorithms, and Systems, 3rd edn. Springer (2008)
Sha, D.Y., Cheng-Yu, H.: A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research 35, 3243–3261 (2008)
Herroelen, W., Leus, R.: Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research 165, 289–306 (2005)
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)
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)
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)
Wang, J.: A fuzzy robust scheduling approach for product development projects. European Journal of Operational Research 152, 180–194 (2004)
Kasperski, A., Kule, M.: Choosing robust solutions in discrete optimization problems with fuzzy costs. Fuzzy Sets and Systems 160, 667–682 (2009)
Daniels, R.L., Carrillo, J.E.: β-robust scheduling for single-machine systems with uncertain processing times. IIE Transactions 29, 977–985 (1997)
Aiche, F., Abbas, M., Dubois, D.: Chance-constrained programming with fuzzy stochastic coefficients. Fuzzy Optimization and Decision Making 12, 125–152 (2013)
Fortemps, P.: Jobshop scheduling with imprecise durations: a fuzzy approach. IEEE Transactions of Fuzzy Systems 7, 557–569 (1997)
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)
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)
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)
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)
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)
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)
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)
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)
Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1986)
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)
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)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)
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)
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Palacios, J.J., González-Rodríguez, I., Vela, C.R., Puente Peinador, J. (2014). β-Robust Solutions for the Fuzzy Open Shop Scheduling. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-08795-5_46
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DOI: https://doi.org/10.1007/978-3-319-08795-5_46
Publisher Name: Springer, Cham
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