A Study of Schedule Robustness for Job Shop with Uncertainty

  • Inés González-Rodríguez
  • Jorge Puente
  • Ramiro Varela
  • Camino R. Vela
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5290)


We consider a job shop problem with uncertain processing times modelled as triangular fuzzy numbers and propose a methodology to study solution robustness with respect to different perturbations in the durations. This methodology is applied to obtain experimental results for several problem instances, using a hybrid genetic algorithm that minimises the expected makespan. We conclude that taking into account the uncertainty information provided by fuzzy numbers produces proactive solutions, coping well with posterior changes in processing times.


Fuzzy Number Hybrid Genetic Algorithm Possibility Distribution Task Duration Critical Block 
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  1. 1.
    Brucker, P., Knust, S.: Complex Scheduling. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  2. 2.
    Herroelen, W., Leus, R.: Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research 165, 289–306 (2005)zbMATHCrossRefGoogle Scholar
  3. 3.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Słowiński, R., Hapke, M. (eds.): Scheduling Under Fuzziness. Studies in Fuzziness and Soft Computing, vol. 37. Physica-Verlag (2000)Google Scholar
  5. 5.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Petrovic, S., Fayad, S., Petrovic, D.: Sensitivity analysis of a fuzzy multiobjective scheduling problem. Int. Journal of Production Research 46(12), 3327–3344 (2007)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Fortemps, P.: Jobshop scheduling with imprecise durations: a fuzzy approach. IEEE Transactions of Fuzzy Systems 7, 557–569 (1997)CrossRefGoogle Scholar
  9. 9.
    González Rodríguez, I., Vela, C.R., Puente, J.: A memetic approach to fuzzy job shop based on expectation model. In: Proceedings of IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2007, London, pp. 692–697 (2007)Google Scholar
  10. 10.
    Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)CrossRefGoogle Scholar
  11. 11.
    Jin, Y., Branke, J.: Evolutionay optimization in uncertain environments–a survey. IEEE Transactions on Evolutionary Computation 9, 303–317 (2005)CrossRefGoogle Scholar
  12. 12.
    Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Transactions on Systems, Man, and Cybernetics–Part C 67(3), 392–403 (1998)CrossRefGoogle Scholar
  13. 13.
    Van Laarhoven, P., Aarts, E., Lenstra, K.: Job shop scheduling by simulated annealing. Operations Research 40, 113–125 (1992)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Branke, J., Mattfeld, D.: Anticipation and flexibility in dynamic scheduling. International Journal of Production Research 43, 3103–3129 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Inés González-Rodríguez
    • 1
  • Jorge Puente
    • 2
  • Ramiro Varela
    • 2
  • Camino R. Vela
    • 2
  1. 1.Department of Mathematics, Statistics and ComputingUniversity of CantabriaSpain
  2. 2.A.I. Centre and Department of Computer ScienceUniversity of OviedoSpain

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