Sampling Method for the Flow Shop with Uncertain Parameters

  • Paweł Rajba
  • Mieczysław Wodecki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10244)


In the classic approach for optimization problems modelling well defined parameters are assumed. However, in real life problems we find ourself very often in a situation where parameters are not defined precisely. This may have many sources like inaccurate measurement, inability to establishing precise values, randomness, inconsistent information or subjectivity.

In this paper we propose a sampling method for solving optimization problems with uncertain parameters modeled by random variables. Moreover, by applying confidence intervals theory, the execution time has been significantly reduced. We will also show an application of the method for the flowshop problem with deadlines and parameters modeled by random variables with the normal distribution.


Flowshop with deadlines Uncertain parameters Tabu search Normal distribution 


  1. 1.
    Aarts, A., Lenstra, J.K.: Local Search in Combinatorial Optimization. Wiley, New York (1997)zbMATHGoogle Scholar
  2. 2.
    Wodecki, M., Bożzejko, W.: Solving the flow shop problem by parallel simulated annealing. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 236–244. Springer, Heidelberg (2002). doi: 10.1007/3-540-48086-2_26 CrossRefGoogle Scholar
  3. 3.
    Bożejko, W., Wodecki, M.: On the theoretical properties of swap multimoves. Oper. Res. Lett. 35(2), 227–231 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bożejko, W., Rajba, P., Wodecki, M.: Scheduling problem with uncertain parameters in just in time system. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014. LNCS, vol. 8468, pp. 456–467. Springer, Cham (2014). doi: 10.1007/978-3-319-07176-3_40 CrossRefGoogle Scholar
  5. 5.
    Dean B.C.: Approximation algorithms for stochastic scheduling problems. Ph.D. thesis, MIT (2005)Google Scholar
  6. 6.
    Grabowski, J., Wodecki, M.: A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion. Comput. Oper. Res. 31, 1891–1909 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Jang, W., Klein, C.M.: Minimizing the expected number of tardy jobs when processing times are normally distributed. Oper. Res. Lett. 30, 100–106 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Nowicki, E., Smutnicki, C.: A fast tabu search algorithm for permutation flow shop problem. Eur. J. Oper. Res. 91, 160–175 (1996)CrossRefzbMATHGoogle Scholar
  9. 9.
    Rajba, P., Wodecki, M.: Stability of scheduling with random processing times on one machine. Applicationes Mathematicae 39(2), 169–183 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Righter R., Stochastic scheduling. In: Shaked, M., Shandhkumar (eds.) Stochastic Orders. Academic Press, San Diego (1994)Google Scholar
  11. 11.
    Sioud, A., Gagné, C., Gravel, M.: Minimizing total tardiness in a hybrid flexible flowshop with sequence dependent setup times. In: INFOCOMP 2014: The Fourth International Conference on Advanced Communications and Computation 2014, pp. 13–18 (2014)Google Scholar
  12. 12.
    Taillard, E.: Benchmarks for basic scheduling problems. EJOR 64(2), 278–285 (1993)CrossRefzbMATHGoogle Scholar
  13. 13.
    Van den Akker, M., Hoogeveen, H.: Minimizing the number of late jobs in a stochastic setting using a chance constraint. J. Sched. 11, 59–69 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Vondrák, J.: Probabilistic methods in combinatorial and stochastic optimization. Ph.D. thesis, MIT (2005)Google Scholar
  15. 15.
    Zhu, X., Cai, X.: General stochastic single-machine scheduling with regular cost functions. Math. Comput. Modell. 26(3), 95–108 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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