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Exact solutions for the two-machine robust flow shop with budgeted uncertainty

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  • Levorato, Mario
  • Figueiredo, Rosa
  • Frota, Yuri

Abstract

This work proposes an exact solution approach for the two-machine robust flow shop problem, where operation processing times are uncertain and vary in a given interval. Based on the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the makespan of the restricted worst-case scenario, where only a subset of job processing times will oscillate to their worst-case values. To our knowledge, this is the first work to obtain optimal solutions to this problem, by extending two classical MILP formulations for the deterministic case and combining them with a Column-and-Constraint Generation framework. For this purpose, a dynamic programming algorithm was also developed, allowing the identification of worst-case scenarios in polynomial time. Experiments on a set of literature instances confirm the efficacy of our approach, including a case study that shows little overhead in the expected solution value of obtained robust solutions.

Suggested Citation

  • Levorato, Mario & Figueiredo, Rosa & Frota, Yuri, 2022. "Exact solutions for the two-machine robust flow shop with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 300(1), pages 46-57.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:1:p:46-57
    DOI: 10.1016/j.ejor.2021.10.021
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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    3. Ruiz Duarte, José Luis & Fan, Neng & Jin, Tongdan, 2020. "Multi-process production scheduling with variable renewable integration and demand response," European Journal of Operational Research, Elsevier, vol. 281(1), pages 186-200.
    4. Kuo-Ching Ying, 2015. "Scheduling the two-machine flowshop to hedge against processing time uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(9), pages 1413-1425, September.
    5. Yakov Shafransky & Viktor Shinkarevich, 2020. "On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty," Journal of Scheduling, Springer, vol. 23(6), pages 745-749, December.
    6. Kasperski, Adam & Kurpisz, Adam & Zieliński, Paweł, 2012. "Approximating a two-machine flow shop scheduling under discrete scenario uncertainty," European Journal of Operational Research, Elsevier, vol. 217(1), pages 36-43.
    7. Harvey M. Wagner, 1959. "An integer linear‐programming model for machine scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 6(2), pages 131-140, June.
    8. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    9. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    10. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    11. Michał Ćwik & Jerzy Józefczyk, 2018. "Heuristic algorithms for the minmax regret flow-shop problem with interval processing times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 215-238, March.
    12. Framinan, Jose M. & Perez-Gonzalez, Paz, 2015. "On heuristic solutions for the stochastic flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 246(2), pages 413-420.
    13. T-C Lai & Y N Sotskov, 1999. "Sequencing with uncertain numerical data for makespan minimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(3), pages 230-243, March.
    14. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    15. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    16. Feizollahi, Mohammad Javad & Feyzollahi, Hadi, 2015. "Robust quadratic assignment problem with budgeted uncertain flows," Operations Research Perspectives, Elsevier, vol. 2(C), pages 114-123.
    17. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    18. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    19. Averbakh, Igor, 2006. "The minmax regret permutation flow-shop problem with two jobs," European Journal of Operational Research, Elsevier, vol. 169(3), pages 761-766, March.
    20. Tseng, Fan T. & Stafford, Edward F. & Gupta, Jatinder N. D., 2004. "An empirical analysis of integer programming formulations for the permutation flowshop," Omega, Elsevier, vol. 32(4), pages 285-293, August.
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