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A capacitated lot sizing problem with stochastic setup times and overtime

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  • Taş, Duygu
  • Gendreau, Michel
  • Jabali, Ola
  • Jans, Raf

Abstract

In this paper, we study a Capacitated Lot Sizing Problem with Stochastic Setup Times and Overtime (CLSP-SSTO). We describe a mathematical model that considers both regular costs (including production, setup and inventory holding costs) and expected overtime costs (related to the excess usage of capacity). The CLSP-SSTO is formulated as a two-stage stochastic programming problem. A procedure is proposed to exactly compute the expected overtime for a given setup and production plan when the setup times follow a Gamma distribution. A sample average approximation procedure is applied to obtain upper bounds and a statistical lower bound. This is then used to benchmark the performance of two additional heuristics. A first heuristic is based on changing the capacity in the deterministic counterpart, while the second heuristic artificially modifies the setup time. We conduct our computational experiments on well-known problem instances and provide comprehensive analyses to evaluate the performance of each heuristic.

Suggested Citation

  • Taş, Duygu & Gendreau, Michel & Jabali, Ola & Jans, Raf, 2019. "A capacitated lot sizing problem with stochastic setup times and overtime," European Journal of Operational Research, Elsevier, vol. 273(1), pages 146-159.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:1:p:146-159
    DOI: 10.1016/j.ejor.2018.07.032
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    1. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    2. Horst Tempelmeier, 2013. "Stochastic Lot Sizing Problems," International Series in Operations Research & Management Science, in: J. MacGregor Smith & Barış Tan (ed.), Handbook of Stochastic Models and Analysis of Manufacturing System Operations, edition 127, chapter 0, pages 313-344, Springer.
    3. repec:dau:papers:123456789/2775 is not listed on IDEAS
    4. James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
    5. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    6. N. P. Dellaert & A. G. De Kok & Wang Wei, 2000. "Push and pull strategies in multi‐stage assembly systems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(2), pages 175-189, July.
    7. Jeunet, Jully & Jonard, Nicolas, 2000. "Measuring the performance of lot-sizing techniques in uncertain environments," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 197-208, March.
    8. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    9. Koca, Esra & Yaman, Hande & Selim Aktürk, M., 2015. "Stochastic lot sizing problem with controllable processing times," Omega, Elsevier, vol. 53(C), pages 1-10.
    10. M Denizel & H Süral, 2006. "On alternative mixed integer programming formulations and LP-based heuristics for lot-sizing with setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 389-399, April.
    11. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    12. K S Hindi & K Fleszar & C Charalambous, 2003. "An effective heuristic for the CLSP with set-up times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 490-498, May.
    13. Kuhn, Heinrich, 1997. "A dynamic lot sizing model with exponential machine breakdowns," European Journal of Operational Research, Elsevier, vol. 100(3), pages 514-536, August.
    14. Diaby, M. & Bahl, H. C. & Karwan, M. H. & Zionts, S., 1992. "Capacitated lot-sizing and scheduling by Lagrangean relaxation," European Journal of Operational Research, Elsevier, vol. 59(3), pages 444-458, June.
    15. Ozdamar, Linet & Birbil, Sevket Ilker, 1998. "Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions," European Journal of Operational Research, Elsevier, vol. 110(3), pages 525-547, November.
    16. Beraldi, Patrizia & Ghiani, Gianpaolo & Guerriero, Emanuela & Grieco, Antonio, 2006. "Scenario-based planning for lot-sizing and scheduling with uncertain processing times," International Journal of Production Economics, Elsevier, vol. 101(1), pages 140-149, May.
    17. McIntosh, R. I. & Culley, S. J. & Mileham, A. R. & Owen, G. W., 2001. "Changeover improvement: A maintenance perspective," International Journal of Production Economics, Elsevier, vol. 73(2), pages 153-163, September.
    18. Nourelfath, Mustapha, 2011. "Service level robustness in stochastic production planning under random machine breakdowns," European Journal of Operational Research, Elsevier, vol. 212(1), pages 81-88, July.
    19. Moustapha Diaby & Harish C. Bahl & Mark H. Karwan & Stanley Zionts, 1992. "A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing," Management Science, INFORMS, vol. 38(9), pages 1329-1340, September.
    20. Taş, D. & Gendreau, M. & Dellaert, N. & van Woensel, T. & de Kok, A.G., 2014. "Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach," European Journal of Operational Research, Elsevier, vol. 236(3), pages 789-799.
    21. Dillenberger, Christof & Escudero, Laureano F. & Wollensak, Artur & Zhang, Wu, 1994. "On practical resource allocation for production planning and scheduling with period overlapping setups," European Journal of Operational Research, Elsevier, vol. 75(2), pages 275-286, June.
    22. Süral, Haldun & Denizel, Meltem & Van Wassenhove, Luk N., 2009. "Lagrangean relaxation based heuristics for lot sizing with setup times," European Journal of Operational Research, Elsevier, vol. 194(1), pages 51-63, April.
    23. Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
    24. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    25. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.
    26. Dellaert, N. P. & Melo, M. T., 1998. "Make-to-order policies for a stochastic lot-sizing problem using overtime," International Journal of Production Economics, Elsevier, vol. 56(1), pages 79-97, September.
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    1. Gao, Kaiye & Peng, Rui & Qu, Li & Wu, Shaomin, 2020. "Jointly optimizing lot sizing and maintenance policy for a production system with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 202(C).

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