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An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem

Author

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  • Huseyin Tunc

    (Department of Policy and Strategy Studies, Hacettepe University, Ankara, Turkey)

  • Onur A. Kilic

    (Department of Operations, University of Groningen, 9700 AV Groningen, Netherlands)

  • S. Armagan Tarim

    (Department of Management, Cankaya University, Ankara, 06800 Turkey; Cork University Business School, University College Cork, T12 K8AF, Ireland)

  • Roberto Rossi

    (Business School, University of Edinburgh, Edinburgh EH8 9JS, United Kingdom)

Abstract

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function—as is the case in earlier formulations—it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach.

Suggested Citation

  • Huseyin Tunc & Onur A. Kilic & S. Armagan Tarim & Roberto Rossi, 2018. "An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 492-506, August.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:3:p:492-506
    DOI: 10.1287/ijoc.2017.0792
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    References listed on IDEAS

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    1. Kilic, Onur A. & Tarim, S. Armagan, 2011. "An investigation of setup instability in non-stationary stochastic inventory systems," International Journal of Production Economics, Elsevier, vol. 133(1), pages 286-292, September.
    2. Tarim, S. Armagan & Smith, Barbara M., 2008. "Constraint programming for computing non-stationary (R, S) inventory policies," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1004-1021, September.
    3. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    4. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    5. 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.
    6. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    7. Roberto Rossi & S. Tarim & Brahim Hnich & Steven Prestwich, 2012. "Constraint programming for stochastic inventory systems under shortage cost," Annals of Operations Research, Springer, vol. 195(1), pages 49-71, May.
    8. Tarim, S. Armagan & Dogru, Mustafa K. & Özen, Ulas & Rossi, Roberto, 2011. "An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints," European Journal of Operational Research, Elsevier, vol. 215(3), pages 563-571, December.
    9. Tarim, S. Armagan & Kingsman, Brian G., 2006. "Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand," European Journal of Operational Research, Elsevier, vol. 174(1), pages 581-599, October.
    10. Rossi, Roberto & Tarim, S. Armagan & Hnich, Brahim & Prestwich, Steven, 2011. "A state space augmentation algorithm for the replenishment cycle inventory policy," International Journal of Production Economics, Elsevier, vol. 133(1), pages 377-384, September.
    11. Fatih Mutlu & Sila Çetinkaya & James Bookbinder, 2010. "An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments," IISE Transactions, Taylor & Francis Journals, vol. 42(5), pages 367-377.
    12. 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.
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    Cited by:

    1. Ma, Xiyuan & Rossi, Roberto & Archibald, Thomas Welsh, 2022. "Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy," European Journal of Operational Research, Elsevier, vol. 298(2), pages 573-584.
    2. Visentin, Andrea & Prestwich, Steven & Rossi, Roberto & Tarim, S. Armagan, 2021. "Computing optimal (R,s,S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 91-99.
    3. Rossi, Roberto & Tomasella, Maurizio & Martin-Barragan, Belen & Embley, Tim & Walsh, Christopher & Langston, Matthew, 2019. "The Dynamic Bowser Routing Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 108-126.
    4. Sereshti, Narges & Adulyasak, Yossiri & Jans, Raf, 2021. "The value of aggregate service levels in stochastic lot sizing problems," Omega, Elsevier, vol. 102(C).
    5. Simon Thevenin & Yossiri Adulyasak & Jean-François Cordeau, 2022. "Stochastic Dual Dynamic Programming for Multiechelon Lot Sizing with Component Substitution," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3151-3169, November.
    6. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2021. "Benders decomposition for a stochastic three-level lot sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 291(1), pages 206-217.
    7. Gutierrez-Alcoba, Alejandro & Rossi, Roberto & Martin-Barragan, Belen & Embley, Tim, 2023. "The stochastic inventory routing problem on electric roads," European Journal of Operational Research, Elsevier, vol. 310(1), pages 156-167.
    8. Dural-Selcuk, Gozdem & Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2020. "The benefit of receding horizon control: Near-optimal policies for stochastic inventory control," Omega, Elsevier, vol. 97(C).

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