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Constraint programming for stochastic inventory systems under shortage cost

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  • Roberto Rossi
  • S. Tarim
  • Brahim Hnich
  • Steven Prestwich

Abstract

One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function. Copyright The Author(s) 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:49-71:10.1007/s10479-011-0936-x
    DOI: 10.1007/s10479-011-0936-x
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    References listed on IDEAS

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    1. Tang, Christopher S., 2006. "Perspectives in supply chain risk management," International Journal of Production Economics, Elsevier, vol. 103(2), pages 451-488, October.
    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.
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    12. 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.
    13. Tempelmeier, Horst, 2007. "On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 181(1), pages 184-194, August.
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    Cited by:

    1. W. A. Rijpkema & E. M. T. Hendrix & R. Rossi & J. G. A. J. Vorst, 2016. "Application of stochastic programming to reduce uncertainty in quality-based supply planning of slaughterhouses," Annals of Operations Research, Springer, vol. 239(2), pages 613-624, April.
    2. 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.
    3. Shib Sana, 2015. "An EOQ model for stochastic demand for limited capacity of own warehouse," Annals of Operations Research, Springer, vol. 233(1), pages 383-399, October.
    4. 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.
    5. M. Güler & Taner Bilgiç & Refik Güllü, 2015. "Joint pricing and inventory control for additive demand models with reference effects," Annals of Operations Research, Springer, vol. 226(1), pages 255-276, March.
    6. 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).
    7. 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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