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Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem

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  • Özen, Ulaş
  • Doğru, Mustafa K.
  • Armagan Tarim, S.
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    Abstract

    We consider a single-stage inventory system facing non-stationary stochastic demand of the customers in a finite planning horizon. Motivated by the practice, the replenishment times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact replenishment quantities can be deferred until the replenishment time. This operating scheme is refereed to as a “static-dynamic uncertainty” strategy in the literature [3]. We consider dynamic fixed-ordering and linear end-of-period holding costs, as well as dynamic penalty costs, or service levels. We prove that the optimal ordering policy is a base stock policy for both penalty cost and service level constrained models. Since an exponential exhaustive search based on dynamic programming yields the optimal ordering periods and the associated base stock levels, it is not possible to compute the optimal policy parameters for longer planning horizons. Thus, we develop two heuristics. Numerical experiments show that both heuristics perform well in terms of solution quality and scale-up efficiently; hence, any practically relevant large instance can be solved in reasonable time. Finally, we discuss how our results and heuristics can be extended to handle capacity limitations and minimum order quantity considerations.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 40 (2012)
    Issue (Month): 3 ()
    Pages: 348-357

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    Handle: RePEc:eee:jomega:v:40:y:2012:i:3:p:348-357

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    Related research

    Keywords: Static-dynamic uncertainty; Non-stationary; Stochastic demand; Heuristic; Penalty cost; Service level;

    References

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    1. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    2. 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.
    3. Vargas, Vicente, 2009. "An optimal solution for the stochastic version of the Wagner-Whitin dynamic lot-size model," European Journal of Operational Research, Elsevier, vol. 198(2), pages 447-451, October.
    4. Thomas E. Morton & David W. Pentico, 1995. "The Finite Horizon Nonstationary Stochastic Inventory Problem: Near-Myopic Bounds, Heuristics, Testing," Management Science, INFORMS, vol. 41(2), pages 334-343, February.
    5. Paul Zipkin, 1989. "Critical Number Policies for Inventory Models with Periodic Data," Management Science, INFORMS, vol. 35(1), pages 71-80, January.
    6. 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.
    7. Joseph D. Blackburn & Dean H. Kropp & Robert A. Millen, 1986. "A Comparison of Strategies to Dampen Nervousness in MRP Systems," Management Science, INFORMS, vol. 32(4), pages 413-429, April.
    8. 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.
    9. 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.
    10. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    11. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2011. "The cost of using stationary inventory policies when demand is non-stationary," Omega, Elsevier, vol. 39(4), pages 410-415, August.
    12. 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.
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    Cited by:
    1. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2013. "A simple approach for assessing the cost of system nervousness," International Journal of Production Economics, Elsevier, vol. 141(2), pages 619-625.

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