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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.

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:3:p:348-357
    DOI: 10.1016/j.omega.2011.08.002
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    References listed on IDEAS

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    2. Fernando Rojas & Víctor Leiva & Peter Wanke & Camilo Lillo & Jimena Pascual, 2019. "Modeling lot-size with time-dependent demand based on stochastic programming and case study of drug supply in Chile," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-24, March.
    3. 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.
    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. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    6. 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.
    7. Koca, Esra & Yaman, Hande & Selim Aktürk, M., 2015. "Stochastic lot sizing problem with controllable processing times," Omega, Elsevier, vol. 53(C), pages 1-10.
    8. Li, Bo & Huang, Tian, 2022. "Control variable parameterization and optimization method for stochastic linear quadratic models," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    9. Chen, Zhen & Rossi, Roberto, 2021. "A dynamic ordering policy for a stochastic inventory problem with cash constraints," Omega, Elsevier, vol. 102(C).
    10. Choudhary, Devendra & Shankar, Ravi, 2015. "The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn, Sn) policy," Omega, Elsevier, vol. 51(C), pages 59-70.
    11. 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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