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An optimal solution for the stochastic version of the Wagner-Whitin dynamic lot-size model

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  • Vargas, Vicente

Abstract

We present an algorithm for determining the optimal solution over the entire planning horizon for the dynamic lot-size model where demand is stochastic and non-stationary. The optimal solution to the deterministic problem is the well-known Wagner-Whitin algorithm. The present work contributes principally to knowledge building and provides a tool for researchers. One potentially useful contribution to practice is the solution to an important special case, where demand follows normal distributions. Other contributions to practice will likely flow from the development of improved heuristics and the improved basis to evaluate heuristic performance.

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  • 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.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:447-451
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    1. Wallace J. Hopp (Editor-in-Chief), 2004. "Ten Most Influential Papers of Management Science's First Fifty Years," Management Science, INFORMS, vol. 50(12_supple), pages 1763-1763, December.
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    Cited by:

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    2. Vargas, Vicente & Metters, Richard, 2011. "A master production scheduling procedure for stochastic demand and rolling planning horizons," International Journal of Production Economics, Elsevier, vol. 132(2), pages 296-302, August.
    3. 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.
    4. Stößlein, Martin & Kanet, John Jack & Gorman, Mike & Minner, Stefan, 2014. "Time-phased safety stocks planning and its financial impacts: Empirical evidence based on European econometric data," International Journal of Production Economics, Elsevier, vol. 149(C), pages 47-55.
    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. 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.
    7. Govindan, Kannan, 2015. "The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory," European Journal of Operational Research, Elsevier, vol. 242(2), pages 402-423.
    8. Zied Bahroun & Nidhal Belgacem, 2019. "Determination of dynamic safety stocks for cyclic production schedules," Operations Management Research, Springer, vol. 12(1), pages 62-93, June.
    9. Tempelmeier, Horst & Herpers, Sascha, 2011. "Dynamic uncapacitated lot sizing with random demand under a fillrate constraint," European Journal of Operational Research, Elsevier, vol. 212(3), pages 497-507, August.
    10. Koca, Esra & Yaman, Hande & Selim Aktürk, M., 2015. "Stochastic lot sizing problem with controllable processing times," Omega, Elsevier, vol. 53(C), pages 1-10.
    11. Céline Gicquel & Jianqiang Cheng, 2018. "A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand," Annals of Operations Research, Springer, vol. 264(1), pages 123-155, May.
    12. Witthayapraphakorn, Aphisak & Charnsethikul, Peerayuth, 2019. "Benders decomposition with special purpose method for the sub problem in lot sizing problem under uncertain demand," Operations Research Perspectives, Elsevier, vol. 6(C).
    13. Slama, Ilhem & Ben-Ammar, Oussama & Thevenin, Simon & Dolgui, Alexandre & Masmoudi, Faouzi, 2022. "Stochastic program for disassembly lot-sizing under uncertain component refurbishing lead times," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1183-1198.
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    15. 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.
    16. Yang, Liu & Li, Haitao & Campbell, James F. & Sweeney, Donald C., 2017. "Integrated multi-period dynamic inventory classification and control," International Journal of Production Economics, Elsevier, vol. 189(C), pages 86-96.
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    18. 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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