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Two-stage stochastic lot-sizing problem under cost uncertainty

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  • Zhili Zhou
  • Yongpei Guan

Abstract

For production planning problems, cost parameters can be uncertain due to marketing activities and interest rate fluctuation. In this paper, we consider a single-item two-stage stochastic lot-sizing problem under cost parameter uncertainty. Assuming cost parameters will increase or decrease after time period p each with certain probability, we minimize the total expected cost for a finite horizon problem. We develop an extended linear programming formulation in a higher dimensional space that can provide integral solutions by showing that its constraint matrix is totally unimodular. We also project this extended formulation to a lower dimensional space and obtain a corresponding extended formulation in the lower dimensional space. Final computational experiments demonstrate that the extended formulation is more efficient and performs more stable than the two-stage stochastic mixed-integer programming formulation. Copyright Springer Science+Business Media New York 2013

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  • Zhili Zhou & Yongpei Guan, 2013. "Two-stage stochastic lot-sizing problem under cost uncertainty," Annals of Operations Research, Springer, vol. 209(1), pages 207-230, October.
    • Handle: RePEc:spr:annopr:v:209:y:2013:i:1:p:207-230:10.1007/s10479-013-1333-4
    DOI: 10.1007/s10479-013-1333-4
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    1. José Manuel Campa & Linda S. Goldberg, 2005. "Exchange Rate Pass-Through into Import Prices," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 679-690, November.
    2. KÛCÛKYAVUZ, Simge & POCHET, Yves, 2007. "Uncapacitated lot sizing with backlogging: The convex hull," LIDAM Discussion Papers CORE 2007006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Yongpei Guan & Andrew J. Miller, 2008. "Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 56(5), pages 1172-1183, October.
    4. BARANY, Imre & VAN ROY, Tony & WOLSEY, Laurence A., 1984. "Uncapacitated lot-sizing: the convex hull of solutions," LIDAM Reprints CORE 605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Kai Huang & Shabbir Ahmed, 2009. "The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty," Operations Research, INFORMS, vol. 57(4), pages 893-904, August.
    6. Shabbir Ahmed & Renan Garcia, 2003. "Dynamic Capacity Acquisition and Assignment under Uncertainty," Annals of Operations Research, Springer, vol. 124(1), pages 267-283, November.
    7. POCHET, Yves & WOLSEY, Laurence A., 1988. "Lot-size models with backlogging: strong reformulations and cutting planes," LIDAM Reprints CORE 791, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Duncan Simester, 1997. "Note. Optimal Promotion Strategies: A Demand-Sided Characterization," Management Science, INFORMS, vol. 43(2), pages 251-256, February.
    9. Narasimhan, Chakravarthi, 1988. "Competitive Promotional Strategies," The Journal of Business, University of Chicago Press, vol. 61(4), pages 427-449, October.
    10. Pochet, Y. & Wolsey, L. A., 1994. "Polyhedra for lot-sizing with Wagner-Whitin costs," LIDAM Reprints CORE 1129, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    12. 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.
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    Cited by:

    1. 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.
    2. Yongjian Li & Xiaoqiang Cai & Lei Xu & Wenxia Yang, 2016. "Heuristic approach on dynamic lot-sizing model for durable products with end-of-use constraints," Annals of Operations Research, Springer, vol. 242(2), pages 265-283, July.
    3. Kris Lieckens & Nico Vandaele, 2016. "Differential evolution to solve the lot size problem in stochastic supply chain management systems," Annals of Operations Research, Springer, vol. 242(2), pages 239-263, July.
    4. Songsong Chen & Feixiang Gong & Mingqiang Zhang & Jindou Yuan & Siyang Liao & Hongyin Chen & Dezhi Li & Shiming Tian & Xiaojian Hu, 2021. "Planning and Scheduling for Industrial Demand-Side Management: State of the Art, Opportunities and Challenges under Integration of Energy Internet and Industrial Internet," Sustainability, MDPI, vol. 13(14), pages 1-18, July.

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