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Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging

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  • Hark‐Chin Hwang
  • Wilco van den Heuvel

Abstract

This article considers a dynamic lot‐sizing problem with storage capacity limitation in which backlogging is allowed. For general concave procurement and inventory costs, we present an O(T2) dynamic programming algorithm where T is the length of the planning horizon. Furthermore, in case of a fixed‐charge cost structure without speculative motives, we show that the problem can be solved in O(T) time. By carefully choosing decompositions of the problems, we can use classical results like an efficient matrix searching algorithm and geometric techniques to achieve the results. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

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  • Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    • Handle: RePEc:wly:navres:v:59:y:2012:i:3-4:p:244-253
    DOI: 10.1002/nav.21485
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    Cited by:

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    2. Majid Al‐Gwaiz & Xiuli Chao & H. Edwin Romeijn, 2016. "Capacity expansion and cost efficiency improvement in the warehouse problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(5), pages 367-373, August.
    3. José M. Gutiérrez & Beatriz Abdul-Jalbar & Joaquín Sicilia & Inmaculada Rodríguez-Martín, 2021. "Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure," Mathematics, MDPI, vol. 9(6), pages 1-21, March.
    4. Wolsey, L.A., 2015. "Uncapacitated Lot-Sizing with Stock Upper Bounds, Stock Fixed Costs, Stock Overloads and Backlogging: A Tight Formulation," LIDAM Discussion Papers CORE 2015041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Önal, Mehmet & Romeijn, H.Edwin & Sapra, Amar & van den Heuvel, Wilco, 2015. "The economic lot-sizing problem with perishable items and consumption order preference," European Journal of Operational Research, Elsevier, vol. 244(3), pages 881-891.
    6. Belleflamme, Paul & Vergote, Wouter, 2016. "Monopoly price discrimination and privacy: The hidden cost of hiding," Economics Letters, Elsevier, vol. 149(C), pages 141-144.
    7. Önal, Mehmet & van den Heuvel, Wilco & Liu, Tieming, 2012. "A note on “The economic lot sizing problem with inventory bounds”," European Journal of Operational Research, Elsevier, vol. 223(1), pages 290-294.
    8. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.
    9. Ayse Akbalik & Bernard Penz & Christophe Rapine, 2015. "Capacitated lot sizing problems with inventory bounds," Annals of Operations Research, Springer, vol. 229(1), pages 1-18, June.
    10. Chitsaz, Masoud & Cordeau, Jean-François & Jans, Raf, 2020. "A branch-and-cut algorithm for an assembly routing problem," European Journal of Operational Research, Elsevier, vol. 282(3), pages 896-910.

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