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Effective network formulations for lot sizing with backlogging in two-level serial supply chains

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  • Oguz Solyali
  • Meltem Denizel
  • Haldun Süral

Abstract

This study considers the serial lot sizing problem with backlogging in two-level supply chains to determine when and how much to order at a warehouse and ship to a retailer over a T-period planning horizon so that the external known demand occurring at the retailer is satisfied and the total cost at all levels is minimized. In particular, the uncapacitated two-level serial lot sizing problem with backlogging and the two-level serial lot sizing problem with cargo capacity and backlogging are formulated using effective shortest-path network representations, which define the convex hull of their feasible solutions. These representations lead to efficient algorithms with O(T3) time for the uncapacitated problem and O(T6) time for the capacitated problem. Furthermore, a tight reformulation with O(T3) variables and O(T2) constraints (resp. O(T6) variables and O(T5) constraints) is proposed for the uncapacitated (resp. capacitated) problem.

Suggested Citation

  • Oguz Solyali & Meltem Denizel & Haldun Süral, 2016. "Effective network formulations for lot sizing with backlogging in two-level serial supply chains," IISE Transactions, Taylor & Francis Journals, vol. 48(2), pages 146-157, February.
    • Handle: RePEc:taf:uiiexx:v:48:y:2016:i:2:p:146-157
    DOI: 10.1080/0740817X.2015.1027457
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    Cited by:

    1. Hadi Farhangi, 2021. "Multi-Echelon Supply Chains with Lead Times and Uncertain Demands," SN Operations Research Forum, Springer, vol. 2(3), pages 1-25, September.
    2. Hwang, Hark-Chin & Kang, Jangha, 2021. "An improved algorithm for the lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 100(C).
    3. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    4. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2018. "The impact of service level constraints in deterministic lot sizing with backlogging," Omega, Elsevier, vol. 79(C), pages 91-103.
    5. Hwang, Hark-Chin & Kang, Jangha, 2020. "The two-level lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 90(C).

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