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Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales

Author

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  • Gayon, J.-P.
  • Massonnet, G.
  • Rapine, C.
  • Stauffer, G.

Abstract

We consider the One Warehouse Multi-Retailer (OWMR) problem with deterministic time-varying demand in the case where shortages are allowed. Demand may be either backlogged or lost. We present a simple combinatorial algorithm to build an approximate solution from a decomposition of the system into single-echelon subproblems. We establish that the algorithm has a performance guarantee of 3 for the OWMR with backlog under mild assumptions on the cost structure. In addition, we improve this guarantee to 2 in the special case of the Joint-Replenishment Problem (JRP) with backlog. As a by-product of our approach, we show that our decomposition provides a new lower bound of the optimal cost. A similar technique also leads to a 2-approximation for the OWMR problem with lost-sales. In all cases, the complexity of the algorithm is linear in the number of retailers and quadratic in the number of time periods, which makes it a valuable tool for practical applications. To the best of our knowledge, these are the first constant approximations for the OWMR with shortages.

Suggested Citation

  • Gayon, J.-P. & Massonnet, G. & Rapine, C. & Stauffer, G., 2016. "Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales," European Journal of Operational Research, Elsevier, vol. 250(1), pages 155-163.
    • Handle: RePEc:eee:ejores:v:250:y:2016:i:1:p:155-163
    DOI: 10.1016/j.ejor.2015.10.054
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    References listed on IDEAS

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    1. 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).
    2. Retsef Levi & Robin Roundy & David Shmoys & Maxim Sviridenko, 2008. "A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem," Management Science, INFORMS, vol. 54(4), pages 763-776, April.
    3. 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.
    4. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    5. Absi, Nabil & Kedad-Sidhoum, Safia, 2008. "The multi-item capacitated lot-sizing problem with setup times and shortage costs," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1351-1374, March.
    6. Aksen, Deniz & Altinkemer, Kemal & Chand, Suresh, 2003. "The single-item lot-sizing problem with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 147(3), pages 558-566, June.
    7. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    8. Richard A. Sandbothe & Gerald L. Thompson, 1990. "A Forward Algorithm for the Capacitated Lot Size Model with Stockouts," Operations Research, INFORMS, vol. 38(3), pages 474-486, June.
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    Cited by:

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    2. Kaynov, Illya & van Knippenberg, Marijn & Menkovski, Vlado & van Breemen, Albert & van Jaarsveld, Willem, 2024. "Deep Reinforcement Learning for One-Warehouse Multi-Retailer inventory management," International Journal of Production Economics, Elsevier, vol. 267(C).
    3. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.
    4. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    5. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    6. Jean-Philippe Gayon & Guillaume Massonnet & Christophe Rapine & Gautier Stauffer, 2017. "Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 854-875, August.
    7. Weihong Hu & Zhuoting Yu & Alejandro Toriello & Maged M. Dessouky, 2020. "Decomposition‐based approximation algorithms for the one‐warehouse multi‐retailer problem with concave batch order costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 503-523, October.

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