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An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem


  • Danny Segev

    () (Department of Statistics, University of Haifa, Haifa 31905, Israel)


The main contribution of this paper is to propose a new dynamic-programming approach that (epsilon) -approximates the joint replenishment problem, with stationary demands and holding costs, in its discrete-time finite-horizon setting. Our first and foremost objective is to show that the computation time of classical dynamic-programming algorithms can be improved on by orders of magnitude when one is willing to lose an (epsilon) -factor in optimality. Based on synthesizing ideas such as commodity aggregation, approximate dynamic programming, and a few guessing tricks, we show that one can attain any required degree of accuracy in near-polynomial time.

Suggested Citation

  • Danny Segev, 2014. "An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 432-444, May.
  • Handle: RePEc:inm:ormoor:v:39:y:2014:i:2:p:432-444
    DOI: 10.1287/moor.2013.0611

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    References listed on IDEAS

    1. Awi Federgruen & Michal Tzur, 1994. "The Joint Replenishment Problem with Time-Varying Costs and Demands: Efficient, Asymptotic and ε-Optimal Solutions," Operations Research, INFORMS, vol. 42(6), pages 1067-1086, December.
    2. Dev Joneja, 1990. "The Joint Replenishment Problem: New Heuristics and Worst Case Performance Bounds," Operations Research, INFORMS, vol. 38(4), pages 711-723, August.
    3. Daniel Adelman & Diego Klabjan, 2005. "Duality and Existence of Optimal Policies in Generalized Joint Replenishment," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 28-50, February.
    4. BARANY, Imre & VAN ROY, Tony & WOLSEY, Laurence A., 1984. "Uncapacitated lot-sizing: the convex hull of solutions," CORE Discussion Papers RP 605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. 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.
    7. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    8. Willard I. Zangwill, 1966. "A Deterministic Multiproduct, Multi-Facility Production and Inventory Model," Operations Research, INFORMS, vol. 14(3), pages 486-507, June.
    9. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    10. 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.
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