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Decomposition‐based approximation algorithms for the one‐warehouse multi‐retailer problem with concave batch order costs

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  • Weihong Hu
  • Zhuoting Yu
  • Alejandro Toriello
  • Maged M. Dessouky

Abstract

We study the one‐warehouse multi‐retailer problem under deterministic dynamic demand and concave batch order costs, where order batches have an identical capacity and the order cost function for each facility is concave within the batch. Under appropriate assumptions on holding cost structure, we obtain lower bounds via a decomposition that splits the two‐echelon problem into single‐facility subproblems, then propose approximation algorithms by judiciously recombining the subproblem solutions. For piecewise linear concave batch order costs with a constant number of slopes we obtain a constant‐factor approximation, while for general concave batch costs we propose an approximation within a logarithmic factor of optimality. We also extend some results to subadditive order and/or holding costs.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:67:y:2020:i:7:p:503-523
    DOI: 10.1002/nav.21927
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    References listed on IDEAS

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