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Asymptotically Optimal Lagrangian Policies for Multi-Warehouse, Multi-Store Systems with Lost Sales

Author

Listed:
  • Sentao Miao

    (Desautels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada)

  • Stefanus Jasin

    (Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

  • Xiuli Chao

    (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We consider a periodic-review inventory control problem for the Multi-Warehouse Multi-Store system with lost sales. We focus on a time horizon during which the system receives no external replenishment. Specifically, each warehouse has a finite initial inventory at the beginning of the horizon, which is then periodically allocated to the stores in each period in order to minimize the total expected lost-sales costs, holding costs, and shipping costs. This is a hard problem and the structure of its optimal policy is extremely complex. We develop simple heuristics based on Lagrangian relaxation that are easy to compute and implement, and have provably near-optimal performances. In particular, we show that the losses of our heuristics are sublinear in both the length of the time horizon and the number of stores . This improves the performance of existing heuristics in the literature whose losses are only sublinear in the number of stores. Numerical study shows that the heuristics perform very well. We also extend our analysis to the setting of positive delivery lead times.

Suggested Citation

  • Sentao Miao & Stefanus Jasin & Xiuli Chao, 2022. "Asymptotically Optimal Lagrangian Policies for Multi-Warehouse, Multi-Store Systems with Lost Sales," Operations Research, INFORMS, vol. 70(1), pages 141-159, January.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:1:p:141-159
    DOI: 10.1287/opre.2021.2161
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