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Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs


  • Huanan Zhang

    () (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Cong Shi

    () (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Xiuli Chao

    () (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)


We develop the first approximation algorithm for periodic-review perishable inventory systems with setup costs. The ordering lead time is zero. The model allows for correlated demand processes that generalize the well-known approaches to model dynamic demand forecast updates. The structure of optimal policies for this fundamental class of problems is not known in the literature. Thus, finding provably near-optimal control policies has been an open challenge. We develop a randomized proportional-balancing policy (RPB) that can be efficiently implemented in an online manner, and we show that it admits a worst-case performance guarantee between 3 and 4. The main challenge in our analysis is to compare the setup costs between RPB and the optimal policy in the presence of inventory perishability, which departs significantly from the previous works in the literature. The numerical results show that the average performance of RPB is good (within 1% of optimality under i.i.d. demands and within 7% under correlated demands).

Suggested Citation

  • Huanan Zhang & Cong Shi & Xiuli Chao, 2016. "Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs," Operations Research, INFORMS, vol. 64(2), pages 432-440, April.
  • Handle: RePEc:inm:oropre:v:64:y:2016:i:2:p:432-440

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