Closing the gap: A learning algorithm for lost-sales inventory systems with lead times

Huanan Zhang, Xiuli Chao, Cong Shi

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We consider a periodic-review, single-product inventory system with lost sales and positive lead times under censored demand. In contrast to the classical inventory literature, we assume the firm does not know the demand distribution a priori and makes an adaptive inventory-ordering decision in each period based only on the past sales (censored demand) data. The standard performance measure is regret, which is the cost difference between a learning algorithm and the clairvoyant (full-information) benchmark. When the benchmark is chosen to be the (full-information) optimal base-stock policy, Huh et al. [Huh WT, Janakiraman G, Muckstadt JA, Rusmevichientong P (2009a) An adaptive algorithm for finding the optimal base-stock policy in lost sales inventory systems with censored demand. Math. Oper. Res. 34(2):397-416.] developed a nonparametric learning algorithm with a cubic-root convergence rate on regret. An important open question is whether there exists a nonparametric learning algorithm whose regret rate matches the theoretical lower bound of any learning algorithms. In this work, we provide an affirmative answer to this question. More precisely, we propose a new nonparametric algorithm termed the simulated cycle-update policy and establish a square-root convergence rate on regret, which is proven to be the lower bound of any learning algorithm. Our algorithm uses a random cycle-updating rule based on an auxiliary simulated system running in parallel and also involves two new concepts, namely the withheld on-hand inventory and the double-phase cycle gradient estimation. The techniques developed are effective for learning a stochastic system with complex system dynamics and lasting impact of decisions.

Original languageEnglish (US)
Pages (from-to)1962-1980
Number of pages19
JournalManagement Science
Issue number5
StatePublished - May 2020

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research


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