Discrete-item inventory control involving unknown censored demand and convex inventory costs

Jian Yang, Jim Shi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study inventory control involving lost sales and hence censored demand. In a long-run average framework, the demand distribution is largely unknown. As long as the stationary inventory costs are strictly convex to the extent that the second lost item costs strictly more than the first one, the regret would be (Formula presented.). Our discrete-item setting has rendered the presence or absence of strong censoring indicators or equivalently, being knowledgeable or ignorant of one more demand request after the depletion of the inventory, a critical issue and any gradient-based method designed for the continuous-item case ineffective. We propose a policy that deliberately orders up to very high levels in designated learning periods and in the remaining doing periods, uses base-stock levels tailored to near-empirical distributions formed over the learning periods. A matching (Formula presented.) upper bound can be achieved by this policy. The results can hold even when items are nonperishable. Numerical experiments further illustrate the relative competitiveness of our separate learning-doing policy.

Original languageEnglish (US)
Pages (from-to)45-64
Number of pages20
JournalProduction and Operations Management
Issue number1
StatePublished - Jan 2023

All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation


  • censored demand
  • convex inventory costs
  • demand ambiguity
  • inventory control
  • regret analysis


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