Optimal inventory control with shrinkage and observed sales

Alain Bensoussan, Metin Çakanyildirim, Meng Li, Suresh P. Sethi

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study a discrete-time periodic-review inventory system where the unmet demand is lost, and the excess inventory is subject to shrinkage. We first derive the state evolution and then introduce unnormalized conditional probabilities to transform the nonlinear state evolution into a linear one. We then prove the existence and uniqueness of the solution for the Bellman equation in the case of unbounded costs and show that the solution yields the value function.

Original languageEnglish (US)
Pages (from-to)589-603
Number of pages15
Issue number4
StatePublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation


  • demand
  • existence
  • inventory
  • shrinkage
  • uniqueness


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