A periodic-review base-stock inventory system with sales rejection

Yanyi Xu, Arnab Bisi, Maqbool Dada

Research output: Contribution to journalReview articlepeer-review


We consider a system in which an order is placed every T periods to bring the inventory position up to the base stock S. We accept demand until the inventory position reaches a sales rejection threshold M. Our objective is to find the optimal values of S and M that minimize the long-run average cost per period. We establish the stationary distribution of our system and develop structural properties of the optimal solution that facilitate computation. In particular, we show that in an optimal solution, the optimal value of M is nonnegative under some reasonable conditions. Hence, in our model a mixture of backorders and lost sales may occur. Additionally, we compare our system against traditional systems in which demand during stockouts is either fully backordered or lost.

Original languageEnglish (US)
Pages (from-to)742-753
Number of pages12
JournalOperations Research
Issue number3
StatePublished - May 1 2011


  • (R1 T ) systems
  • Backorders
  • Base stock systems
  • Lost sales
  • Stochastic inventory models

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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