Structural properties of the lost sales problem with fractional lead times

Y. Xu, Sang Phil Kim, A. Bisi, Suresh Chand, Maqbool Dada

Research output: Contribution to journalArticlepeer-review


We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L, is placed to bring the inventory position to R. Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R, review period T, and lead time L. Then, we develop an algorithm to find the optimal stationary R. Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T.

Original languageEnglish (US)
Pages (from-to)410-416
Number of pages7
JournalOperations Research Letters
Issue number5
StatePublished - Sep 2019


  • Base-stock policy
  • Fractional lead time
  • Lost sales
  • Stochastic inventory system

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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