Exact analysis of (R, s, S) inventory control systems with lost sales and zero lead time

Nazanin Esmaili, Bryan A. Norman, Jayant Rajgopal

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study an (R, s, S) inventory control policy with stochastic demand, lost sales, zero lead-time and a target service level to be satisfied. The system is modeled as a discrete time Markov chain for which we present a novel approach to derive exact closed-form solutions for the limiting distribution of the on-hand inventory level at the end of a review period, given the reorder level (s) and order-up-to level (S). We then establish a relationship between the limiting distributions for adjacent values of the reorder point that is used in an efficient recursive algorithm to determine the optimal parameter values of the (R, s, S) replenishment policy. The algorithm is easy to implement and entails less effort than solving the steady-state equations for the corresponding Markov model. Point-of-use hospital inventory systems share the essential characteristics of the inventory system we model, and a case study using real data from such a system shows that with our approach, optimal policies with significant savings in inventory management effort are easily obtained for a large family of items.

Original languageEnglish
Pages (from-to)123-132
Number of pages10
JournalNaval Research Logistics
Issue number2
StatePublished - Mar 2019


  • (R, s, S) inventory control policy
  • discrete time Markov chains
  • lost sales


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