A comparison of the optimal costs of two canonical inventory systems

Ganesh Janakiraman, Sridhar Seshadri, J. George Shanthikumar

Research output: Contribution to journalArticlepeer-review


We compare two inventory systems, one in which excess demand is lost and the other in which excess demand is back-ordered. Both systems are reviewed periodically. They experience the same sequence of identically and independently distributed random demands. Holding and shortage costs are considered. The holding cost parameter is identical; however, the cost of a lost sale could be different from the per-period cost of backlogging a unit sale. When these costs are equal, we prove that the optimal expected cost for managing the system with lost sales is lower. When the cost of a lost sale is greater, we establish a relationship between these parameters that ensures that the reverse inequality is true. These results are useful for designing inventory systems. We also introduce a new stochastic comparison technique in this paper.

Original languageEnglish (US)
Pages (from-to)866-875
Number of pages10
JournalOperations Research
Issue number5
StatePublished - Sep 2007
Externally publishedYes


  • Inventory
  • Production: stochastic

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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