Technical Note-Average Cost Optimality in Partially Observable Lost-Sales Inventory Systems

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We consider a partially observable lost-sales inventory system, in which the inventory level is observed only when it reaches zero. We use the vanishing discount factor approach to prove the existence of a stationary optimal policy for the average cost minimization. As our main methodological contribution, we provide a way to verify the key condition of the vanishing discount factor approach-the uniform boundedness of the relative discounted value function. To accomplish that, we construct a valid policy, which, in a certain sense, “copies” the actions of another policy for the process with a different initial state. To the best of our knowledge, this paper is the first one on partially observable inventory models under the average cost criterion.

Original languageEnglish (US)
Pages (from-to)2390-2396
Number of pages7
JournalOperations Research
Issue number6
StatePublished - Nov 1 2023


  • Markov decision process
  • average cost
  • lost sales
  • optimality inequality
  • partial observations

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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