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

Xingyu Bai (), Xin Chen () and Alexander L. Stolyar ()
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Xingyu Bai: Industrial Enterprise and Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Xin Chen: Industrial Enterprise and Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Alexander L. Stolyar: Industrial Enterprise and Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801; Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801

Operations Research, 2023, vol. 71, issue 6, 2390-2396

Abstract: 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.

Keywords: Stochastic Models; Markov decision process; average cost; optimality inequality; partial observations; lost sales (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:71:y:2023:i:6:p:2390-2396

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