Inventory replenishment control under supply uncertainty

Taesu Cheong, Chelsea C. White

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α{pipe}a), where ∑α=0aP(α{pipe}a) = 1. Let z=d-x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ * is such that δ *(z)=0 for z≤0, δ *(z)≥z≥0, and δ *(z)-z is monotonically non-decreasing for z≥0. Such a "staircase" structure has a simple parametric description, which can help to accelerate value iteration and policy iteration.

Original languageEnglish
Pages (from-to)581-592
Number of pages12
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - 2013 Sept
Externally publishedYes


  • Inventory systems
  • Markov decision processes
  • Periodic review
  • Random yields
  • Supply uncertainty

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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