Ergodic Control for a Mean Reverting Inventory Model

Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


In this paper, an inventory control problem with a mean reverting inventory model is considered. The demand is assumed to follow a continuous diffusion process and a mean-reverting process which will take into account of the demand dependent of the inventory level. By choosing when and how much to stock, the objective is to minimize the long-run average cost, which consists of transaction cost for each replenishment, holding and shortage costs associated with the inventory level. An approach for deriving the average cost value of infinite time horizon is developed. By applying the theory of stochastic impulse control, we show that a unique (s; S) policy is indeed optimal. The main contribution of this work is to present a method to derive the (s; S) policy and hence the minimal long-run average cost.

Original languageEnglish
Pages (from-to)857-876
Number of pages20
JournalJournal of Industrial and Management Optimization
Issue number3
Publication statusPublished - 1 Jul 2018


  • Dynamic programming
  • Ergodic control
  • Inventory policy
  • Mean reverting model
  • Stochastic impulse control

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics


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