Optimality of (s; S) policies with nonlinear processes

Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


It is observed empirically that mean-reverting processes are more realistic in modeling the inventory level of a company. In a typical mean- reverting process, the inventory level is assumed to be linearly dependent on the deviation of the inventory level from the long-term mean. However, when the deviation is large, it is reasonable to assume that the company might want to increase the intensity of interference to the inventory level significantly rather than in a linear manner. In this paper, we attempt to model inventory replenishment as a nonlinear continuous feedback process. We study both infinite horizon discounted cost and the long-run average cost, and derive the corresponding optimal (s; S) policy.

Original languageEnglish
Pages (from-to)161-185
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
Publication statusPublished - Jan 2017


  • (s,S) policy
  • Inventory control
  • Nonlinear mean-reverting process

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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