Ergodic control for a mean reverting inventory model

Jingzhen Liu; Ka Fai Cedric Yiu; Alain Bensoussan

doi:10.3934/jimo.2017079

Article Contents

2018, Volume 14, Issue 3: 857-876. Doi: 10.3934/jimo.2017079

This issue Previous Article Linearized block-wise alternating direction method of multipliers for multiple-block convex programming Next Article Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels

Ergodic control for a mean reverting inventory model

1.
School of Insurance, Central University of Finance and Economics, Beijing 100081, China
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China
3.
Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong, China
4.
Naveen Jindal School of Management, University of Texas at Dallas, USA

Received: April 30, 2015

Revised: July 31, 2017

Early access: August 2017

Published: June 2018

This research is supported by Natural and Science Natural Foundation of China(11771466,11301559,11471171), the 111 project(B17050), the National Science Foundation under grants DMS-1303775, DMS-1612880, and the Research Grants Council of the Hong Kong Special Administrative Region (CityU 500113, CityU 113 03 316). The second author is supported by PolyU grant G-YBKM.

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K61, 49J40, 90C39; Secondary: 93E20.

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References

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