Joint replenishment and manufacturing activities control in a two stage unreliable supply chain
This paper deals with dynamic stochastic situations faced by supply chains. In this context, various interactions, disparate decisions and random phenomena must be considered. These issues are considered in this paper through a two stage supply chain control problem. The supplier and the transformation stage are both subject to random events such as periods of unavailability due to internal difficulties or market constraints. Our objective is to find information sharing control policies for the supply and production activities that minimises the expected discounted cost of ordering, inventories/backlog and transformation over an infinite horizon. This is an optimal control problem with state constraints and hybrid dynamics of the production and replenishment activities. It is shown that, from a mathematical point of view, the considered problem is difficult to tackle and it calls upon optimal and impulsive control theory notions. A dynamic stochastic model is thus proposed. The existence of an optimal control policy and Hamilton-Jacobi-Bellman optimality condition in terms of the value function of the problem are derived and discussed. A numerical schema is then proposed to solve the obtained optimality conditions equations. A complete control policy is finally developed. The confirmation of such a policy structure is illustrated through sensitivity analysis. Some particular cases are also presented and discussed.
Keywords: (s, Q) policy; hedging point policy; impulsive control; production rates; replenishment policy; stochastic optimal control
Document Type: Research Article
Affiliations: 1: Department of Automated Production Engineering, LCCSP Laboratory, 2: Department of Mechanical Engineering, LITP Laboratory, Ecole de Technologie Superieure, University of Quebec, Quebec, Canada H3C 1K3
Publication date: 01 January 2009
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