Control of Unreliable Cooperative Multi-Site Production Systems

In this paper we consider a two site, cooperative, failure prone production system. The failure/repair process of each site is an independent Markov process. Each site may comply with possible shortage of the other site by sending to it a given quantity of products, with a penalty, modeling for example a transportation cost. General properties of the optimal policy are derived through the Hamilton Jacobi Bellman (HJB) equations, according to which the backlog/inventory space of the system is partitioned in regions, each characterized by a constant production rate. A general numerical procedure, which could be also exploited to face several problems approached through a HJB formulation, is developed and applied to the problem considered in this paper to derive the optimal policy and the corresponding optimal cost. An analysis of the effect of system parameters on the optimal policy as well as a comparison with analytical results known for the single site problem are also included in the paper.