Ingénierie et gestion industrielles

Distribution of Inventory Level on a Repairable Parts System under Performance-Based Contract

Abstract

Liu Jiliang, Liu Mingwu, Feng Mengying and Zhang Xu

Mirzahosseinian develop a closed-loop inventory system consisting of a repair facility and a single warehouse, for a repairable parts system operating under a Performance-Based Logistics contract. They model the closed-loop inventory system as a multi-server queueing model (M/M/m queue) where component failures follow Poisson distribution and the repair times at the service facility are exponential. The model sets up the balance equations of the steady-state probability distribution of inventory level. This paper extends their model. A recursive method is utilized and an analytic steady-state probability distribution of inventory level is derived. It also demonstrates by numerical experiments that the analytic steady-state probability distribution is correct. We obtain the analytic system performances and the metrics, which contribute to system cost optimization.