A Series Expansion Approach to Risk Analysis of an Inventory System with Sourcing

In this paper we extend the series expansion approach for uni-chain Markov processes to a special case of finite multi-chains with possible transient states. We will show that multi-chain Markov models arise naturally in simple models such as a single item inventory system with sourcing, i.e., with the possibility to choose between different suppliers for replenishment. Numerical examples are provided to illustrate the performance of the series expansion algorithm to the risk analysis of this type of inventory systems.