A new perspective on inventory systems

In this article a single item inventory model with backlogging is analyzed, which is a generalization of the most well-known simple models. This formulation enables us to separate the analysis of the system to the analysis of the control rule (reduced to the analysis of a Markov chain) and of the time stationary distribution for the arrival process of customers. This facilitates a much better understanding of such systems. A simple sample path argument enables a straightforward derivation of average holding costs, ordering costs, services measures. A recently developed algorithm of Laplace transform inversion technique provides us with an efficient tool for the computation of these cost expressions.