An Approximation To The Stationary Distribution Of A Multidimensional Markov Process

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Abstract
In this paper we present an approximate, non-iterative method for calculating the stationary distribution of a multidimensional Markov process. Although the method has more general applications, we illustrate it for a particular example of a repairable item inventory model with returns. We analyze two versions of this model. In the first version we assume that all failed items are repairable, whereas in the second version we assume that some of the failed items are irreparable and hence are scrapped. Each version gives rise to multidimensional state spaces that are extremely large even for problems with a relatively small number of items. Because of the large state spaces, the emphasis of this paper is on developing an approximation for the stationary distribution. We show that this approximation is not only easy to calculate but is also quite accurate across a broad range of problem parameters.

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