We consider an order up to level policy for perishable items with random lifetime. We investigate two cases: the first one is the case where excess demand is completely lost and the second one deals with full backorders. Demands arrive according to a Poisson process. The lifetime of each item is assumed to be exponentially distributed and the procurement lead time is constant. We also assume that there is at most one outstanding order at any time. We model this inventory system as a Markov process in which stationary regime can be characterised. This model allows us to get insights on the impact of the model parameters on the overall system performance in terms of costs.
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Kouki et al. (2013) studied this question.