Abstract
A base-stock inventory system for perishables with Markovian demand and general lead-time and lifetime distributions is investigated. Using a queueing network model, we derive explicit expressions of the stationary distribution of the inventory state together with the total expected cost in a base-stock system with lost-sales. Next, we show some monotonicity properties of the cost function and propose a procedure to derive the optimal base-stock. Extensions to the backorders case and to a dual-sourcing system with multiple warehouses are also provided. Our results generalize existing ones from the literature where the lifetime and the lead-time follow either deterministic or exponential distributions. Finally, we investigate the effect of the lifetime and lead-time variability on the system cost and the optimal base-stock level. In particular, we show the substantial errors made when assuming deterministic or exponential distributions for the lifetime. This further shows the need to have results beyond exponential or deterministic assumptions.
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