A state-dependent perishability (s, S) inventory model with random batch demands

We consider continuous-review perishable inventory models with random lead times and state-dependent Poisson demand. The paper revises an earlier work of Barron and Baron (IISE Trans 1-52, 2019). While the former studies unit Poisson demands, this paper deals with demand uncertainty and allows for random batch demands. We conduct a comprehensive analysis of two main models that have different lead times and perish times under backorders or lost sales. Thus, our models can be applied to many industries, in situations where the system is subject to random perishability, random lead time, and demand uncertainty. With a probabilistic approach, we derive a long-run average cost function under the (S, s) replenishment policy. Numerical examples are used to demonstrate the impact of changing batch size and other system parameters on the optimal policy. Our numerical study indicates that, although the Markovian policy can be used as a good approximation of the average total cost, it performs better for a general perish time. We further show that the optimal cost may differ for a different average batch size, while the batch variability seems to provide some robustness.