Economic production quantity for a decaying item with stochastic demand and positive lead time

This paper considers a single-item, single-location production-inventory system subject to decay and random demand. Production occurs on a single machine at a constant and finite production rate. Shortages are allowed and partially backordered, while the other fraction of unmet demand is lost. A continuous review, lot size-reorder point policy is implemented to determine the size and the timing of production orders. The typical zero-lead time assumption made in existing economic production quantity models for a decaying inventory with random demand is relaxed here: when a production order is issued, a positive lead time is required before production starts. The long-run expected total cost per time unit is derived characterizing the stock dynamics as an Ito over bar diffusion. Several properties concerning the inventory dynamics and the cost function are demonstrated, and an optimization procedure that finds the optimal solution for the developed cost function is presented. Numerical experiments are carried out with a twofold objective: (i) to validate the inventory model through simulation, and (ii) to evaluate the model sensitivity with respect to variations in parameter values.