Production planning for a deteriorating item with stochastic demand and consumer choice

This paper concerns inventory control of a deteriorating product with non-negligible procurement lead-time that perishes after a known number of periods. Demand for fresh products during each period is represented as a random variable with known probability distribution, but only a fraction of this demand is satisfied during any given period due to item deterioration. We derive the expected profit function for a two-period problem with one production opportunity before the selling season begins and a single product type with two-period shelf life. For the case in which demand during both periods is uniform, independent, and identically distributed, we identify sufficient conditions for the existence of an optimal solution and present a straightforward procedure for obtaining the solution.