Higher-Order Approximations for the Perishable-Inventory Problem

Computation of an optimal policy for ordering a perishable commodity with a fixed lifetime of m periods requires the solution of a dynamic program whose state variable has dimension m − 1. Unless m is small, the computations quickly become unreasonable. By bounding the expected outdating function and using an approximate transfer function, we obtain an approximation of the original problem that can be computed as if the lifetime were r < m periods. When r = 2, it is demonstrated under reasonable assumptions that the appropriate function to be minimized each period is quasi-convex. We include computations that compare this approximation to both the optimal policy and a critical number approximation.