Myopic Approximations for the Perishable Inventory Problem

Abstract

Recent work in describing optimal ordering policies for perishable inventory casts the problem as a multi-dimensional dynamic program, the dimensionality being one less than the useful lifetime of the product, m. As m becomes large the computational problem becomes severe so that developing approximations is a key problem. A bound on the perishing cost is obtained that is a function only of the total inventory on hand. Substituting this bound and an approximate transfer function, optimal policies can be computed myopically for the new problem. When the demand density possesses a monotone likelihood ratio, it is shown the function to be minimized is strictly pseudo-convex. Sample computations for special cases indicate that the approximation results in costs which are generally less than one percent higher than the optimal.