The convergence of Gallego's iterative method for distribution-free inventory models

Abstract

For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.