In this paper, we develop an economic order quantity (EOQ) model for fixed shelf-life items and a non-increasing demand. The objective of this model is to maximize the total profit. We find the criterion to decide (i) the interior maximum solution or (ii) the boundary maximum solution. Eight numerical examples are given to illustrate all possible scenarios of this generalized model. Our results identify a scenario for which the maximum profit is always negative. This is highly relevant for firms in the public sector operating at a financial loss.

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.