<b>Technical Note</b>—Preservation of Quasi-<i>K</i>-Concavity and Its Applications

Abstract

In this paper, we establish a new preservation property of quasi-K-concavity under certain optimization operations. One important application of the result is to analyze joint inventory-pricing models for single-product periodic-review inventory systems with concave ordering costs. At each period, an ordering quantity and a selling price of the product are determined simultaneously. Demand is random but sensitive to the price. The objective is to maximize the total expected discounted profit over a finite planning horizon. Assuming that demand is a deterministic function of the selling price plus a random perturbation with a positive Pólya or uniform distribution, we show that a generalized (s, S, p) policy is optimal.