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Preservation of quasi-\(K\)-concavity and its applications. (English) Zbl 1231.90020
Summary: 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.

90B05 Inventory, storage, reservoirs
90C26 Nonconvex programming, global optimization
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