Technical Note—Preservation of Quasi-K-Concavity and Its Applications

Xin Chen · Yuhan Zhang · Sean X. Zhou

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Supply Chain and Inventory Management Advanced Queuing Theory Analysis Optimization and Search Problems

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.

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References

1960MATHEMATICAL METHODS IN THE SOCIAL SCIENCES, 1959 2002Foundations of Stochastic Inventory Theory 2005The Optimality of (S,s) Policies in the Dynamic Inventory Problem 2004Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case 2004Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case 2005Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales 2012Pricing and Inventory Management 1971On the Optimality of Generalized (s, S) Policies

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2014Inventory Control with a Fixed Cost and a Piecewise Linear Convex Cost 2018Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs 2021The joint stochastic lot sizing and pricing problem

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