S-Convexity and Gross Substitutability

• 成果类型: Article
• 署名作者: Chen, Xin; Li, Menglong
• 署名单位: University System of Georgia; Georgia Institute of Technology; City University of Hong Kong
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2394
• 发表日期: 2024
• 页码: 1242-1254
• 关键词: transshipment control; inventory policies; joint inventory; equilibrium; models; management; polyhedra

摘要

We propose a new concept of S-convex functions (and its variant, semi strictly quasi -S-(SSQS)-convex functions) to study substitute structures in economics and operations models with continuous variables. We develop a host of fundamental properties and characterizations of S-convex functions, including various preservation properties, conjugate relationships with submodular and convex functions, and characterizations using Hessians. For a divisible market, we show that the utility function satisfies gross substitutability if and only if it is S-concave under mild regularity conditions. In a parametric maximization model with a box constraint, we show that the set of optimal solutions is nonincreasing in the parameters if the objective function is (SSQS-) S-concave. Furthermore, we prove that S-convexity is necessary for the property of nonincreasing optimal solutions under some conditions. Our monotonicity result is applied to analyze two notable inventory models: a single-product inventory model with multiple unreliable suppliers and a classic multiproduct dynamic inventory model with lost sales.