Discrete Convex Analysis and Its Applications in Operations: A Survey

• 成果类型: Article
• 署名作者: Chen, Xin; Li, Menglong
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: PRODUCTION AND OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1059-1478
• DOI: 10.1111/poms.13234
• 发表日期: 2021
• 页码: 1904-1926
• 关键词: discrete convexity; Inventory management; Appointment Scheduling; bike sharing

摘要

Discrete convexity, in particular,L-convexity andM-convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely,L-convexity andM-convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much more simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.