L~■-convexity and its applications in operations

作     者：Xin CHEN 

作者机构：Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign Changsha University of Science and Technology 

出 版 物：《Frontiers of Engineering Management》 (工程管理前沿（英文版）)

年 卷 期：2017年第4卷第3期

页      面：283-294页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 

基　　金：supported by National ScienceFoundation (NSF) Grants CMMI-1363261, CMMI-1538451, CMMI1635160 National Science Foundation of China (NSFC) Grants 71520107001 

主　　题：L■-convexity lattice programming perishable inventory models random capacity 

摘      要：L■-convexity, one of the central concepts in discrete convex analysis, receives significant attentions in the operations literature in recent years as it provides a powerful tool to derive structures of optimal policies and allows for efficient computational procedures. In this paper, we present a survey of key properties of L■-convexity and some closely related results in lattice programming, several of which were developed recently and motivated by operations applications. As a new contribution to the literature, we establish the relationship between a notion called m-differential monotonicity and L■-convexity. We then illustrate the techniques of applying L■-convexity through a detailed analysis of a perishable inventory model and a joint inventory and transshipment control model with random capacities.