Discrete Convex Analysis and Its Applications in Operations: A Survey
Discrete Convex Analysis and Its Applications in Operations: A Survey
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DOI：
10.1111/poms.13234
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发表时间：
2019-12
影响因子：
5
通讯作者：
Xin Chen;Menglong Li
中科院分区：
文献类型：
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作者：
Xin Chen;Menglong Li
离散凸性，特别是L - vii - vii和M - vii - vii，提供了一个关键的开放来攻击库存理论中的几个经典问题，以及许多其他操作问题，这些问题来自最近的实践，例如，预约调度和自行车共享。作为一个强大的框架，离散凸分析在文献中越来越受欢迎。本文将对该方法的概况进行综述。我们首先介绍几个关键概念，即L -凸性和M -凸性及其变体，然后讨论对研究操作模型最有用的一些基本性质。然后我们说明这些概念和属性的各种应用。例子包括网络流问题、随机库存控制、预约调度、博弈论、投资组合契约、离散选择模型和共享单车。我们的讨论重点是展示离散凸分析如何对现有问题提供新的见解，和/或带来比文献中先前方法更简单的分析和算法开发。我们还提出了一些新的研究结果和分析。
Discrete convexity, in particular, L ♮ ‐convexity and M ♮ ‐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 and M ♮ ‐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.