Abstract: Given a metric space and some customers whose locations are known, facility location is to locate new facilities so that some target determined by new facilities and customers achieves the optimality. Continuous facility location is a type of important problem in location, where new facilities are located in some continuous area of the metric space. This paper focuses on reviewing the research work of models, methods and applications in continuous facility location field. Firstly, the paper discusses some important elements in continuous facility location including the number of new facilities, distance measuring function and objective function. Then several classical models and extended models of continuous facility location are introduced. This paper also briefly summaries common optimization methods and techniques for continuous facility location, including conjugate duality, global optimization, optimization under uncertainty, variational inequality and Voronoi diagrams. At last, the paper gives a few important applications and proposes some future research directions of continuous facility location.

Key words: continuous facility location, classical models, extended models, optimization methods, applications of facility location

摘要： 给定度量空间和该空间中的若干顾客,设施选址为在该度量空间中确定新设施的位置使得某种目标达到最优。连续设施选址是设施选址中的一类重要问题,其中的设施可在度量空间的某连续区域上进行选址。本文对连续设施选址的模型、算法和应用方面的工作进行了综述。文章首先讨论了连续设施选址中几个重要元素,包括新设施个数、距离度量函数、目标函数;然后介绍了连续选址中的几种经典模型和拓展模型;接着概述了求解连续选址问题的常用优化方法和技术,包括共轭对偶、全局优化、不确定优化、变分不等式方法、维诺图;最后介绍了连续设施选址的重要应用并给出了研究展望。

关键词: 连续设施选址, 经典模型, 拓展模型, 优化方法, 设施选址应用