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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 77-82.doi: 10.6040/j.issn.1671-9352.0.2019.914

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基于网络选址的设施系统可靠性

魏宗田1,方慧1,李银奎2   

  1. 1.西安建筑科技大学理学院, 陕西 西安 710055;2.青海民族大学数学与统计学院, 青海 西宁 810000
  • 出版日期:2020-10-20 发布日期:2020-10-07
  • 作者简介:魏宗田(1964— ),男,博士,教授,研究方向为图论、组合优化及其应用. E-mail:ztwei@xauat.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(1661066);青海省自然科学基金资助项目(2017ZJ701)

On the facility systems reliability based on network location

WEI Zong-tian1, FANG Hui1, LI Yin-kui2   

  1. 1. Department of Mathematics, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China;
    2. School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810000, Qinghai, China
  • Online:2020-10-20 Published:2020-10-07

摘要: 将设施系统的结构用网络表示,其中顶点代表服务设施或客户,边代表物品或信息的传输途径。设施系统的可靠性在很大程度上会受网络边失效的影响。为了度量此种情形下的设施系统可靠性,提出可行可靠度概念。基于集合覆盖问题、 p-中值问题和无容量限制固定费用选址问题建立一个综合选址模型,设计邻域搜索算法并求解一个实例。结果表明,在成本增加不多的情况下,考虑边失效情形可以明显提高设施系统的可靠性。

关键词: 设施选址, 网络, 可行可靠度, 边失效, 邻域搜索算法

Abstract: The structure of the facility system is represented by a network, where vertices represent service facilities or customers, and the edges represent the transmission channel of goods or information. The reliability of such a facility system is to a large degree adversely affected by the edge failures in the network. In order to measure the reliability of a network in this situation, a feasible reliability concept is proposed. Based on the three classical facility location problems, set covering location problem, p-median problem and uncapacitated fixed charge location problem, a comprehensive location model is established. A heuristic algorithm is designed for solving the discrete optimal problem. It is shown by an instance that the system reliability can be improved obviously with a little cost increase.

Key words: facility location, network, feasible reliability, edge failure, neighbor search algorithm

中图分类号: 

  • O157.5
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