The probabilistic uncapacitated open vehicle routing location problem

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Networks Pub Date : 2023-04-06 DOI:10.1002/net.22147

I. Averbakh, Wei Yu

引用次数: 0

Abstract

Suppose that m$$ m $$ mobile service units are located at a base station (depot) in a transportation network with n$$ n $$ nodes. On any day, the nodes of the network may generate calls for service independently with known probabilities. The calls are centrally allocated to the service units who then visit the allocated customers on shortest open tours, that is, for each service unit, the way back to the depot from the last served customer is not counted towards the length of the tour. It is required to find an optimal location for the depot to minimize the expected travel distance. We obtain bounds on the approximation ratios for two simple and fast heuristics for the problem on a general network. For the problem on a tree, we present an O(nm+1)$$ O\left({n}^{m+1}\right) $$ exact algorithm.

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概率无能力开放车辆路径定位问题

假设m$$m$$移动服务单元位于具有n$$n$$节点的交通网络中的基站（仓库）。在任何一天，网络的节点都可以以已知的概率独立地生成服务呼叫。呼叫被集中分配给服务单元，然后服务单元在最短的开放行程中访问分配的客户，也就是说，对于每个服务单元，从最后服务的客户返回仓库的路不计入行程长度。需要为车辆段找到一个最佳位置，以最大限度地缩短预期的行驶距离。对于一般网络上的问题，我们得到了两个简单快速启发式算法的近似比的界。对于树上的问题，我们提出了一个O（nm+1）$$O\left（｛n｝^｛m+1｝\right）$$精确算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.