文献类型：期刊文献

英文题名：Distance constrained vehicle routing problem to minimize the total cost: algorithms and complexity

作者：Yu, Wei[1];Liu, Zhaohui[1];Bao, Xiaoguang[2]

机构：[1]East China Univ Sci & Technol, Dept Math, 130 Meilong Rd, Shanghai 200237, Peoples R China;[2]Shanghai Ocean Univ, Coll Informat Technol, 999 Huchenghuan Rd, Shanghai 201306, Peoples R China

年份：2022

卷号：43

期号：5

起止页码：1405

外文期刊名：JOURNAL OF COMBINATORIAL OPTIMIZATION

收录：;EI(收录号：20204609484097);WOS:【SCI-EXPANDED(收录号:WOS:000588237400001)】；

基金：We are grateful to the anonymous referees for their valuable and constructive comments. This research is supported by the National Natural Science Foundation of China under Grants Numbers 11671135, 11871213, 11701363, the Natural Science Foundation of Shanghai under Grant Number 19ZR1411800 and the Fundamental Research Fund for the Central Universities under Grant Number 22220184028.

语种：英文

外文关键词：Vehicle routing; Cycle cover; Path cover; Approximation algorithm; Complexity; Integrality gap

摘要：Given lambda > 0, an undirected complete graph G = (V, E) with nonnegative edge-weight function obeying the triangle inequality and a depot vertex r is an element of V, a set {C-1,..., C-k} of cycles is called a lambda-bounded r -cycle cover if V subset of boolean OR(k)(i=1) V(C-i) and each cycle (C)i contains r and has a length of at most lambda. The Distance Constrained Vehicle Routing Problem with the objective of minimizing the total cost (DVRP-TC) aims to find a lambda-bounded r -cycle cover {C-1,..., C-k} such that the sum of the total length of the cycles and gamma k is minimized, where. is an input indicating the assignment cost of a single cycle. For DVRP-TC on tree metric, we show a 2-approximation algorithm and give an LP relaxation whose integrality gap lies in the interval [2, 5/2]. For the unrooted version of DVRP-TC, we devise a 5-approximation algorithm and give an LP relaxation whose integrality gap is between 2 and 25. For unrooted DVRP-TC on tree metric we develop a 3-approximation algorithm. For unrooted DVRP-TC on line metric we obtain an O(n(3)) time exact algorithm, where n is the number of vertices. Moreover, we give some examples to demonstrate that our results can also be applied to the path-version of (unrooted) DVRP-TC.