A Branch-Cut-and-Price Approach for the Single-Trip and Multi-Trip Two-Echelon Vehicle Routing Problem with Time Windows

车辆路径问题 数学优化 整数规划 计算机科学 分支机构和价格 TRIPS体系结构 布线(电子设计自动化) 合并(业务) 列生成 分支和切割 运筹学 调度(生产过程) 数学 经济 会计 并行计算 计算机网络
作者
Guillaume Marquès,Ruslan Sadykov,Rémy Dupas,Rémy Dupas
出处
期刊:Transportation Science [Institute for Operations Research and the Management Sciences]
卷期号:56 (6): 1598-1617 被引量:26
标识
DOI:10.1287/trsc.2022.1136
摘要

The paper studies the two-echelon capacitated vehicle routing problem with time windows, in which delivery of freight from depots to customers is performed using intermediate facilities called satellites. We consider the variant of the problem with precedence constraints for unloading and loading freight at satellites. In this variant allows for storage and consolidation of freight at satellites. Thus, the total transportation cost may decrease in comparison with the alternative variant with exact freight synchronization at satellites. We suggest a mixed integer programming formulation for the problem with an exponential number of route variables and an exponential number of precedence constraints that link first-echelon and second-echelon routes. Routes at the second echelon connecting satellites and clients may consist of multiple trips and visit several satellites. A branch-cut-and-price algorithm is proposed to solve efficiently the problem. This is the first exact algorithm in the literature for the multi-trip variant of the problem. We also present a postprocessing procedure to check whether the solution can be transformed to avoid freight consolidation and storage without increasing its transportation cost. It is shown that all single-trip literature instances solved to optimality admit optimal solutions of the same cost for both variants of the problem either with precedence constraints or with exact synchronization constraints. Experimental results reveal that our algorithm can be used to solve these instances significantly faster than another recent approach proposed in the literature.
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