段凤华

(湖南科技大学商学院，中国 湘潭　411000)

带碳费约束的同时取送车辆路径问题研究

段凤华*

(湖南科技大学商学院，中国 湘潭411000)

摘要在基本车辆路径问题基础上增加“同时取送”、“时间窗”与“碳费”三个约束条件，发展为带碳费约束的有软时间窗同时取送车辆路径问题．建立了相应的数学模型，设计了以Or-opt为邻域结构、增加碳费惩罚机制的禁忌搜索算法对模型求解．通过与相关文献进行比较，显示了禁忌搜索算法搜索速度和寻优能力的优越性．物流企业若能采用以较好算法开发的车辆调度软件，将能削减其碳费，提升自身经济效益和社会效益．

关键词车辆路径问题；同时取送货；软时窗；碳费；禁忌搜索

The Simultaneous Pick-up and Delivery VRP with Carbon Emissions Fee

DUANFeng-hua*

(School of Business, University of Science and Technology, Xiangtan 411000, China)

AbstractAdding simultaneous pick-up and delivery, soft time windows and carbon emissions constraints, the corresponding mathematical model is established to solve the basic vehicle routing problem, and the tabu search (TS) algorithm is designed to solve the problem based on Or-opt for the neighborhood structure and evaluation mechanisms with carbon emissions fee. Compared with relevant literatures, the TS is proved to be superior in speed and optimization capabilities. If logistics enterprises use good algorithm to develop scheduling software, the carbon emissions will be reduced and the economic and social benefits will be upgraded.

Key wordsvehicle routing problem; simultaneous pick-up and delivery; soft time windows; carbon emissions fee; tabu search

在物流配送活动中，同时取送货现象广泛存在，如快递业，既要将快件、包裹送给客户，又要从客户处带回需要寄出的快件或包裹；啤酒行业，销售商需要用车辆将啤酒产品送到客户处，可能同时又需要回收空瓶等等．另一方面，大量车辆行驶在路上，汽车尾气排放过多，已成为全球空气污染加重、特别是诸多地方雾霾弥漫的重要原因．一般而言，在车辆排量既定、路况相似的情况下，运输距离是影响油耗的最主要因素，而油耗是决定车辆碳排放量的关键因素，因此，本文将车辆运输距离转化为碳排放量，进而转化为碳费．在安排车辆行驶线路时，同时考虑碳费，以兼顾配送成本最小化和减少环境破坏，具有理论价值和现实意义．

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