摘要：在全球应对气候变化的背景下，低碳经济理念应运而生。物流业在低碳经济的发展中受到的影响越来越明显，同时物流业对国民经济的发展起着举足轻重的作用，因此发展低碳物流是十分必要的。物流线路优化问题一直是物流配送中的最基本问题之一，由于其应用的广泛性和明显的经济效益，一直受到国内外学者的广泛关注。因此在当前的经济发展中以低碳的视角来研究物流线路优化问题无疑具有重要的理论意义和实际意义。
本文首先分析了物流线路优化问题的研究背景以及研究现状并对现状进行了分析研究。接着介绍了物流线路优化问题的基本概念和物流线路优化问题的分类及构成要素，使得对物流线路优化问题有了整体的认识。然后着重介绍了碳足迹的基本概念以及计算碳排放量的公式，并将汽车碳排放量的计算公式引入VRP数学模型中，建立了一个以最小碳排放量为目标函数的改进VRP数学模型并对相关参数、函数进行了定义说明。最后对以最小碳排放量为目标函数的改进VRP数学模型进行了算法设计，并用Lingo软件编写了程序代码以分枝定界法对算例进行了求解和结果分析，得出了符合实际的结果。
关键字：碳足迹；物流线路优化问题；数学建模；分枝定界算法
Abstract：In the background of global climate change, low carbon economy concept came into our world. The low carbon economy receives more and more attention on the development of logistics industry .At the same time, the logistics industry plays an important role in the development of the national economy. It is very necessary to develop low carbon logistics. Vehicle routing problem has been a basic problem of logistics distribution, due to its extensive application and the benefit to economic, a wide of foreign scholars pay close attention to vehicle routing problem. Therefore, it has important theoretical significance and practical significance, if we can discuss vehicle routing problem from the perspective of low carbon in the present economic.
At first this paper analyzes the background of vehicle routing problem and the situation of research. Then it introduces logistics vehicle routing problem of the basic concepts classification and elements which makes the logistics vehicle routing problem with a whole understanding. Then mainly introduces the basic concept of carbon footprint and calculation formula of carbon emissions, the latter part of this paper introduced the car carbon emissions into the formula of the mathematical model of VRP, established a model of VRP with minimum carbon emissions as the objective function. Finally make a algorithm design of the VRP model with minimum carbon emissions as objective function , and write the program with Lingo software code to branch and bound method and analysis the result, it is concluded that the practical result.
Keywords: carbon footprint; vehicle routing problem; mathematical modeling;
Branch and bound
随着社会商业化和经济全球化的高度发展，许多服务商和物流商已经认识到物流线路优化的重要性。物流线路优化问题是物流组织的关键环节，如何选择合理有效的线路优化方案将对顾客的服务水平和配送成本产生直接的影响，物流线路优化的任务是以顾客需求分布和车辆相关数据为依据，以总费用最低、单位能耗产能最高为目标，选派车辆，设计运输工具、时间和线路的组合，确定每辆车的行驶线路和服务对象，追求经济和环境效益的最大化和实现过程的最优化。
本文提出的低碳经济视角下的物流线路优化设计模型和相关问题的评价研究对物流线路优化问题的研究起着积极的意义。在VRP数学模型的基础上增加了碳排放量的目标函数，设计出了改进后的优化模型，这对VRP的研究提出了更高的要求也拓宽了研究的视角。在即将被“碳交易”主宰的未来，以碳排放量作为目标函数的物流线路模型更加具有实用性，也更加直观的反映出能耗、成本等企业关注的问题。
