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New mathematical models of the generalized vehicle routing problem and extensions

机译：广义车辆路径问题和扩展的新数学模型

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The generalized vehicle routing problem (GVRP) is an extension of the vehicle routing problem (VRP) and was introduced by Ghiani and Improta [1]. The GVRP is the problem of designing optimal delivery or collection routes from a given depot to a number of predefined, mutually exclusive and exhaustive node-sets (clusters) which includes exactly one node from each cluster, subject to capacity restrictions. The aim of this paper is to provide two new models of the GVRP based on integer programming. The first model, called the node formulation is similar to the Kara-Bektas. formulation [2], but produces a stronger lower bound. The second one, called the flow formulation, is completely new. We show as well that under specific circumstances the proposed models of the GVRP reduces to the well known routing problems. Finally, the GVRP is extended for the case in which the vertices of any cluster of each tour are contiguous. This case is defined as the clustered generalized vehicle routing problem and both of the proposed formulations of GVRP are adapted to clustered case.
机译：通用车辆路径问题（GVRP）是车辆路径问题（VRP）的扩展，由Ghiani和Improta提出[1]。 GVRP的问题是设计从给定仓库到许多预定义，互斥和穷举的节点集（群集）的最佳交付或收集路径，其中每个群集仅包含每个群集中的一个节点，并且受容量限制。本文的目的是提供两种基于整数编程的GVRP新模型。第一个模型称为节点公式，类似于Kara-Bektas。公式[2]，但产生更强的下界。第二个称为流程公式化，是全新的。我们还表明，在特定情况下，GVRP的建议模型可以减少众所周知的路由问题。最后，对于每个巡回线的任何聚类的顶点都是连续的情况，可以扩展GVRP。这种情况被定义为聚类的广义车辆路径问题，GVRP的两个拟议公式都适用于聚类的情况。

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