In this paper, we study three types of heterogeneous fixed fleet vehicle routing problems, which are capacitated vehicle routing problem, open vehicle routing problem and split delivery vehicle routing problem. We propose new multiobjective linear binary and mixed integer programming models for these problems, where the first objective is the minimization of a total routing and usage costs for vehicles, and the second one is the vehicle type minimization, respectively. The proposed mathematical models are all illustrated on test problems, which are investigated in two groups: small-sized problems and the large-sized ones. The small-sized test problems are first scalarized by using the weighted sum scalarization method, and then GAMS software is used to compute efficient solutions. The large-sized test problems are solved by utilizing the tabu search algorithm.

中文翻译：

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异构固定车队车辆路径问题的多目标数学模型和求解方法

在本文中，我们研究了三种类型的异构固定车队车辆选路问题，分别是容量车辆选路问题，开放式车辆选路问题和分离式交付车辆选路问题。针对这些问题，我们提出了新的多目标线性二进制和混合整数规划模型，其中第一个目标是最小化车辆的总行驶路线和使用成本，第二个目标是最小化车辆类型。所提出的数学模型都说明了测试问题，将其分为两组：小型问题和大型问题。首先使用加权和标量方法对小型测试问题进行标量，然后使用GAMS软件计算有效的解决方案。