This paper introduces the heterogeneous vehicle routing problem with time windows and a limited number of resources (HVRPTW-LR), a practical extension of the classical vehicle routing problem in which routes to be designed share common scarce resources. The HVRPTW-LR arises when a limited number of resources, such as vehicles, drivers, instruments, and so on, are available but are insufficient to serve all customers in a route planning. Therefore, the route design involves the selection of customers to be visited at each route and resources to be used. Applications to this problem are found in real services companies with high seasonal demand which attend to different types of works and have to decide on how to effectively manage their resources. For designing optimal routes, a hierarchical objective function is considered, maximizing the total number of served customers as the primary objective, and minimizing the travel costs as secondary. A mathematical model of linear programming is introduced to describe and understand all constraints clearly. The problem is first heuristically solved by a semi-parallel insertion heuristic. Then, solutions are improved by a hybrid variable neighborhood descent metaheuristic based on a Tabu Search algorithm for the exploration of the neighborhood and a holding list. Experiments are conducted on numerous sets of benchmark instances from the literature to evaluate the performance of the proposed algorithm. Results show that the algorithm proposed in this paper has a good performance and can be easily applied for solving numerous vehicle routing problem variants from the literature. A new set of benchmark cases for the HVRPTW-LR are also presented and solved.

本文介绍了具有时间窗和有限数量资源的异构车辆路径问题（HVRPTW-LR），这是经典车辆路径问题的实际扩展，其中要设计的路径共享公共稀缺资源。HVRPTW-LR在有限的资源（例如车辆，驾驶员，仪表等）可用但不足以在路线规划中为所有客户提供服务时出现。因此，路线设计涉及选择每个路线上要拜访的客户以及要使用的资源。在季节性需求较高的真实服务公司中发现了此问题的应用，这些公司参加了不同类型的工作，并且必须决定如何有效地管理其资源。在设计最佳路线时，要考虑分层目标函数，首要目标是最大程度地提高服务客户总数，次要目的是使差旅成本最小化。引入了线性规划的数学模型来清楚地描述和理解所有约束。首先通过半平行插入启发式启发式解决该问题。然后，通过基于禁忌搜索算法的混合变量邻域下降元启发式算法对邻域和保持列表进行探索，从而改进了解决方案。从文献中对许多基准实例集进行了实验，以评估所提出算法的性能。结果表明，本文提出的算法具有良好的性能，可以很容易地应用于解决文献中众多车辆路径问题的变体。