Abstract We study a generalization of the Skill VRP that incorporates time windows aspects, precedence and synchronization constraints. Specifically, we are given a logistic network where nodes correspond to customers, and where each customer requires a set of (partially ordered) operations. A set of technicians is available to perform such operations, and each technician is qualified to execute only a subset of them, depending on his skill. By referring to a specific context such as Health Care, customers are patients while technicians are caregivers. In a Field Service context, instead, customers are usually referred to as clients while technicians as field technicians. The innovative aspect is that some operations may require a special device, which must be transported at the customer site and must be present at the customer location together with a technician qualified to use it. Given technician dependent traveling costs, we address the problem of defining the tours for the technicians and for the special device, while respecting the skill compatibility between customers and technicians, and the time windows, precedence and synchronization constraints. We propose a Mixed Integer Linear Programming (MILP) model for the generalized Skill VRP, and present some lower bounding techniques based on the proposed formulation. Preliminary computational experiments show that some lower bounding techniques may rapidly produce good lower bounds, thanks to quite effective valid inequalities. The returned percentage optimality gaps, estimated also thanks to a simple matheuristic, are in fact quite small for several scenarios of medium to large size, by encouraging the use of the proposed lower bounding techniques both as building blocks for designing exact approaches, and also as valuable tools to evaluate the efficacy of more sophisticated heuristic approaches to the problem.

中文翻译：

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Skill VRP 的时间限制和设备管理：数学模型和下限技术

摘要 我们研究了包含时间窗口方面、优先级和同步约束的技能 VRP 的概括。具体来说，我们给出了一个物流网络，其中节点对应于客户，每个客户都需要一组（部分有序的）操作。一组技术人员可用于执行此类操作，并且每个技术人员都有资格执行其中的一部分，具体取决于他的技能。通过引用特定的上下文（例如医疗保健），客户是患者，而技术人员是护理人员。相反，在现场服务上下文中，客户通常称为客户，而技术人员称为现场技术人员。创新的方面是一些操作可能需要特殊的设备，必须在客户现场运输，并且必须与有资格使用它的技术人员一起出现在客户地点。考虑到技术人员相关的差旅成本，我们解决了为技术人员和特殊设备定义行程的问题，同时尊重客户和技术人员之间的技能兼容性，以及时间窗口、优先级和同步限制。我们为广义技能 VRP 提出了混合整数线性规划 (MILP) 模型，并基于所提出的公式提出了一些下界技术。初步的计算实验表明，由于非常有效的有效不等式，一些下界技术可能会迅速产生良好的下界。返回的百分比最优差距，估计也归功于一个简单的数学，