In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be linked by means of a given graph structure (provided that two facilities are allowed to be linked if a given distance is not exceed). We propose a mathematical programming framework for the problem and different resolution strategies. First, we provide a Mixed Integer Non Linear Programming formulation for the problem and derive some geometrical properties that allow us to reformulate it as an equivalent pure integer linear programming problem. We propose two branch-&-cut approaches by relaxing some sets of constraints of the former formulation. We also develop a math-heuristic algorithm for the problem capable to solve instances of larger sizes. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.

在本文中，我们分析了最大覆盖位置问题的连续版本，其中要求通过给定的图结构链接设施（前提是如果给定距离不超过两个设施，则允许链接两个设施）。我们针对该问题和不同的解决方案策略提出了一个数学编程框架。首先，我们为问题提供了混合整数非线性规划公式，并推导了一些几何性质，使我们可以将其重新构造为等效的纯整数线性规划问题。我们通过放宽对前一个公式的某些约束集，提出了两种“切分法”方法。我们还针对能够解决较大尺寸实例的问题开发了一种数学启发式算法。