Optimization of maintenance services of a company working in the gas metering sector is investigated. In particular, daily tasks of operators are optimized by exploiting the paradigm of vehicle routing problems with a set of predefined time windows that overlap one with the others and four competing objectives to take into account. First, an exact integer formulation is presented that can be solved only for a reduced number of customer sites to visit. Then, a heuristic approach is proposed to find approximate solutions with huge savings on the computational effort, also for high-dimensional instances. Numerical results on both real and synthetic scenarios showcase the effectiveness of the approach.

中文翻译：

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燃气计量维护服务的优化：具有一组预定义重叠时间窗口的多目标车辆路线问题

对一家在燃气计量行业工作的公司的维护服务优化进行了调查。特别是，操作员的日常任务通过利用具有一组预定义时间窗口的车辆路径问题范式来优化，这些时间窗口彼此重叠，并且要考虑四个竞争目标。首先，提出了一个精确的整数公式，它只能在访问的客户站点数量减少时才能解决。然后，提出了一种启发式方法来寻找近似解，同时极大地节省计算量，也适用于高维实例。真实和合成场景的数值结果展示了该方法的有效性。