This paper deals with a robust location-arc routing problem with uncertainty on demand and traversing cost parameters. In this regard, a deterministic mathematical model is presented inspired by those available in the related literature and then, a robust optimization approach is used to deal with uncertainty. Due to the complexity of the deterministic and uncertain mathematical models, this paper finds the lower and upper bounds of the solutions to estimate a suitable range in which the optimum values exist. The lower and upper bounds are obtained by modifying the developed mathematical models and developing a two-phase heuristic algorithm, respectively. Furthermore, three single-solution-based meta-heuristics, called hill climbing, late acceptance hill climbing, and Tabu search are employed to enhance the upper bounds. According to the robust optimization approach, the paper on hand proposes a manual sorting method to approximate the value of uncertain parameters to be used in the heuristics and meta-heuristics. Finally, the paper evaluates the models, manually sorting method, heuristic, and meta-heuristic algorithms using some numerical examples and finds that all of them works appropriately.

本文讨论了一个鲁棒的位置弧路由问题，该问题具有需求不确定性和遍历成本参数。在这方面，受相关文献中可用的启发，提出了确定性数学模型，然后，使用鲁棒的优化方法来处理不确定性。由于确定性和不确定性数学模型的复杂性，本文找到了解决方案的上下界，以估计存在最佳值的合适范围。下限和上限分别通过修改开发的数学模型和开发两阶段启发式算法来获得。此外，采用了三种基于单解的元启发式方法，分别称为爬山，后期验收爬山和禁忌搜索，以提高上限。根据稳健的优化方法，本文提出了一种手动排序方法，以近似估计要在启发式和元启发式中使用的不确定参数的值。最后，本文使用一些数值示例对模型，人工排序方法，启发式算法和元启发式算法进行了评估，发现它们都可以正常工作。