A robust location-arc routing problem under uncertainty: mathematical model with lower and upper bounds

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.