عنوان مقاله [English]
In location-arc routing problems, unlike the well-known locating-routing problems, demand is on the arc and using deadheading arcs is permitted. Few studies have focused on this issue. In this research, a three-objective complex linear mathematical model for the multi-period location-arc routing problem under uncertainty with the time window is presented. The objectives of the model are included in the minimization of cost, cash-in-transit, and vehicle waiting time. The time window, minimizing cash-in-transit, and definition threshold for routes risk based on safety indicators, reduces the transportation risk indirectly. The proposed model is based on Bertsimas and Sim model and the ε-constraint method is used to solve 22 standard problems based on the proposed model. In addition, the robust model is validated with the realization model. The results show that the robust model versus deterministic model has better performs at higher conservatism levels and increases the uncertainty at each level of conservatism leading to higher costs.