A Location-Arc Routing Problem (LARP) is a practical problem, while a few mathematical programming models have been considered for this problem. In this paper, a mixed non-linear programming model is presented for a multi-period LARP with the time windows under demand uncertainty. The time windows modeling in the arc routing problem is rarely. To the best our knowledge, it is the first time that the robust LARP model is verified and an optimal solution is presented for it. For this purpose, the CPLEX solver is used for solving the treasury location problems of a bank as a case study. These problems are node-based with close nods and can be transformed into arc-based. Therefore, the method LRP and LARP models can be used to solve these problems. The comparing results of the LRP and LARP models prove that the LARP has a better performance regarding timing and optimal solution. Furthermore, comparing the results of deterministic and robust LARP models for this case study shows the validity of the robust optimization approach.