A mathematical model for the capacitated location-arc routing problem with deadlines and heterogeneous fleet

This paper considers a Capacitated Location-Arc Routing Problem (CLARP) with Deadlines (CLARPD) and a fleet of capacitated heterogeneous vehicles. The proposed mixed integer programming model determines a subset of potential depots to be opened, the served roads within predefined deadlines, and the vehicles assigned to each open depot. In addition, efficient routing plans are determined to minimize total establishment and traveling costs. Since the CLARP is NP-hard, a Genetic Algorithm (GA) is presented to consider proposed operators, and a constructive heuristic to generate initial solutions. In addition, a Simulated Annealing (SA) algorithm is investigated to compare the performance of the GA. Computational experiments are carried out for several test instances. The computational results show that the proposed GA is promising. Finally, sensitivity analysis confirms that the developed model can meet arc routing timing requirements more precisely compared to the classical Capacitated Arc Routing Problem (CARP).