Heuristics for the lexicographic max-ordering vehicle routing problem

In this paper, we propose fast heuristics for the vehicle routing problem (VRP) with lexicographic max-order objective. A fixed number of vehicles, which are based at a depot, are to serve customers with known demands. The lexicographic max-order objective is introduced by asking to minimize lexicographically the sorted route lengths. Based on a model for this problem, several approaches are studied and new heuristic solution procedures are discussed resulting in the development of a sequential insertion heuristic and a modified savings algorithm in several variants. Comparisons between the algorithms are performed on instances of the VRP library VRPLIB. Finally, based on the results from the computational experiments, conclusions about the applicability and efficiency of the presented algorithms are drawn.