Branch-and-price and heuristic column generation for the generalized truck-and-trailer routing problem

The generalized truck-and-trailer routing problem (GTTRP) constitutes a uni¯ed model for vehicle routing problems with trailers and a fixed lorry-trailer assignment. The GTTRP is a generalization of the truck-and-trailer routing problem (TTRP), which itself is an extension of the well-known vehicle routing problem (VRP). In the GTTRP, the vehicle fleet consists of single lorries and lorry-trailer combinations. Some customers may be visited only by a single lorry or by a lorry without its trailer, some may also be visited by a lorry-trailer combination. In addition to the customer locations, there is another relevant type of location, called transshipment location, where trailers can be parked and where a load transfer from a lorry to its trailer can be performed. In this paper, two mixed-integer programming (MIP) formulations for the GTTRP are presented. Moreover, an exact solution procedure for the problem, a branch-and-price algorithm, and heuristic variants of this algorithm are described. Computational experiments with the algorithms are presented and discussed. The experiments are performed on randomly generated instances structured to resemble real-world situations and on TTRP benchmark instances from the literature. The results of the experiments show that instances of realistic structure and size can be solved in short time and with high solution quality by a heuristic algorithm based on column generation.