Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems

•We propose a new Branch-Cut-and-Price algorithm for heterogeneous vehicle routing.•The same algorithm can also solve multi-depot and site-dependent vehicle routing.•Techniques from previous works are combined and improved.•Experiments show that many instances with 200 customers can now be solved.•A new set of 100 benchmark instances is proposed. This paper considers a family of Vehicle Routing Problem (VRP) variants that generalize the classical Capacitated VRP by taking into account the possibility that vehicles differ by capacity, costs, depot allocation, or even by the subset of customers that they can visit. This work proposes a Branch-Cut-and-Price algorithm that adapts advanced features found in the best performing exact algorithms for homogeneous fleet VRPs. The original contributions include: (i) the use of Extended Capacity Cuts, defined over a pseudo-polynomially large extended formulation, together with Rank-1 Cuts, defined over the Set Partitioning Formulation; (ii) the concept of vehicle-type dependent memory for Rank-1 Cuts; and (iii) a new family of lifted Extended Capacity Cuts that takes advantage of the vehicle-type dependent route enumeration. The algorithm was extensively tested in instances of the literature and was shown to be significantly better than previous exact algorithms, finding optimal solutions for many instances with up to 200 customers and also for some larger instances. A new set of benchmark instances is also proposed.