Constraint programming-based solution approaches for three-dimensional loading capacitated vehicle routing problems

•Novel Constraint Programming (CP) models are proposed for the 3l-CVRP.•CP based decomposition models are more effective than the MIP model.•A hybrid CP model is proposed for large-size problems.•New best solutions are obtained for 36 benchmark instances. This paper presents constraint programming-based solution approaches for the three-dimensional loading capacitated vehicle routing problem (3l-CVRP) that consists of vehicle routing and three-dimensional loading problems in distribution logistics. Despite the practical benefits in the logistics world, the 3l-CVRP has not been extensively studied in the literature for its high combinatorial complexity. Therefore, we developed integrated and decomposed constraint programming-based solution methods in this study. The decomposed models outperformed the mixed-integer programming model proposed earlier in the literature for small-size problems. Furthermore, we solved the well-known benchmark problems with a decomposed model using constraint programming for the vehicle routing part of the problem and an evolutionary algorithm for the loading part. The computational study results show that the best-known results are improved in 36 of 93 problems.