Nested vs. Joint Optimization of Vehicle Routing Problems with Three-dimensional Loading Constraints

In the paper we examine a modification of the classical Vehicle Routing Problem (VRP) in which three-dimensional shapes of transported cargo are accounted for. This approach, in contrast to the standard capacitated VRP (CVRP) formulation, is appropriate when transported commodities are not perfectly divisible, but have fixed and heterogeneous dimensions. However, nesting a version of a three-dimensional Container Loading Problem (CLP) as a subproblem of the standard CVRP formulation adds a significant amount of optimization complexity. In this paper two approaches - a nested and a joint one - to solving the VRP with 3D loading constraints are proposed and compared on artificial test cases as well as on a real life case study.