A two phase hybrid method to support 2D and 3D vehicle loading

In this work we deal with a vehicle loading problem where a heterogeneous fleet of vehicles must be loaded with a set of items. Differently from the traditional vehicle loading problems, there is also a set of optional items that may be loaded in order to maximize the used capacity of the selected vehicles. The problem is decomposed in two subproblems: i) selection; ii) packing. In the former subproblem vehicles and items (including optional items) are chosen for the weekly delivery. In the latter the items selected for each vehicle are packed in the vehicle. We propose an integer programming formulation to solve the selection subproblem and an evolutionary algorithm for the packing subproblem. They work cooperatively, the solution of each one depending on the solution of the other one. We show the results for several instances, and also compare the results for instances of the literature without optional items, showing that although proposed to this specific problem, the method is general enough to compete with the best methods in other packing problems.integer programming formulation