A branch-and-price algorithm for the vehicle routing problem with 2-dimensional loading constraints

Abstract

In this paper, we describe a branch-and-price algorithm for the capacitated vehicle routing problem with 2-dimensional loading constraints and a virtually unlimited number of vehicles. The column generation subproblem is solved heuristically through variable neighborhood search. Branch-and-price is used when it is not possible to add more attractive columns to the current restricted master problem, and the solution remains fractional. In order to accelerate the convergence of the algorithm, a family of valid dual inequalities is presented. Computational results are provided to evaluate the performance of the algorithm and to compare the different branching strategies proposed.