A branch-and-price algorithm for the heterogeneous fleet green vehicle routing problem with time windows

Heterogeneous fleet vehicles can be used to reduce carbon emissions. We propose an improved branch-and-price (BAP) algorithm to precisely solve the heterogeneous fleet green vehicle routing problem with time windows (HFGVRPTW). In the improved BAP, to speed up the solution for the pricing problem, we develop a multi-vehicle approximate dynamic programming (MVADP) algorithm that is based on the labeling algorithm. The MVADP algorithm reduces labels by integrating the calculation of pricing problems for all vehicle types. In addition, to rapidly obtain a tighter upper bound, we propose an integer branch method. For each branch, we solve the master problem with the integer constraint by the CPLEX solver using the columns produced by column generation. We retain the smaller of the obtained integer solution and the current upper bound, and the branches are thus reduced significantly. Extensive computational experiments were performed on the Solomon benchmark instances. The results show that the branches and computational time were reduced significantly by the improved BAP algorithm. (C) 2019 Elsevier Ltd. All rights reserved.