Solving the battery swap station location-routing problem with a mixed fleet of electric and conventional vehicles using a heuristic branch-and-price algorithm with an adaptive selection scheme

In this paper, a battery swap station location and routing problem with time windows and a mixed fleet of electric and conventional vehicles (BSS-MF-LRPTW) is proposed. This problem is motivated by a real-life logistics application by extending the existing electric vehicle battery swap stations location routing problem (BSS-EV-LRP). The BSS-MF-LRPTW aims to simultaneously determine the locations of battery swap stations (BSSs) and the routing plan of a mixed fleet under the driving range, the load capacity limitation, and time windows. An integer programming (IP) model is developed for the proposed BSS-MF-LRPTW. As there are a large number of variables and complicating constraints of the IP model, we break it up into the master problem and the subproblem, based on Danzig-Wolfe decomposition. To enhance the tractability of the problem, we follow up with a heuristic branch-and-price algorithm with an adaptive selection scheme (HBP-ASS), which integrates the exact policy with a heuristic strategy. The HBP-ASS develops heuristic versions of the dynamic programming algorithm by designing seven operators for heuristic label extension and dominance. An adaptive selection scheme is presented to decide which operator is employed. The performance of the proposed HBP-ASS is evaluated based on an extensive computational study. The results show that the HBP-ASS can obtain the exact solution to small-scale instances much more quickly than commercial branch-and-bound/cut solvers such as CPLEX. Also, for all tested cases, the HBP-ASS can find better solutions to large-scale instances within a shorter time than the existing heuristics - adaptive large neighborhood search. Furthermore, sensitivity analyses are carried out to provide managerial insights.