A branch-and-price algorithm for two-echelon electric vehicle routing problem

Motivated by express and e-commerce companies' distribution practices, we study a two-echelon electric vehicle routing problem. In this problem, fuel-powered vehicles are used to transport goods from a depot to intermediate facilities (satellites) in the first echelon, whereas electric vehicles, which have limited driving ranges and need to be recharged at recharging stations, are used to transfer goods from the satellites to customers in the second echelon. We model the problem as an arc flow model and decompose the model into a master problem and pricing subproblem. We propose a branch-and-price algorithm to solve it. We use column generation to solve the restricted master problem to provide lower bounds. By enumerating all the subsets of the satellites, we generate feasible columns by solving the elementary shortest path problem with resource constraints in the first echelon. Then, we design a bidirectional labeling algorithm to generate feasible routes in the second echelon. Comparing the performance of our proposed algorithm with that of CPLEX in solving a set of small-sized instances, we demonstrate the former's effectiveness. We further assess our algorithm in solving two sets of larger scale instances. We also examine the impacts of some model parameters on the solution.