A branch-and-price algorithm for a green location routing problem with multi-type charging infrastructure

In this paper, we present a green location routing problem with multi-type charging infrastructure (GLRP-CI), which aims to determine simultaneous decisions on locating depots, reinforcing them with battery swapping infrastructure (BSI) or recharging infrastructure (FCI), and routing electric vehicles (EVs) in the distribution system. The problem is formulated as an arc-based formulation, and the objective is to minimize the total cost, including the daily fixed costs of depots equipped with BSI or FCI, the travel cost of EVs, the holding cost of batteries, and the electricity cost for charging, with the potential profit of sending energy back into the electric grid subtracted from the objective function. Some analytical properties of special cases of the problem are also investigated. We develop a branch-and-price (B&P) algorithm to solve this problem, in which initial feasible columns are given by a hybrid heuristic algorithm, the pricing subproblems are solved by the label-setting algorithm, and the global lower bound is raised by the Lagrangian lower bound. The proposed B&P algorithm is validated by extensive computational experiments, and it performs well compared with commercial branch-and-bound/cut solvers such as CPLEX in terms of computational speed and solution quality. Through sensitivity analysis, we explore the interaction between key factors (such as the configuration of EVs and the price of energy sent back to the grid) and the use of BSI- or FCI-type depot location strategies.