Hub location problem with a mixed green fleet

Abstract

This study presents a new strategic hub location problem with a mixed fleet of vehicles, including diesel-based vehicles, electric vehicles, and unmanned aerial vehicles. Each vehicle type has a different cost structure, payload capacity, and traveling range. The objective function minimizes the sum of the recharging (or refueling) cost, driver cost, fixed vehicle cost, and waiting cost for vehicles and drivers at recharging stations. While the transportation cost (including the recharging cost, driver cost, and vehicle cost) depends on the traveled distance, the recharging fee and waiting cost depend on the number of visits to recharging stations. We develop a mixed-integer linear programming formulation with preprocessing rules and also propose a relax-and-fix heuristic approach. The computational experiments are conducted over well-known CAB and TR data sets, and also a new German data set. The computational results evaluate the performance of the relax-and-fix heuristics and analyze the impact of varying fuel prices, limits on the use of vehicle types, different fleet compositions, different cost structures, and a hypothetical drone with a larger payload capacity and a longer flying range. Results show how the optimal fleet mix, in particular the use of electric vehicles and drones, and the optimal network vary around the world, as these depend on the geographic scope of the services, the distribution of nodes and arc lengths, and the relative costs for fuel (electricity or diesel).