Minimum Cost Path Problem for Plug-in Hybrid Electric Vehicles

We introduce a practically important and theoretically challenging problem: finding the minimum cost path for plug-in hybrid electric vehicles (PHEVs) in a network with refueling and battery switching stations, considering electricity and gasoline as sources of energy with different cost structures and limitations. We show that this problem is NP-complete even though its electric vehicle and conventional vehicle special cases are polynomially solvable. We propose three solution techniques: (1) a mixed integer quadratically constrained program that incorporates non-fuel costs such as vehicle depreciation, battery degradation and stopping, (2) a dynamic programming based heuristic and (3) a shortest path heuristic. We conduct extensive computational experiments using both real world road network data and artificially generated road networks of various sizes and provide significant insights about the effects of driver preferences and the availability of battery switching stations on the PHEV economics. In particular, our findings show that increasing the number of battery switching stations may not be enough to overcome the range anxiety of the drivers.