A Mathematical Model on the Optimal Number of Hydrogen Stations with Respect to the Diffusion of Fuel Cell Vehicles

In this paper, the optimal numbers of gas and hydrogen stations are examined. Recently, the possibility of gasoline vehicles being replaced with fuel cell vehicles (FCV) is being examined in the coming hydrogen society. The realization of this scenario however needs a large number of hydrogen refueling stations, which hardly exist at the present. We first calculate the optimal number of hydrogen stations to minimize the sum of two types of cost: 1) operation cost of hydrogen stations and 2) transportation cost of FCVs to the nearest stations. Next, we incorporate the diffusion rate of FCVs into the model to determine the optimal number of gas stations and that of hydrogen stations simultaneously. We also provide an advanced model that considers hybrid stations, with which both gasoline and FCVs can refuel. These models clarify that the optimal number of total stations varies with the diffusion rate of FCVs. If only gas and hydrogen stations are assumed, more stations are needed in the transition period. If hybrid stations are introduced, the number of total stations takes minimum value during the transition period. Moreover, the optimal solution indicates that all stations should become hybrid stations in the middle of the transition. Finally, the models are applied to Yokohama City in Japan and the solutions of the models are examined.