In this article, we present two numerical methods to create a database for the approximation of the value function of a bilevel optimal control problem. The first method is based on the computation of the value function via indirect simple shooting, which implies to find the roots of a function. The second one consists in solving a Cauchy problem. These two techniques are compared, in terms of prior information, computation cost and data distribution, on an industrial application: the torque split and gear shift optimal control problem on hybrid electric vehicles.