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 zeros of functions. The second one amounts to solve Cauchy problems. 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.