Abstract : In this work, we study a minimal time problem for a Partial Differential Equation of transport type, that arises in crowd models. The control is a Lipschitz vector field localized on a fixed control set ω. We provide a complete answer for the minimal time problem. After considering the discrete case, we show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in ω to feed the desired final configuration. We also give a numerical method to compute the minimal time and to build the corresponding control. These results are illustrated by some numerical simulations.