Given a model based on a conservation law, we study how the solution depends from the initial/boundary datum, from the flow and from various constraints. With this tool, several control problems can be addressed and the existence of an optimal control can be proved. Models describing escape dynamics of pedestrians, traffic at toll gates, open canals management and fluid flow in gas pipelines fall within this framework. In particular, a necessary condition for optimality is obtained, which applies to a supply chain model.