In order to improve the travel time of surface public transport vehicles (bus, tramway, etc.)

In this work, a decomposition method for computing a solution of a shortterm hydrothermal scheduling problem is presented. An oligopolistic electricity market composed of two types of power generation units, thermal and hydroelectric, is considered. The hydroelectric units have also the possibility of pumping back water, paying in that case for the electricity consumed. The Nash equilibrium analytic condition is stated as a variational inclusion and it is shown that the associated operator has a structure suitable for decomposition, in particular by applying the variable metric hybrid proximal decomposition technique (VMHPDM). The application of VMHPDM is illustrated in several examples and numerical results for each example are presented.