Inland waterway efficiency through skipper collaboration and joint speed optimization

We address the problem of minimizing aggregated fuel consumption by vessels in an inland waterway, e.g., a river, with single lock. The vessel depends on its velocity and slower it moves, less consumes. Given entry times into waterway deadlines before which they need to leave we start from optimal velocities that minimize their private consumption, where assume selfish behavior skippers. Presence lock possible congestion make computationally challenging. First, prove general, Nash equilibrium might not exist, i.e., if there is no supervision vessels’ velocities, exist strategy profile can unilaterally deviate decrease consumption. Next, introduce simple methods guarantee existence equilibrium. Unfortunately, though be computed, such stable solution high compared social optimum, total minimized. Therefore, propose mechanism involving payments between vessels, guaranteeing while This studied for both offline setting, all information known beforehand, online only know time deadline when enters waterway.