Energy-efficient transportation over flowing water

Transportation of water is necessary to manage the water levels in rivers to ensure minimum depths for freight, to buffer water to avoid flooding downstream during wet periods, or to save water for anticipated dry periods. This manipulation of water flows influences the speed of the water in the rivers and canals, and thereby it affects the speed and energy consumption of vessels used for transportation over water. When considering the problem of scheduling micro-ferries in a harbour, the influence of fluctuating water speeds (due to the tide or river flows) can be taken into account in the aim of providing energy-efficient schedules for pick-ups and deliveries of passengers. This paper introduces the effect of flowing water on energy-efficient scheduling, and it proposes a mixed-integer linear programming formulation for solving the problem.