An online strategy for piecewise linear scheduling of hydroelectric station

A multi-period online strategy is proposed to deal with the hydroelectric station scheduling problem during the flood season when arrival time of flood peak is uncertain. The purpose of the strategy is to minimize the total loss. The strategy bases on the online competitive analysis, and makes a trade-off between the losses caused by low water head and by surplus water. The strategy equalizes and minimizes all the upper bounds of total losses brought by the arrival of the flood peak at different periods. The competitive ratio of the online strategy is given and the optimality of the strategy is proved. The competitive ratio is only related to the online loss, and the upper bound of total loss gets its minimum if and only if all the lengths of periods are equal and losses brought by the arrival of flood peak at all the endpoints of the periods are equal. Numerical tests and comparisons with the traditional strategy show that the total loss using the proposed strategy decreases by 7.09%.