Currently research on joint operation of a large reservoir and its re-regulating reservoir focuses on either water quantity regulation or water head regulation. The accuracy of relevant models is in need of improvement if the influence of factors such as water flow hysteresis and the aftereffect of tail water level variation are taken into consideration. In this paper, given the actual production of Pankou-Xiaoxuan cascade hydropower stations that combines two operation modes (‘electricity to water’ and ‘water to electricity’), a coupling model of their short-term optimal operation is developed, which considers Xiaoxuan reservoir’s regulating effect on Pankou reservoir’s outflow volume and water head. Factors such as water flow hysteresis and the aftereffect of tail water level variation are also considered to enhance the model’s accuracy. The Backward Propagation (BP) neural network is employed for precise calculation of the downstream reservoir’s inflow and the upstream reservoir’s tail water level. Besides, we put forth Accompanying Progressive Optimality Algorithm (APOA) to solve the coupling model with aftereffect. An example is given to verify the scientificity of the proposed model and the advantages of APOA. Through analysis of the model calculation results, the optimal operation rules of the cascade reservoirs are obtained in terms of water quantity regulation and water head regulation, which can provide scientific reference for cascade reservoirs’ optimal operation.

In decision-making with interval numbers, there are problems such as how to reduce the loss of decision information to improve decision accuracy and the difficulty of using interval numbers for sorting. On the basis of fully considering the subjective and objective weights of indexes, the grey entropy method (GEM) is improved by taking advantage of the Mahalanobis-Taguchi System (MTS) in which the orthogonal design has few tests but much obtained information, and the Mahalanobis distance can reflect the correlation between indexes. Then, the signal-to-noise ratio is integrated with the improved degree of balance and approach, and a multi-dimensional interval number decision model based on MTS and GEM is put forth. This model is applied to selecting the optimal scheme of controlling the Pankou reservoir’s water level in flood season. Compared with the decision results of other methods, the optimal scheme selected by the proposed model can achieve greater benefits within an acceptable risk range and thus better coordinate the balance between risk and benefit, which verifies the feasibility and validity of the model.