Purpose: Public–private partnership (PPP) projects are increasingly significant in many countries. The purpose of this paper is to assess the impact of critical success factors (CSFs) on PPP projects and comprehensively consider the interrelations and interaction among dimensions and factors to achieve a better understanding of PPP project management. Design/methodology/approach: An evaluation index system for PPP projects such as the presented case study is proposed based on a literature review and a survey. Then, interpretative structural modeling is used to transform the CSFs dimension into a multi-level hierarchical model to reflect the driven-dependency relation of each dimension; the fuzzy analytic network process model optimized by moment estimation theory is used to investigate the impact of CSFs by considering their internal impact. Findings: Regarding the project used as the case study, the driving force and dependence for driving layer and dependent layer are determined. Moreover, in driving layer, efficient and well-structured payment mechanism is the most important CSF if considering the internship and interaction among CSFs, and efficient and well-structured payment mechanism and good governance provide most positive interaction; in dependent layer, population of beneficiaries is the most important CSF if considering the internship and interaction among CSFs, and public client’s satisfaction provides most positive interaction. Originality/value: This paper developed an evaluation model to explore the interrelationships of dimensions and factors and then determine the impact of CSFs. The model propose in this paper relaxes the independence assumptions of traditional methods and is more in line with reality; besides, weighting method is optimized to obtain more objective and reasonable evaluation results. Through an empirical study, the validity of the model has been verified; therefore, the study can help project stakeholders better understand the CSFs and further improve project performance.

The multi-objective operation of reservoirs is impacted by several uncertainties, thus there are many difficulties to determine the optimal operation scheme under a given acceptable risk level. In this paper, improvements are made to optimize the traditional vector space model, and then the multi-dimensional vector space decision model is proposed to enhance the significant difference of evaluation results. To accomplish this, firstly, structuring the proposed schemes by non-inferior solutions of the multi-objective operation risk analysis model; secondly, obtaining the mapping distance between the vector of the proposed schemes and that of the ideal one. Next, we develop an optimal vector space decision model for multi-objective operation risk analysis of reservoirs. Finally, the feasibility and effectiveness of the model are verified by results of an example. The methodology in this paper proves simple and clear, with a particularly noteworthy advantage in terms of the distinctiveness among computed results.

In order to alleviate the problem of ‘curse of dimensionality’ in traditional dynamic programming algorithm for cascade reservoirs optimal operation, this study conducts parallel analysis on optimal operation model for maximum output of cascade hydropower stations from the perspective of time and space, and proposed the decomposition–combination model and its solution for optimal operation for cascade reservoir with parallel computation. Finally, the optimal operation for a three‐reservoir cascade system is taken as the case, and the result shows that, for the same discrete points, the result derived by the model proposed in this study could achieve the same result with traditional dynamic programming algorithm, and presents better performance in terms of increasing the solution speed.