Water environment treatment ppp projects optimal payment mechanism based on multi-stage dynamic programming model

Purpose: The optimal payment in the whole operation and maintenance period of water environment treatment PPP projects has become the main approach to realize sustainable development of projects. This study is aimed at constructing an effective payment model for the whole life period of projects to achieve win-win among all stakeholders, so as to provide a theoretical reference and managerial implications for the public sector in the whole operation and maintenance period. Design/methodology/approach: In the whole operation and maintenance period of water environment treatment PPP projects, this article investigates how the public sector optimizes the payment in the whole operation and maintenance period of projects. Firstly, the projects' whole operation and maintenance period is divided into several stages according to the performance appraisal period. And then, the multi-stage dynamic programming model is constructed to design the payment construct model for the public sector in each performance appraisal stage. The payment from the public sector is the decision variable, and the deduction from the private sector is a random variable. Findings: The optimal payment model showed that the relatively less objective weight of public sector leaded to its relatively more total payment and vice versa. Therefore, the sustainable development of the projects can only be ensured when the objective weights both of them should be balanced. Additionally, the deduction from the performance appraisal of private sector plays an important role in the model construction. The larger deduction the private sector undertakes, the smaller profits private sector has. Since the deduction at each stage is a random variable, the deduction varies with the different probability distributions obeyed by the practical deduction in each stage. Research limitations/implications: The findings from this study have provided theoretical and application references, and some managerial implications are also given. First, the improvement of the pricing system of public sector should be accelerated. Second, the reasonable profit of the private sector must be guaranteed. While pursuing the maximization of social benefits, the public sector should make full use of the price sharing mechanism in the market and supervise the real income situation of the private sector. Third is increasing the public to participate in pricing. Additionally, it is a limitation that the deduction is assumed to conform to a uniform distribution in this study. Other probability distributions on deduction can be essentially further sought, so as to be more line with the actual situation of the projects. Originality/value: The optimal payment in whole operation and maintenance period of the projects has become an important issue, which is a key to project success. This study constructs a multi-stage dynamic programming model to optimize payment in the whole period of projects. Additionally, this study adds its value through deeply developing the new theories of optimal payment to more suitable for the practical problems, so that to optimize the design of payment mechanism. Meanwhile, a valuable reference for public and private sectors is provided to ensure the sustainable development of the projects.