Two Benefit Allocation Mechanisms Of Water Saving Management Contract Model

In recent years,the shortage of water resources has become the focus of international attention and research.China is a severely water-stressed country,and the problem of water shortage has severely restricted its economic and social development.A large number of water control practices at home and abroad have shown that water-saving is a critical measure to solve the problem of water shortage.Water-Saving Management Contract(WSMC)is a new water-saving mode that uses saved water resources to pay for water-saving transformation costs,which can effectively reduce water consumption and improve water-use efficiency.However,the lack of a water-saving benefit allocation scheme seriously hinders the implementation and promotion of WSMC projects.We aim to establish revenue distribution mechanisms for the Shared Water-Saving Model and Fixed Return on Investment Model of WSMC projects.For Shared Water-Saving Model,a modified expected Shapley value method is developed,in which alliance revenues are characterized as uncertain variables.Firstly,risk,input,and effort are identified as key influencing factors to improve the deficiencies in the distribution of benefits only based on the contribution of participants.Secondly,equity criteria,including symmetry,efficiency,and additivity are redefined based on correction factors to measure the fairness of the allocation scheme.Thirdly,we prove that the allocation result obtained by the proposed method satisfies the equity criteria and is unique.Finally,a water-saving project launched by Hebei University of Engineering is studied to illustrate the applicability of the proposed method.The result shows that the benefit allocation model significantly improves participant motivation of water users and enhances the cooperative relationship.For Fixed Return on Investment Model,a profit incentive model for agents is proposed under the framework of principal-agent.Firstly,users’ incentive contract to water-saving service companies is designed with the renovation cost and water-saving amount as incentive factors.Simultaneously,the output function of the amount of water savings is developed.Secondly,to maximize the user’s expected utility,the user’s incentive model for water-saving service companies is established which is solved by using the backstepping method.Thirdly,we analyze the changing law of the optimal solution in the equilibrium state and compare the choices and behaviors of participants in different situations.Finally,we analyze the changes in the share ratio and effort level with contract parameters through numerical examples.The results indicate that our incentive mechanism can not only enhance the enthusiasm of water-saving service companies to work hard,but also increase the expected utility of users.Two benefit distribution models are established for profit allocation in WSMC projects under different modes,which provides a decision-making basis for participants to implement WSMC projects and is conducive to developing markets for WSMC projects.In addition,the research will perfect the benefit distribution method and broaden the application scope of cooperative game theory and incentive theory.