An inexact multi-stage interval-parameter partial information programming model for water resources management under uncertainties

The urban water shortage crisis around the world is increasing. In this study, an inexact multi-stage interval-parameter partial information programming model (IMIPM) is proposed for urban water resources planning and management under uncertainties. Optimization techniques of two-stage stochastic programming (TSP), interval-parameter programming (IPP), linear partial information theory (LPI) and multistage stochastic programming (MSP) are combined into one general framework. IMIPM is used to tackle uncertainties like interval numbers, water inflow probabilities expressed as linear partial information, dynamic features in a long planning time and joint probabilities in water resources management. It is applied to Harbin where the manager needs to allocate water from multi-water sources to multi-water users during multi-planning time periods. Four water flow probability scenarios are obtained, which are associated with uncertainties of urban rainfall information. The results show that the dynamics features and uncertainties of system parameters (such as water allocation targets and shortage) are considered in this model by generating a set of representative scenarios within a multistage context. The results also imply that IMIPM can truly reflect the actual urban water resources management situation, and provide managers with decision-making space and technical support to promote the sustainable development of economics and the ecological environment in cities.