Mathematical models for the best water usage strategy

In this paper, we investigate the best water usage strategy problem of China. Firstly, based on the historical date from 2004 to 2012, we forecast the fresh water supply and demand in each province in the near future by GM(1,1) model. Then we calculate the supply-demand gap and the pure fresh water surplus in each province, and partition all provinces into water-supplying provinces and water-demanding provinces according to their signs of pure fresh water surplus. We formulate the problem into a linear programming model and a mix integer linear programming model respectively. The total costs in each model are calculated by the data of 2012. The total costs obtained from the mix integer linear programming model are 18680.59 billion yuan, which are 51883.53 billion yuan less than that obtained by the linear programming model. The results show that we can reduce the total costs of water usage by using multiple methods including pipeline transportation, desalinization and conservation etc.