A dynamic distribution method composed of mathematical programming and heuristic method and its application to water management

This paper describes a two-step method for a dynamic water distribution considering storage at reservoirs. The dynamic distribution is reduced to a minimum cost flow problem by an extended network model. At first a minimum cost flow which satisfies preservation conditions at each node and limit conditions at each arc is found very rapidly with a kind of split simplex method. This is because the method, which is called the multi-stage primal method, is described by only integral operations. Next, the flow is modified along the loops which have zero cost and the minimum cost does not increase. This heuristic method make the flow satisfy conditions for convenient operation of pumps and valves. Waterworks bureaus in large cities want a good method for dynamic water distribution to make effective use of limited water resource. However, the scale of the problem is too large to solve under limited machine environment. Moreover, it is very difficult to get the solution that satisfies conditions for the operation of pumps and valves. The proposed method can get over such trouble. Wide-area water management system applied this method has already realized in a certain large city and its merit has been verified. [In Japanese.]