Optimization of Drinking Water Network: Incorporating Continuity Constraints

The optimization of production and transport costs in a drinking water network has been modelized using various operational research methods in recent years. For several years we have been building models used on large water networks, managed in real time. For short calculation times, linear programming has been chosen. Our optimization model is based on an objective function that minimizes the daily proportional costs and on physical constraints such as tank size. In order to calculate the flows being able to forward on the network an hydraulic model is used. In certain networks, one constraint has not yet been incorporated into optimization models. It is associated with the operating conditions of the water treatment plant. To avoid problems with water quality, a waterworks must be able to operate continuously. The problem is difficult to solve because Bellman's principle of optimality cannot be applied. To take account of this extra operating constraint, we propose a method based on linear programming with mixed variables. We introduce set-up, stop and start-up variables. The optimization model is resolved using the Cplex Solver. The Solver uses several shortcuts that reduce the time taken by a conventional branch and bound algorithm. This method provides satisfaction by maintaining computing times compatible with real time network management. For example, we can solve the optimization of a real network with two different resources (river and groundwater), five tanks supplying 20,000 inhabitants in about 30 seconds.