A survey of mathematical optimization models and algorithms for designing and extending irrigation and wastewater networks

This paper presents a state of the art survey of network models and algorithms that can be used as planning tools in irrigation and wastewater systems. It is shown that the problem of designing or extending such systems basically leads to the same type of mathematical optimization model. The difficulty in solving this model lies mainly in the properties of the objective function. Trying to minimize construction and/or operating costs of a system typically results in a concave cost (objective) function due to economies of scale. A number of ways to attack such models are discussed and compared, including linear programing, integer programing, and specially designed exact and heuristic algorithms. The usefulness of each approach is evaluated in terms of the validity of the model, the computational complexity of the algorithm, the properties of the solution, the availability of software, and the capability for sensitivity analysis.