A Linearized Mathematical Formulation for Combined Centralized and Distributed Waste Water Treatment Network Design

Abstract

Waste water treatment (WWT) is a very important issue affecting both the environment and public health in the twenty-first century. The increasing earth’s population together with the growing urbanism leads to the need of redesigning effective WWT. In this paper, the problem of optimal Waste Water Treatment Network Design (WWTND) is addressed. To this end, various parameters affecting the problem have been taken into consideration, such as the distance between the residential areas and the treatment plants, estimations for future population of towns and costs of expanding existing network or building a new one. The last parameter of cost has a lot of components (pipeline cost, treatment plant cost, etc.), all of which are non-linear functions depending on the amount of waste water produced and treated within the network. The authors have developed a mathematical model for the solution of WWTND problem and have applied piecewise linearization in order to deal with the non-linear terms. The developed model has been implemented on an area in Luxemburg, for which data were collected. The results prove the model’s validity and usefulness, while its solution is computationally affordable. © 2022, The Author(s).