An adaptive Lagrangian relaxation-based algorithm for a coordinated water supply and wastewater collection network design problem

The last century has seen an increased prevalence and duration of droughts as well as the water shortage especially in Middle East countries like Iran. This urgent situation in Iran such as Urmia Lake in the west Azerbaijan province is a motivation for us to model a new coordinated water supply and wastewater collection network design problem. Due to the uncertainty, as one of inherent sections of the water supply chain, a two-stage stochastic programming approach is used to formulate the problem. To solve the proposed model, a Lagrangian relaxation-based algorithm formulated by a new adaptive strategy is employed. This algorithm considers both upper and lower bounds of the problem to reach a performance solution. The proposed algorithm is compared with two similar algorithms from the literature to reveal its performance. As such, the efficiency of the proposed model is evaluated by some sensitivity analyses. Finally, a comprehensive discussion is provided to show the main findings and practical insights of this research.