Fixed-flowrate total water network synthesis under uncertainty with risk management

This work addresses the problem of integrated water network synthesis under uncertainty with risk management. We consider a superstructure consisting of water sources, regenerators, and sinks that leads to a mixed-integer quadratically-constrained quadratic program (MIQCQP) for a fixed-flowrate total water network synthesis problem. Uncertainty in the problem is accounted for via a recourse-based two-stage stochastic programming formulation with discrete scenarios that gives rise to a multiscenario MIQCQP comprising network design in the first stage and its operation in the second stage acting as recourse. In addition, we extend the model to address risk management using the Conditional Value-at-Risk (CVaR) metric. Because a large number of scenarios is often required to capture the underlying uncertainty of the problem, causing the model to suffer from the curse of dimensionality, we propose a stepwise solution strategy to reduce the computational load. We illustrate this methodology on a case study inspired from the water network of a petroleum refinery in Malaysia. The presence of nonconvex bilinear terms necessitates the use of global optimization techniques for which we employ a new global MIQCQP solver, GAMS/GloMIQO and verify the solutions with BARON. Our computational results show that total water network synthesis under uncertainty with risk management problems can be solved to global optimality in reasonable time.