  In this paper, a new mixed integer nonlinear programming formulation is
proposed for optimally placing and operating pressure reducing valves and
chlorine booster stations in water distribution networks. The objective is the
minimization of average zone pressure, while penalizing deviations from a
target chlorine concentration. We propose a relax-tighten-round algorithm based
on tightened polyhedral relaxations and a rounding scheme to compute feasible
solutions, with bounds on their optimality gaps. This is because off-the-shelf
global optimization solvers failed to compute feasible solutions for the
considered non-convex mixed integer nonlinear program. The implemented
algorithm is evaluated using three benchmarking water networks, and they are
shown to outperform off-the-shelf solvers, for these case studies. The proposed
heuristic has enabled the computation of good quality feasible solutions in
most instances, with bounds on the optimality gaps that are comparable to the
order of uncertainty observed in operational water network models.
