Two-Stage Stochastic Approach to the Optimal Location of Booster Disinfection Stations

Abstract

Secondary or booster disinfection is the addition of disinfectant at distinct locations of a water network to achieve control of the microorganisms in drinking water. This work describes a simplified stochastic approach for the optimal location of booster disinfection stations in water distribution networks. The model minimizes the expected total cost involved in the installation of booster stations and the mass of disinfectant needed to satisfy the residual concentration constraints within the network. Inherent uncertainties in water quality simulations, such as water demand and the chemical reactions of the disinfectant that are occurring within the system, indirectly incorporate uncertainties on the model parameters. Hence, the problem has been formulated as a first-stage-integer two-stage stochastic mixed-integer linear program with recourse (SMILPwR). The parameters needed for the solution are obtained through the water quality simulator EPANET 2.0, and the resulting formulation has been solved through a generalized framework based on the stochastic decomposition algorithm. Our paper describes the model and the algorithmic framework, and it compares the deterministic and stochastic optimal solutions. Differences between the stochastic and deterministic objective functions as high as 112% show the significant impact of uncertainties in booster disinfection.