Dynamic Fuzzy-Probabilistic Model Using a Chance-Constrained Programming Approach for Optimising the Performance of Wastewater Treatment Systems

Abstract

This study presents an innovative optimisation approach using a chance-constrained probabilistic-fuzzy optimization model to improve the performance of facultative ponds, which play a crucial role in wastewater treatment systems. The study focuses on optimising the treatment process based on the biological oxygen demand parameter. In this framework, several parameters, including the biological oxygen demand degradation rate, are modelled as random variables with specified probability distributions, while others, such as wastewater load, are treated as fuzzy variables with decision-maker-defined membership functions. Under these uncertainties, the objective is to maximise the treated wastewater volume while ensuring adequate safety margins for both objective and constraint functions through chance-constrained approaches. A practical case study of a wastewater treatment facility located in Bantul, Indonesia, is used to determine the optimal wastewater flow rates and processing durations. The findings show that the proposed model effectively addresses the optimization problem by producing the optimal volume of wastewater entering the inlet per day and the detention time, offering a valuable decision-support tool for similar wastewater treatment settings.