Probabilistic-fuzzy programming model with chance-constrained to optimize wastewater treatment plants: A case study with the Bantul wastewater treatment plant layout

Department of Mathematics, Diponegoro University, Semarang, Indonesia

^* Corresponding author: adiqyaarmanda@students.undip.ac.id

Abstract

This study introduces a novel optimization approach, employing chance-constrained probabilistic-fuzzy uncertain programming, to enhance the efficiency of facultative ponds in wastewater management systems. Unlike traditional deterministic or stochastic models, this approach integrates both probabilistic and fuzzy uncertainties capturing real-world variations in Biological Oxygen Demand (BOD) degradation rates and wastewater loads. The model addresses the decision-making scenario where some uncertain parameters, like the rate of BOD reduction, are probabilistic with some probability density functions, and some other uncertain parameters, like wastewater load, are represented as fuzzy variables with membership functions determined by the decision-maker. Amid this uncertainty, the goal is to maximize the volume of wastewater treated while maintaining adequate safety margins via chance-based rules is implemented to the objective and the constraints. Using the layout of the Bantul residential wastewater treatment plant located in Yogyakarta, Indonesia, this research succeeded in determining optimal decisions regarding processing time and wastewater flow rate. Consequently, it is inferred that the developed model effectively resolves the problem at hand, rendering it applicable for decision-makers in similar contexts.