A Fuzzy Random Chance-Constrained Programming for Water Distribution System under Uncertainty

Abstract

In this paper, a model with integration of interval programming (IP), chance-constrained programming (CCP), and fuzzy random variables (FRVs), termed as an inexact fuzzy random chance-constrained programming (IFRCCP) model, was proposed to deal with the fuzzy and random uncertainties in optimization of booster cost for a water distribution system (WDS) under uncertainty. The IFRCCP model was applied to a WDS to verify the efficiency of the method. After formulating the IFRCCP model, the booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits, and decreased with the violation levels of the lower limits. Moreover, the nodal chlorine concentrations are more uniform with the increase of booster numbers. The booster costs under trapezoidal distribution FRVs are greater than that under triangular distribution FRVs. Moreover, the uniformity of nodal chlorine concentration under triangular fuzzy distributions is larger than that under trapezoidal fuzzy distributions. The results obtained can help managers to make schemes on booster optimization under fuzzy and random uncertainties.