Multiobjective Two-Phase Fuzzy Optimization Approaches in Management of Water Resources

This study determines the optimal operational strategies for a complex water resource system. These strategies are derived from four conflicting objective functions: maximization of net irrigation benefits, maximization of employment generation, minimization of cultivation cost, and maximization of revenue generation from industrial and municipal supplies. Multiobjective fuzzy linear programming (MOFLP) models, i.e., the maximum-minimum (max-min) operator, two-phase MOFLP (TPMOFLP), and fuzzy compromise approach (average operator), are derived from the individual linear programming solutions of these objective functions. The performances of the derived MOFLP models are compared for inflows that have different probabilities of exceedance with reference to the overall degree of satisfaction, irrigation intensity, and optimized values of the relevant objective functions. The cropping pattern obtained from the recommended MOFLP model, i.e., average operator Case-I (overall degree of satisfaction $\lambda =0.75$), is compared with the actual cropping pattern in the command area in recent years to highlight the need for the developed model. The irrigation intensity for the whole command area from the recommended MOFLP model (104.6%) has been found to be significantly higher than the actual cropping patterns adopted in recent years. The net irrigation benefits, employment generation, cost of cultivation, and municipal and industrial revenue obtained from the recommended MOFLP model are Rs 11,058.27 million, 33,414.62 thousand work days, Rs 5,622.20 million, and Rs 2,686.25 million, respectively. Additionally, the performance of the water resource system using the recommended model is simulated based on 36 years of historical data and 100 years of synthetically generated data and is measured in terms of the performance indices reported by previous studies. The analyses show that the irrigation deficit will increase from $11.22\times {10}^6{\mathrm{m}}^3$ for the past 36 years to $26.67\times {10}^6{\mathrm{m}}^3$ over the next 100 years. The monthly (MFID) and annual frequency irrigation deficits (AFID) will rise from 7.17% (past) to 13.92% (in next 100 years) and from 52.77% (past) to 82% (in next 100 years), respectively.