Multiobjective Intuitionistic Fuzzy Optimization Approach in Optimal Irrigation Planning and Operation of Reservoir

Abstract

The present study includes the formulation of a Multiobjective Intuitionistic Fuzzy Linear Programming model for optimal scheduling of crops in the command area of the Ukai-Kakrapar Irrigation project, Gujarat, India. The crisp linear programming approach has been used to obtain the optimal solutions of four conflicting objectives, viz., maximization of net irrigation benefits, employment generation, minimization of cost of cultivation, and maximization of revenue generation from industrial and municipal supplies. The crisp solutions were, in turn, used to develop Intuitionistic Fuzzy Optimization Multiobjective fuzzy linear programming (IFO MOFLP), IFO MOFLP with hesitation index, and two-phase IFO MOFLP (TPIFO MOFLP) models. The performance of IFO MOFLP, IFO MOFLP with hesitation index, and TPIFO MOFLP models are compared in terms of the degree of acceptance, degree of rejection, and hesitation index for inflows at 75% probability of exceedance. The results obtained from IFO MOFLP, IFO MOFLP with hesitation index, and TPIFO MOFLP are also compared with the Compromised MOFLP (Average Operator Case-I) solutions given by Mirajkar and Patel (2016) for the same command area. The irrigation intensity for the entire command area from the proposed TPIFO MOFLP model (112.19%) is considerably higher than those obtained from the Average Operator Case-I (104.60%) model proposed by Mirajkar and Patel (2016). The net irrigation benefits, employment generation, cost of cultivation, and revenue generation from municipal and industrial supplies, resulting from the proposed TPIFO MOFLP model are Rs 10,836.19 million, 34,980.4 thousand workdays, Rs 5,672.23 million, and Rs 2,314.03 million, respectively along with the degree of acceptance, α=0.68, degree of rejection, β =0.19 and degree of hesitation, π =0.13. The corresponding values reported from the Compromised MOFLP model (Average Operator Case-I) (Mirajkar and Patel,2016) were Rs 11,058.27 million, 33,414.62 thousand workdays, Rs 5,622.20 million, and Rs 2,686.25 million, respectively. The releases from the reservoir corresponding to the proposed TPIFO MOFLP model are comparatively lesser than the Compromised MOFLP (Average Operator Case-I) model,indicating the optimal allocation of available water in the command area. Apart from giving better values of selected objective functions, the proposed model also gives additional uncertainty measures like degree of acceptance, degree of rejection, and degree of hesitation which would help the planner to make better decisions for a real-world problem.