Multipurpose Reservoir Operating Policies: A Fully Fuzzy Linear Programming Approach

Authors
Department of Civil Engineering, Government College of Engineering, Aurangabad-431005, Maharashtra State, India.
Abstract
A Fully Fuzzy Linear Programming (FFLP) formulation for the reservoir operation of a multipurpose reservoir in presented in the ongoing paper. In the real world, water resources systems usually have complexities among social, economic, natural resources and environmental aspects, which lead to multi-objective problems of significant uncertainties in system parameters, objectives and in their interactions. These uncertainties in FFLP reservoir operation model are considered by being treated as fuzzy sets. In the present study, an FFLP reservoir operation model is developed where all parameters and decision variables are fuzzy numbers. The developed model is demonstrated through a case study of Jayakwadi reservoir stage–II, Maharashtra, India with the objectives of maximization of annual releases for irrigation and hydropower generation. The FFLP reservoir operation model is solved to obtain a compromised solution by simultaneously optimizing the fuzzified objectives and the corresponding degree of truthfulness, using linear membership function. The degree of correspondence (Correspondence) obtained is equal to 0.78 and the corresponding annual releases for irrigation amount of 367 Mm3 and while annual releases for hydropower generation being 216 Mm3. the present study clearly demonstrates that, use of FFLP in multipurpose reservoir system optimization presents a potential alternative to attain an optimal operating policy.

Keywords


1. Aktar, T. and Simonovic, S.P. 2004. Modeling uncertainties in short term reservoir operation using fuzzy sets and genetic algorithm, Hydrolog. Sci. J., 49(6):1081-1097.
2. Allahrivarnloo, T., Lotf, Z.F. and Kiasary, Kh. M. 2008. Solving fully fuzzy linear programming problem by ranking function, Int. J. Appl. Math. Sci., 2(1): 19-32.
3. Arikan, F. and Gungor, Z. 2007. A two-phase approach for multi-objective programming problems with fuzzy coefficients, Inform. Sci., 177(23):5191–5202.
4. Azamathulla, H. Md., Wu, F-C., Ghani A. A., Narulkar, S. M., Zakaria, N.A. and Chnag, C. K. 2008. Comparison between genetic algorithm and linear programming approach for real time operation, J. Hydro-environment Research, 2(3): 172-181.
5. Bellman, R. and Zadeh, L. A. 1970. Decision making in fuzzy environment, Manag. Sci., 17 (4): B141-B164.
6. Carron, J. C., Zagona F. A. and Fulp T. J. 2006. Modeling uncertainty in an object oriented reservoir operation model, J. Irrigat. Drain. Eng., 132(2): 104-110.
7. Choudhari, S. A. and Anand Raj P. 2009. Multiobjective multireservoir operation in fuzzy environment, Water Resour. Manag., 24(10):2057-2073.
8. Dehghan, M., Hashemi, B. and Ghatee, M. 2006. Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput., 179(1): 328-343.
9. Fontane, D. G., Gates, T. G. and Moncada, E. 1997. Planning reservoir operations with imprecise objectives, J. Water. Resour. Plann. Manag., 123(3):154-162.
10. Ganesan, K. and Veeramani, P. 2006. Fuzzy linear programming with trapezoidal fuzzy numbers, Ann. Oper. Res., 143(1): 305-315.
11. Jairaj, P. G. and Vedula, S. 2000. Multireservoir system optimization using fuzzy mathematical programming, Water Resour. Manag., 14(6):457–472.
12. Jimenez, M. and Bibao, A. 2009. Pareto-optimal solutions in fuzzy multi-objective linear programming, Fuzzy Set Syst., 160(18): 2714-2721.
13. Klir, G. J. and Yuan, B. 2007. Fuzzy sets and fuzzy logic: theory and applications, Prentice-Hall, India, New Delhi.
14. Kumar, A., Kaur, J. and Singh, P. 2011. A new method for solving fully fuzzy linear programming problem, Appl. Math. Model., 35(2),:817-823.
15. Li, XQ., Zhang, B. and Li, H. 2006. Computing efficient solutions to fuzzy multiple objective linear programming problems, Fuzzy Set Syst., 157(10): 1328-1332.
16. Li, YP, and Huang, G. H. 2009. Fuzzy Stochastic based violation analysis method for planning water resources management systems with uncertain information, Inform. Sci., 179(24): 4261-4276.
17. Liu, H. K. 2010. On the solution of fully fuzzy linear programming, International Journal of Computational and Mathematical Sciences, 4(1):29-33.
18. Lotif, H. F., Allahrivarnloo, T., Jondabeh A. M. and Alizadeh L. 2009. Solving fully fuzzy linear programming using lexicography method and fuzzy approximate solutions, Appl. Math. Model., 33(7): 3151-3156.
19. Mujumdar, P. P. and Ghosh S. 2008. Fuzzy logic based approaches in water resources system modeling, Water Sci. Tech. Libr., 68(3):165-176.
20. Nazemi, A. R., Akbarzadeh T. AR. and Hosseini. M. S. 2002. Fuzzy-stochastic linear programming in water resources engineering, Fuzzy Information Processing Society, Proceedings, NAFIPS, 227-232.
21. Panigrahi, D. P. and Mujumdar P. P. 2000. Reservoir operation modeling with fuzzy logic, Water Resour. Manag., 14(2):89-109.
22. Rani, D. and Moreira, M. M. 2009. Simulation-optimization modeling: A survey and potential application in reservoir optimization modeling, Water Resour. Manag., 24(6):1107-1138.
23. Regulwar, D. G. and Anand Raj, P. 2008. Development of 3-D optimal surface for operation policies of a multireservoir in fuzzy environment using genetic algorithm for river basin development and management, Water Resour. Manag., 22(5): 595-610.
24. Regulwar, D. G. and Anand Raj, P. 2009. Multiobjective multireservoir optimization in fuzzy environment for river basin development and management, J. Water Resource Protect., 4(1):271-280
25. Regulwar, D. G. and Gurav, J. B. 2010. Irrigation planning under uncertainty-A multiobjetive fuzzy linear programming approach, Water Resour. Manag., 25(5): 1387-1416.
26. Regulwar, D. G. and Kamodkar, R. U. 2010. Derivation of multipurpose single reservoir policies with fuzzy constraints, J Water Resource Protect., 2(12):1028-1039.
27. Rommelfanger, H. 1996. Fuzzy linear programming and applications, Eur. J. Oper. Res. 92(3):512-527.
28. Sahindis, N. V. 2004. Optimization under uncertainty: State of the art and opportunities, Comput. Chem. Eng., 28(6-7):971-983.
29. Shrestha, B. Duckstein, P. L. and Stakhiv, E. Z. 1996. A fuzzy rule based reservoir operation, Water Resour. Manag., 122(3):262-269.
30. Stanciulescu, C., Foremps, P. Installe, M. and Wertz, V. 2003. Multiobjective fuzzy linear programming with fuzzy decision variables, Eur. J. Oper. Res. 149(3): 654-675.
31. Wang, H. F. and Wang, M. L. 1997. A fuzzy multiobjective linear programming, Fuzzy Set Syst., 86(1):61-72.
32. Yeh, W. G. W. 1985. Reservoir management and operational models: A state-of-the-art review, Water Resour. Res., 21(12):1797-1818.
33. Zahraie, B. and Hosseini, S.M. 2010. Development of reservoir operation policies using integrated optimization-simulation approach. J Agr. Sci. Tech., 12(4); 433-446.
34. Zimmermann, H. J. 1978.Fuzzy programming and linear programming with several objective functions, Fuzzy Set Syst., 1(1): 45-55.
35. Zimmermann, H. J. 1996. Fuzzy set theory and its applications. Allied Publishers, New Delhi.