A new approach for solving fuzzy multi-objective quadratic programming of water resource allocation problem

Nasseri, Hadi; Baghban, Abdollah; Mahdavi, Iraj

doi:10.22116/jiems.2019.92259

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Mathematics Science, University of Mazandaran, Babolsar, Iran.

² Mazandaran University of Science and Technology, Babolsar, Iran.

https://doi.org/10.22116/jiems.2019.92259

Abstract

This paper describes an application of fuzzy multi-objective quadratic model with flexible constraints for optimal allocation of limited available water resources among different water-user sectors. Due to the fact that, water resource allocation problem is one of the practical and essential subjects in real world and many of the parameters may be faced by uncertainty. In this paper, we present α - cut approach for transforming fuzzy multi-objective quadratic programming model with flexible constraints into a crisp form. By using this approach a multi-parametric multi-objective programming model corresponding to α and parameters of flexible constraints is obtained. One of the advantages of this model is that the α - cut level is not determined by the decision makers. Actually, this model itself can calculate the α - cut level. In order to achieve a desired Pareto optimal value of multi-parametric multi-objective model, we use goal programming method for illustration of water resource allocation with sensitivity analysis of lower bound of parameters in flexible constraints. To illustrate the efficiency of the proposed approach, we apply it for a real case problem of water resource allocation.

Keywords

20.1001.1.2476308.2019.6.2.5.6

References

Archibald, T., and Marshall, S., (2018). "Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty", Environmental Modelling & Assessment, pp. 1-25.

Babel, M., Das Gupta, A., and Nayak, D., (2005). "A Model for Optimal Allocation of Water to Competing Demands", Water Resource Management, Vol. 19, pp. 693-712.

Bellman, R. E., and Zadeh, L. A., (1970). "Decision-making in a fuzzy environment", Management science. INFORMS, Vol. 17, No. 4, p. B-141.

Brown, P., Cochrane, T., and Krom, T., (2010). "Optimal on-farm irrigation scheduling with a seasonal water limit using simulated annealing", Agricultural Water Management, Vol. 97, pp. 892-900.

Charnes, A., and Cooper, W., (1959). "constraint programming", Management science, Vol. 6, pp. 73-79.

Chongfeng, R., and Hongbo, Z., (2018). "A Fuzzy Max–Min Decision Bi-Level Fuzzy Programming Model for Water Resources Optimization Allocation under Uncertainty", Water, Vol. 10, No. 4.

Compose, L., and Verdegay, J., (1989). "Linear programming problems and ranking of fuzzy number", Fuzzy sets and systems, Vol. 32, pp. 1-11.

Delgado, M., Verdegay, J., and Vila, M., (1989). "A general model for fuzzy linear programming", Fuzzy sets and systems, Vol. 29, pp. 21-29.

Dubois, D. J., (1980). Fuzzy sets and systems: theory and applications. Academic press.

Ehrgott, M., and Wiecek, M. M., (2005). "Multiobjective programming", in Multiple criteria Decision Analysis: State of the art surveys. Springer, pp. 667-708.

Gandibleux, X., (2002). Multiple criteria optimization: state of the art annotated bibliographic surveys. Springer.

Hosseini Safa, H., Morid, S., and Moghaddasi, M., (2012). "Incorporating Economy and Long-term Inflow Forecasting Uncertainty into Decision-making for Agricultural Water Allocation during Droughts", Water Resource Management, Vol. 26, pp. 2267-2281.

Ijaz, A., and Deshan, T., (2016). "Multi-objective Linear Programming for OptimalWater Allocation Based on Satisfaction and Economic Criterion", Arabian Journal for Science and Engineering, Vol. 41, pp. 1421-1433.

Khummongkol, R., Sutivong, D., and Kuntanakulwong, S., (2007). "Water Resource Management Using Multi-objective Optimization and Rainfall Forecast", in 2007 International Conference on Convergence Information Technology, pp. 2449-2454.

Mansoori, A., Effati, S., and Eshaghnezhad, M., (2018). "A neural network to solve quadratic programming problems with fuzzy parameters", Fuzzy Optimization and Decision Making. Springer, Vol. 17, No. 1, pp. 75–101.

Nasseri, S., and Ebrahimnejad, A., (2010). "A fuzzy optimal simplex algorithm and its application for solving flexible linear programming problems", European Journal Industrial of Engineering, Vol. 4, No. 3, pp. 372-389.

Nasseri, S., and Ramzannia-Keshteli, G., (2018). "A goal programming approach for fuzzy flexible linear programming problems", Journal of Applied Mathematics, Lahijan Azad University, In pressin.

Panigrahi, M., Panda, G., and Nanda, S., (2008). "Convex fuzzy mapping with differentiability and its application in fuzzy optimization", European Journal of Operational Research. Elsevier, Vol. 185, No. 1, pp. 47–62.

Roozbahani, R., Schreider, S., and Abbasi, B., (2013). "Economic Sharing of Basin Water Resources between Competing Stakeholders", Water Resource Management, pp. 2965-2988.

Tsakiris, G., and Spiliotis, M., (2004). "Fuzzy linear programming for Problems of water allocation under uncertainty", European water, Vol. 7, No. 8, pp. 25-37.

Verdegay, J. L., Gupta, M. M., and Sánchez, E., (1982). "Fuzzy information and decision processes", North-Holland, 1982, ch. Fuzzy mathematical programming.

Verdegay, J., (1984). "A dual approach to solving the fuzzy linear programming problem", Fuzzy sets and systems, Vol. 14, pp. 131-141.

Wang, G., and Wu, C., (2003). "Directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming", Fuzzy Sets and Systems, Vol. 138, No 3, pp. 559-591.

Wang, H., Zhang, C., and Guo, P., (2018). "An Interval Quadratic Fuzzy Dependent-Chance Programming Model for Optimal IrrigationWater Allocation under Uncertainty", Water, Vol. 10, No. 6, pp. 1-17.

Werner’s, B., (1987). "Interactive multiple objective programming subject to flexible constraint", European Journal of Operation Research, Vol. 31, pp. 342-349.

Zadeh, L., (1987). "Fuzzy sets as a basis for a theory of possibility", Fuzzy sets and systems, Vol. 1, pp. 3-28.

Zadeh, L. A., (1965). "Fuzzy sets", Information and control, Vol. 8, No. 3, pp. 338-353.

Journal of Industrial Engineering and Management Studies

A new approach for solving fuzzy multi-objective quadratic programming of water resource allocation problem

References

References

Volume 6, Issue 2
December 2019
Pages 78-102

A new approach for solving fuzzy multi-objective quadratic programming of water resource allocation problem

References

References

Volume 6, Issue 2December 2019Pages 78-102

Volume 6, Issue 2
December 2019
Pages 78-102