Abstract
In this article, we consider Multi-Objective Stochastic Linear Programming Problem (MOSLPP) and present a general iterative-interactive optimization process (IIOP) for determining preferable Pareto optimal solution in fuzzy environment. Sakawa et al. originally presented an interactive method to optimize MOSLPP in fuzzy environment. They considered the expectation of each fuzzy objective function of MOSLPP to simultaneously attain respective goal. Accordingly, they had set initial reference membership level as unity for all cases. However, we observe in existing methods that expectations of conflicting objective functions cannot simultaneously attain respective goals in fuzzy environment. In addition, we cannot effectively specify any objective function as main objective function that has highest priority of the decision maker, in fuzzy environment in several other multi-objective optimization methods. Here in proposed IIOP, decision maker can set an objective function as main objective function. Next, we employ trade-off ratios among membership functions of expectations of objective functions in fuzzy environment to elicit corresponding reference membership levels and thereby determine preferable Pareto optimal solution to MOSLPP in fuzzy environment. We illustrate proposed IIOP through numerical application of a multi-objective supply chain management model along with numerical examples. We present managerial insights by performing sensitivity analysis of key parameters of this model. Finally, we draw conclusions.
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References
Aissaoui, N., Haouari, M., Hassini, E.: Supplier selection and order lot sizing modelling: a review. Comput. Oper. Res. 34(12), 3516–3540 (2006)
Bahmani, B.F., Farjah, E., Azizipanah, R.: An efficient scenario-based and fuzzy self-adaptive learning particle swarm optimization approach for dynamic economic emission dispatch considering load and wind power uncertainties. Energy 50(1), 232–244 (2013)
Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)
Chakraborty, D., Jana, D.K., Roy, T.K.: A new approach to solve multi-objective multi-choice multi-item Atanassov’s intuitionistic fuzzy transportation problem using chance operator. J. Intell. Fuzzy Syst. 28(2), 843–865 (2015)
Chan, F.T.S., Chung, S.H., Wadhwa, S.: A hybrid genetic algorithm for production and distribution. Omega Int. J. Manag. Sci. 33, 345–355 (2005)
Dempe, S., Ruziye, A.: On the calculation of a membership function for the solution of a fuzzy linear optimization problem. Fuzzy Sets Syst. 188(1), 58–67 (2012)
Ebrahimnejad, A., Verdegay, J.L.: A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers. J. Intell. Fuzzy Syst. 27(1), 173–185 (2014)
Elhedhli, S., Goffin, J.L.: Efficient production-distribution system design. Manage. Sci. 51(7), 1151–1164 (2005)
Garai, A., Mandal, P., Roy, T.K.: Multipollutant air quality management strategies: T-sets based optimization method under imprecise environment. Int. J. Fuzzy Syst. 19(6), 1927–1939 (2017)
Garai, A., Mandal, P., Roy, T.K.: Intuitionistic fuzzy T-sets based optimization method for production-distribution planning in supply chain management. OPSEARCH 53(4), 950–975 (2016)
Garai, A., Mandal, P., Roy, T.K.: Interactive intuitionistic fuzzy method in multi-objective optimization. Int. J. Fuzzy Comput. Model. 2(1), 14 (2016)
Garai, A., Mandal, P., Roy, T.K.: Intuitionistic fuzzy T-sets based solution method for multi-objective linear programming problems under imprecise environment. Notes Intuit. Fuzzy Sets. 21(4), 104–123 (2015)
Garg, H.: Fuzzy multiobjective reliability optimization problem of industrial systems using swarm particle optimization. J. Ind. Math. 2013, 9p (2013). Article ID 872450
Garg, H.: Mult-objective optimization problem of system reliability under intuitionistic fuzzy set environment using cuckoo search algorithm. J. Intell. Fuzzy Syst. 29, 1653–1669 (2015)
Garg, H., Rani, M., Sharma, S.P., Vishwakarma, Y.: Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system. J. Manuf. Syst. 33(2), 353–367 (2014)
Garg, H., Rani, M., Sharma, S.P., Vishwakarma, Y.: Intuitionistic fuzzy optimization method for solving multi-objective reliability optimization problems in interval environment. Expert Syst. Appl. 41(7), 3157–3167 (2014)
Garg, H., Sharma, S.P.: Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput. Ind. Eng. 64(1), 247–255 (2013)
Ghodsypour, S.H., Brien, C.O.: A decision support system for supplier selection using an integrated analytical hierarchy process and linear programming. Int. J. Prod. Econ. 56–7(20), 199–212 (1998)
Jimenez, M., Bilbao, A.: Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets Syst. 150, 2714–2721 (2009)
Lai, Y.J., Hwang, C.L.: Fuzzy multi-objective decision making: methods and applications. In: Lecture Notes in Economics and Mathematical Systems, vol. 404, Springer, New York (1994)
Liang, T.F.: Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets Syst. 157, 1303–1316 (2006)
Luhandjula, M.K.: Fuzzy optimization: Milestones and perspectives. Fuzzy Sets Syst. 274(1), 4–11 (2015)
Park, Y.B.: An integrated approach for production and distribution planning in supply chain management. Int. J. Prod. Res. 43(6), 1205–1224 (2005)
Sakawa, M., Yano, H., Nishizaki, I.: Linear and Multi-objective Programming with Fuzzy Stochastic Extensions. Springer, New York (2013)
Sakawa, M., Matsui, T.: An interactive fuzzy satisficing method for multi objective stochastic integer programming with simple recourse. Appl. Math. 3, 1245–1251 (2012)
Sakawa, M., Yano, H., Yumine, T.: An interactive fuzzy satisficing method for multi-objective linear-programming problems and its application. In: IEEE Transactions on Systems, Man and Cybernetics, SMC-17, pp. 654–661 (1987)
Sakawa, M., Yano, H.: Interactive decision making for multi-nonlinear programming using augmented min-max problems. Fuzzy Sets Syst. 20(1), 31–43 (1986)
Salehi, S., Selamat, A., Mashiinchi, M.R., Fujita, H.: The synergistic combination of particle swarm optimization and fuzzy sets to design granular classifier. Knowl.-Based Syst. 76, 200–218 (2015)
Sirias, D., Mehra, S.: Quantity discount versus lead time-dependent discount in an inter-organizational supply chain. Int. J. Prod. Res. 43(16), 3481–3496 (2005)
Su, S.F., Chen, M.C.: Enhanced fuzzy systems for type 2 fuzzy and their application in dynamic system identification. In: 16th World Congress of the International Fuzzy Systems Association. Atlantis Press (2015)
Wei, G., Wang, H., Zhao, X., Lin, R.: Hesitant triangular fuzzy information aggregation in multi-attribute decision making. J. Intell. Fuzzy Syst. Appl. Eng. Technol. 26(3), 1201–1209 (2014)
Werners, B.: An interactive fuzzy programming system. Fuzzy Sets Syst. 23, 131–147 (1987)
Wierzbicki, A.P.: Reference point approaches, multicriteria decision making. Int. Series Oper. Res. Manag. Sci. 21, 237–275 (1999)
Wierzbicki, A.P.: The use of reference objectives in multi objective optimization–Theoretical implications and practical experiences. International Institute for Applied Systems Analysis, Laxenburg, Austria (1979)
Wu, Y.-K., Liu, C.-C., Lur, Y.-Y.: Pareto-optimal solution for multi-objective linear programming problems with fuzzy goals. Fuzzy Optim. Decis. Making 14(1), 43–55 (2015)
Xia, W., Wu, Z.: Supplier selection with multiple criteria in volume discount environments, Omega: Internat. J. Manag. Sci. 35, 494–504 (2007)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zimmermann, H.J.: Applications of fuzzy set theory to mathematical programming. Inf. Sci. 36, 29–58 (1985)
Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)
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Garai, A., Chowdhury, S., Biswas, S., Roy, T.K. (2020). Optimization of Multi-objective Stochastic Linear Programming Problem in Fuzzy Environment: An Iterative-Interactive Optimization Process. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_21
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