A Direct Solution Approach to Supply Chain Network Design with fuzzy Decision Variables

Abstract

One of the main problems of supply chain network design is uncertainty. To consider this, designing of a three-echelon supply chain in a fuzzy environment is discussed in this paper. Since satisfaction of some constraints in supply chain is vital and necessary, so this research proposes a direct solution approach to find the solution which represents the trade-off between feasibility degree of constraints and satisfaction degree of the goal. Furthermore, another novation of this paper is optimizing a supply chain network design problem containing both of the parameters and decision variables as fuzzy number. Each fuzzy mathematical programming model with fuzzy decision variables can be solved effectively by employing direct solution approach. A numerical example is discussed and analyzed in order to show efficiency of the proposed approach

Keywords


[1] Pishvaee, M.S., Torabi, S.A., “A possibilistic programming approach for closed-loop supply chain network design under uncertainty”, Fuzzy Sets and Systems, No. 161, pp. 2668–2683, 2010.
[2] Pishvaee, M. S., Torabi, S.A. and Razmi, J,. “Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty”, Computers & Industrial Engineering, No. 62, pp. 624–632, 2012
[3] Kabak, Ö., andÜlengin, F., "Possibilistic linear-programming approach for supply chain networking decisions," European Journal of Operational Research, vol. 209, pp. 253-264, 2011.
[4] Qin, Z., andJi, X., "Logistics network design for product recovery in fuzzy environment," European Journal of Operational Research, vol. 202, pp. 479-490, 2010.
[5] Baykasoǧlu, A., andGöçken, T., "A review and classification of fuzzy mathematical programs," Journal of Intelligent and Fuzzy Systems, vol. 19, pp. 205-229, 2008.
[6] Baykasoǧlu, A., andGöçken, T., "A direct solution approach to fuzzy mathematical programs with fuzzy decision variables," Expert Systems with Applications, vol. 39, pp. 1972-1978, 2012.
[7] Tanaka, H., andAsai, K., "Fuzzy linear programming problems with fuzzy numbers," Fuzzy Sets and Systems, vol. 13, pp. 1-10, 1984.
[8] Tanaka, H., Guo, P., and Zimmermann, H. J., "Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems," Fuzzy Sets and Systems, vol. 113, pp. 323-332, 2000.
[9] Allahviranloo, T., HosseinzadehLotfi, F., Kiasary, M. K., Kiani, N. A., and Alizadeh, L., "Solving fully fuzzy linear programming problem by the ranking function," Applied Mathematical Sciences, vol. 2, pp. 19-32, 2008.
[10] Hashemi, S. M., Modarres, M., Nasrabadi, E., and Nasrabadi, M. M., "Fully fuzzified linear programming, solution and duality," Journal of Intelligent and Fuzzy Systems, vol. 17, pp. 253-261, 2006.
[11] Tapkan, P., ÖZbakıR, L., and Baykasoğlu, A., "Solving fuzzy multiple objective generalized assignment problems directly via bees algorithm and fuzzy ranking," Expert Systems with Applications, vol. 40, pp. 892-898, 2013.
[12] Kumar, A., Kaur, J., and Singh, P., "A new method for solving fully fuzzy linear programming problems," Applied Mathematical Modelling, vol. 35, pp. 817-823, 2011.
[13] Fazlollahtabar, H., Mahdavi, I., and Mohajeri, A., "Applying fuzzy mathematical programming approach to optimize a multiple supply network in uncertain condition with comparative analysis," Applied Soft Computing, pp. 550–562, 2012.
[14] Jiménez, M., "Ranking fuzzy numbers through the comparison of its expected intervals," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 4, pp. 379-388, 1996.
[15] Chen L. H., and Lu, H. W., "An approximate approach for ranking fuzzy numbers based on left and right dominance," Computers and Mathematics with Applications, vol. 41, pp. 1580–1602, 2001.
[16] Torabi S., andHassini, E., "An interactive possibilistic programming approach for multiple objective supply chain master planning," Fuzzy Sets and Systems, vol. 159, pp. 193-214, 2008.
[17] Altiparmak, F., Gen, M., Lin, L., and Karaoglan, I., "A steady-state genetic algorithm for multi-product supply chain network design," Computers & Industrial Engineering, vol. 56, pp. 521-537, 2009.
[18] Wang, H.-F., and Hsu, H.-W., "A closed-loop logistic model with a spanning-tree based genetic algorithm," Computers & Operations Research, vol. 37, pp. 376-389, 2010.