How to cite this paper
Taran, M & Roghanian, E. (2013). A fuzzy multi-objective multi-follower linear Bi-level programming problem to supply chain optimization.Uncertain Supply Chain Management, 1(4), 193-206.
Refrences
Akgul, O., Shah, N., & Papageorgiou, LG. (2010). An optimization framework for a hybrid first/second generation bioethanol supply chain. Computers and Chemical Engineering, 42, 101– 114.
Alborzi, F., Vafaei, H., Gholami, M.H., & Esfahani, M.M.S. (2011). A Multi-Objective Model for Supply Chain Network Design under Stochastic Demand. World Academy of Science, Engineering and Technology, 10, 13-20.
Altiparmak, F., Gen, M., Lin, L., & Paksoy, T. (2006). A genetic algorithm approach for multi-objective optimization of supply chain networks. Computers & Industrial Engineering, 51, 196–215.
Ansari, E., & Zhiani Rezai, H. (2011). Solving Multi-objective Linear Bilevel Multi-follower Programming Problem. Int. J. Industrial Mathematics, 3, 303-316.
Azaron, A., Brown, K.N., Tarim, S.A., & Modarres, M. (2008). A multi-objective stochastic programming approach for supply chain design considering risk. Int. J. Production Economics, 116, 129–138.
Baky, I.A. (2010). Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Applied Mathematical Modeling, 34, 2377–2387.
Calvete, H. I., & Galé, C. (2004). Optimality conditions for the linear fractional/ quadratic bilevel problem. Monograf?as del Seminario Matem?tico Garc?a de Galdeano, 236, 3751–3762.
Calvete, H. I., & Galé, C. (2012). Linear bilevel programming with interval coefficients. Journal of Computational and Applied Mathematics, 31, 285–294.
Chaudhuri, B.B., & Rosenfeld, A. (1999). A modified hausdorff distance between fuzzy sets. Information science, 118,159-171.
Chan, F.T.S., & Chung, S.H. (2004). Multi-criteria genetic optimization for distribution network problems. Int J Adv Manuf Technol, 24, 517–532.
Chen, C.L., & Lee, W.C. (2004). Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Computers and Chemical Engineering, 28, 1131–1144.
Diamond, p. & Kloeden, P. (1994). Metric Spaces of fuzzy sets theory and applications, Word Scientific Publishing, Singapore.
Gao, J., & Liu, B. (2005). Fuzzy Multilevel Programming with a Hybrid Intelligent Algorithm. Computers and Mathematics with Applications, 49, 1539-1548.
Gao, Y., Zhang, G., Lu, J., & Wee, H.M. (2010). Particle swarm optimization for bi-level pricing problems in supply chains. Journal of Global Optimization, 51, 245–254.
Gebreslassie, B.H., Yao, Y., & You, F. (2012). Design Under Uncertainty of Hydrocarbon Biorefinery Supply Chains: Multiobjective Stochastic Programming Models, Decomposition Algorithm, and a Comparison Between CVaR and Downside Risk. American Institute of Chemical Engineers, 58, 2155- 2179.
Guillén, G., Mele, F.D., Bagajewicz, M.J., Espu?a, A., & Puigjaner, L. (2005). Multiobjective supply chain design under uncertainty. Chemical Engineering Science, 60, 1535 – 1553.
Kumar, M., Vrat, P., & Shankar, R. (2006). A fuzzy programming approach for vendor selection problem in a supply chain. Int. J. Production Economics, 101, 273–285.
Kuo, R.J., & Huang, C.C. (2009). Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Computers and Mathematics with Applications, 58, 678-685.
Jiang, Y., Li, X., Huang, C., & Wu, X. (2013). Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem. Applied Mathematics and Computation, 219, 4332–4339.
Jimenez, M., Arenas, M., Bilbao, A., & Rodr?guez, M.V. (2007). Linear programming with fuzzy parameters: An interactive method resolution. European Journal of Operational Research, 177, 1599–1609.
Jula P., & Leachman R.C. (2011). A supply-chain optimization model of the allocation of containerized imports from Asia to the United States. Transportation Research Part E, 47, 609–622.
Jung, J.Y., Blau, G., Pekny, J., Reklaitis, G., & Eversdyk, D. (2004). A simulation based optimization approach to supply chain management under demand uncertainty. Computers and Chemical Engineering, 28, 2087–2106.
Lakhal, S., Martel, A., Kettani, O., & Oral, M. (2001). On the optimization of supply chain networking decisions. European Journal of Operational Research, 129, 259-270.
Li, G. (2012). Fuzzy goal programming – A parametric approach. Information Sciences, 195, 287–295.
Liang, T.F., & Cheng, H.W. (2009). Application of fuzzy sets to manufacturing/ distribution planning decisions with multi-product and multi-time period in supply chains. Expert Systems with Applications, 36, 3367–3377.
Lin, X., Quan-sheng, L., & Wan-sheng T. (2008). Hybrid Intelligent Algorithm for Solving the Bilevel Programming Models with Fuzzy Variables. Systems Engineering - Theory & Practice, 28, 100–104.
Lu, J., Shi, C., & Zhang, G. (2006). On bilevel multi-follower decision making: General framework and solutions. Information Sciences, 176, 1607–1627.
Mele, F. D., Guillen, G., Espuna, A., & Puigjaner, L. (2007). An agent-based approach for supply chain retrofitting under uncertainty. Computers and Chemical Engineering, 31, 722–735.
Mishra, S. (2007). Weighting method for bi-level linear fractional programming problems, European Journal of Operational Research, 183, 296–302.
Mokashi, S.D. and Kokossis, A.C. (2003). Application of dispersion algorithms to supply chain optimization, Computers and Chemical Engineering, 27, 927-949.
Osman, M.S., Abo-Sinna, M.A., Amer, A.H., & Emam, O.E. (2004). A multi-level non-linear multi-objective decision-making under fuzziness. Applied Mathematics and Computation, 153, 239–252.
Paksoy, T., & Pehlivan, N.Y. (2012). A fuzzy linear programming model for the optimization of multi-stage supply chain networks with triangular and trapezoidal membership functions. Journal of the Franklin Institute, 349, 93–109.
Peidro, D., Mula, J., Poler, R., & Verdegay, J.L. (2009). Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and System, 160, 2640–2657.
Pinto-Varelaa, T., Barbosa-P?voab, A.P. F.D., & Novais. A.Q. (2011). Bi-objective optimization approach to the design and planning of supply chains: Economic versus environmental performances. Computers and Chemical Engineering, 35, 1454– 1468.
Sabri, E.H., & Beamon, B.M. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega, 28, 581-598.
Schulz, E.P., Diaz, M.S., & Bandoni, J.A. (2005). Supply chain optimization of large-scale continuous processes. Computers and Chemical Engineering, 29, 1305–1316.
Shi, C., Lu, J., & Zhang, G. (2005-a). An extended Kth-best approach for linear bilevel programming. Applied Mathematics and Computation, 164, 843–855.
Shi, C., Lu, J., & Zhang, G. (2005-b). An extended Kuhn–Tucker approach for linear bilevel programming. Applied Mathematics and Computation, 162, 51–63.
Shi, C., Zhou, H., Lu, J., Zhang, G., & Zhang, Z. (2007). The Kth-best approach for linear bilevel multifollower programming with partial shared variables among followers. Applied Mathematics and Computation, 188, 1686–1698.
Wada, T., Shimizu, Y., & Yoo, J.K. (2001). Entire Supply Chain Optimization in Terms of Hybrid in Approach. European Symposium on Computer Aided Process Engineering, 15, 1591-1596.
Wang, G., Wan, Z., Wang, X., & Lv, Y. (2008). Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem. Computers and Mathematics with Applications, 56, 2550–2555.
Wang, G., Wang, X. & Wan, Z. (2009). A fuzzy interactive decision making algorithm for bilevel multi-followers programming with partial shared variables among followers. Expert Systems with Applications, 36, 10471–10474.
Wang, G., Zhu, K. & Wan, Z. (2010). An approximate programming method based on the simplex method for bilevel programming problem. Computers and Mathematics with Applications, 59, 3355–3360.
Wang, F., Lai, X., & Shi, N. (2010). A multi-objective optimization for green supply chain network design. Decision Support Systems, 51, 262–269.
Yadav, S.R., Muddada, R.R. M.R.,Tiwari, M.K., & Shankar, R. (2009). An algorithm portfolio based solution methodology to solve a supply chain optimization problem. Expert Systems with Applications, 36, 8407–8420.
Yao, J., & Liu L. (2009). Optimization analysis of supply chain scheduling in mass customization. Int. J. Production Economics, 117, 197–211.
Zhang, G., & Lu, J.C. (2010). Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J Glob Optim, 47, 403–419.
Zhang, G., Lu, J., Montero, J., & Zeng, Y. (2010). Model, solution concept, and Kth-best algorithm for linear trilevel programming. Information Sciences, 180. 481–492.
Zheng, Y., Wana, Z., & Wang, G. (2011). A fuzzy interactive method for a class of bilevel multiobjective programming problem. Expert Systems with Applications, 38, 10384–10388.
Zhou, Z., Cheng, S., & Hua, B. (2000). Supply chain optimization of continuous process industries with sustainability considerations. Computers and Chemical Engineering, 24, 1151 – 1158.
Alborzi, F., Vafaei, H., Gholami, M.H., & Esfahani, M.M.S. (2011). A Multi-Objective Model for Supply Chain Network Design under Stochastic Demand. World Academy of Science, Engineering and Technology, 10, 13-20.
Altiparmak, F., Gen, M., Lin, L., & Paksoy, T. (2006). A genetic algorithm approach for multi-objective optimization of supply chain networks. Computers & Industrial Engineering, 51, 196–215.
Ansari, E., & Zhiani Rezai, H. (2011). Solving Multi-objective Linear Bilevel Multi-follower Programming Problem. Int. J. Industrial Mathematics, 3, 303-316.
Azaron, A., Brown, K.N., Tarim, S.A., & Modarres, M. (2008). A multi-objective stochastic programming approach for supply chain design considering risk. Int. J. Production Economics, 116, 129–138.
Baky, I.A. (2010). Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Applied Mathematical Modeling, 34, 2377–2387.
Calvete, H. I., & Galé, C. (2004). Optimality conditions for the linear fractional/ quadratic bilevel problem. Monograf?as del Seminario Matem?tico Garc?a de Galdeano, 236, 3751–3762.
Calvete, H. I., & Galé, C. (2012). Linear bilevel programming with interval coefficients. Journal of Computational and Applied Mathematics, 31, 285–294.
Chaudhuri, B.B., & Rosenfeld, A. (1999). A modified hausdorff distance between fuzzy sets. Information science, 118,159-171.
Chan, F.T.S., & Chung, S.H. (2004). Multi-criteria genetic optimization for distribution network problems. Int J Adv Manuf Technol, 24, 517–532.
Chen, C.L., & Lee, W.C. (2004). Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Computers and Chemical Engineering, 28, 1131–1144.
Diamond, p. & Kloeden, P. (1994). Metric Spaces of fuzzy sets theory and applications, Word Scientific Publishing, Singapore.
Gao, J., & Liu, B. (2005). Fuzzy Multilevel Programming with a Hybrid Intelligent Algorithm. Computers and Mathematics with Applications, 49, 1539-1548.
Gao, Y., Zhang, G., Lu, J., & Wee, H.M. (2010). Particle swarm optimization for bi-level pricing problems in supply chains. Journal of Global Optimization, 51, 245–254.
Gebreslassie, B.H., Yao, Y., & You, F. (2012). Design Under Uncertainty of Hydrocarbon Biorefinery Supply Chains: Multiobjective Stochastic Programming Models, Decomposition Algorithm, and a Comparison Between CVaR and Downside Risk. American Institute of Chemical Engineers, 58, 2155- 2179.
Guillén, G., Mele, F.D., Bagajewicz, M.J., Espu?a, A., & Puigjaner, L. (2005). Multiobjective supply chain design under uncertainty. Chemical Engineering Science, 60, 1535 – 1553.
Kumar, M., Vrat, P., & Shankar, R. (2006). A fuzzy programming approach for vendor selection problem in a supply chain. Int. J. Production Economics, 101, 273–285.
Kuo, R.J., & Huang, C.C. (2009). Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Computers and Mathematics with Applications, 58, 678-685.
Jiang, Y., Li, X., Huang, C., & Wu, X. (2013). Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem. Applied Mathematics and Computation, 219, 4332–4339.
Jimenez, M., Arenas, M., Bilbao, A., & Rodr?guez, M.V. (2007). Linear programming with fuzzy parameters: An interactive method resolution. European Journal of Operational Research, 177, 1599–1609.
Jula P., & Leachman R.C. (2011). A supply-chain optimization model of the allocation of containerized imports from Asia to the United States. Transportation Research Part E, 47, 609–622.
Jung, J.Y., Blau, G., Pekny, J., Reklaitis, G., & Eversdyk, D. (2004). A simulation based optimization approach to supply chain management under demand uncertainty. Computers and Chemical Engineering, 28, 2087–2106.
Lakhal, S., Martel, A., Kettani, O., & Oral, M. (2001). On the optimization of supply chain networking decisions. European Journal of Operational Research, 129, 259-270.
Li, G. (2012). Fuzzy goal programming – A parametric approach. Information Sciences, 195, 287–295.
Liang, T.F., & Cheng, H.W. (2009). Application of fuzzy sets to manufacturing/ distribution planning decisions with multi-product and multi-time period in supply chains. Expert Systems with Applications, 36, 3367–3377.
Lin, X., Quan-sheng, L., & Wan-sheng T. (2008). Hybrid Intelligent Algorithm for Solving the Bilevel Programming Models with Fuzzy Variables. Systems Engineering - Theory & Practice, 28, 100–104.
Lu, J., Shi, C., & Zhang, G. (2006). On bilevel multi-follower decision making: General framework and solutions. Information Sciences, 176, 1607–1627.
Mele, F. D., Guillen, G., Espuna, A., & Puigjaner, L. (2007). An agent-based approach for supply chain retrofitting under uncertainty. Computers and Chemical Engineering, 31, 722–735.
Mishra, S. (2007). Weighting method for bi-level linear fractional programming problems, European Journal of Operational Research, 183, 296–302.
Mokashi, S.D. and Kokossis, A.C. (2003). Application of dispersion algorithms to supply chain optimization, Computers and Chemical Engineering, 27, 927-949.
Osman, M.S., Abo-Sinna, M.A., Amer, A.H., & Emam, O.E. (2004). A multi-level non-linear multi-objective decision-making under fuzziness. Applied Mathematics and Computation, 153, 239–252.
Paksoy, T., & Pehlivan, N.Y. (2012). A fuzzy linear programming model for the optimization of multi-stage supply chain networks with triangular and trapezoidal membership functions. Journal of the Franklin Institute, 349, 93–109.
Peidro, D., Mula, J., Poler, R., & Verdegay, J.L. (2009). Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and System, 160, 2640–2657.
Pinto-Varelaa, T., Barbosa-P?voab, A.P. F.D., & Novais. A.Q. (2011). Bi-objective optimization approach to the design and planning of supply chains: Economic versus environmental performances. Computers and Chemical Engineering, 35, 1454– 1468.
Sabri, E.H., & Beamon, B.M. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega, 28, 581-598.
Schulz, E.P., Diaz, M.S., & Bandoni, J.A. (2005). Supply chain optimization of large-scale continuous processes. Computers and Chemical Engineering, 29, 1305–1316.
Shi, C., Lu, J., & Zhang, G. (2005-a). An extended Kth-best approach for linear bilevel programming. Applied Mathematics and Computation, 164, 843–855.
Shi, C., Lu, J., & Zhang, G. (2005-b). An extended Kuhn–Tucker approach for linear bilevel programming. Applied Mathematics and Computation, 162, 51–63.
Shi, C., Zhou, H., Lu, J., Zhang, G., & Zhang, Z. (2007). The Kth-best approach for linear bilevel multifollower programming with partial shared variables among followers. Applied Mathematics and Computation, 188, 1686–1698.
Wada, T., Shimizu, Y., & Yoo, J.K. (2001). Entire Supply Chain Optimization in Terms of Hybrid in Approach. European Symposium on Computer Aided Process Engineering, 15, 1591-1596.
Wang, G., Wan, Z., Wang, X., & Lv, Y. (2008). Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem. Computers and Mathematics with Applications, 56, 2550–2555.
Wang, G., Wang, X. & Wan, Z. (2009). A fuzzy interactive decision making algorithm for bilevel multi-followers programming with partial shared variables among followers. Expert Systems with Applications, 36, 10471–10474.
Wang, G., Zhu, K. & Wan, Z. (2010). An approximate programming method based on the simplex method for bilevel programming problem. Computers and Mathematics with Applications, 59, 3355–3360.
Wang, F., Lai, X., & Shi, N. (2010). A multi-objective optimization for green supply chain network design. Decision Support Systems, 51, 262–269.
Yadav, S.R., Muddada, R.R. M.R.,Tiwari, M.K., & Shankar, R. (2009). An algorithm portfolio based solution methodology to solve a supply chain optimization problem. Expert Systems with Applications, 36, 8407–8420.
Yao, J., & Liu L. (2009). Optimization analysis of supply chain scheduling in mass customization. Int. J. Production Economics, 117, 197–211.
Zhang, G., & Lu, J.C. (2010). Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J Glob Optim, 47, 403–419.
Zhang, G., Lu, J., Montero, J., & Zeng, Y. (2010). Model, solution concept, and Kth-best algorithm for linear trilevel programming. Information Sciences, 180. 481–492.
Zheng, Y., Wana, Z., & Wang, G. (2011). A fuzzy interactive method for a class of bilevel multiobjective programming problem. Expert Systems with Applications, 38, 10384–10388.
Zhou, Z., Cheng, S., & Hua, B. (2000). Supply chain optimization of continuous process industries with sustainability considerations. Computers and Chemical Engineering, 24, 1151 – 1158.