A fuzzy multi-objective multi-follower linear Bi-level programming problem to supply chain optimization

Uncertain Supply Chain Management

Volumn 1, Issue 4, 2013, Pages 193-206

  Taran, M ^a   Roghanian, E ^a  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Bilevel programming; Fuzzy sets; Multi follower programming; Multi objective decision making; Supply chain optimization

Indexed keywords

EID: 84961747518     PISSN: 22916822     EISSN: 22916830     Source Type: Journal    
DOI: 10.5267/j.uscm.2013.09.003     Document Type: Article

References (50)

1. 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.
2. 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.
3. 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.
4. Ansari, E., & Zhiani Rezai, H. (2011). Solving Multi-objective Linear Bilevel Multi-follower Programming Problem. Int. J. Industrial Mathematics, 3, 303-316.
5. 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.
6. Baky, I.A. (2010). Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Applied Mathematical Modeling, 34, 2377-2387.
7. Calvete, H. I., & Galé, C. (2004). Optimality conditions for the linear fractional/ quadratic bilevel problem. Monografías del Seminario Matemático García de Galdeano, 236, 3751-3762.
8. Calvete, H. I., & Galé, C. (2012). Linear bilevel programming with interval coefficients. Journal of Computational and Applied Mathematics, 31, 285-294.
9. Chaudhuri, B.B., & Rosenfeld, A. (1999). A modified hausdorff distance between fuzzy sets. Information science, 118, 159-171.
10. Chan, F.T.S., & Chung, S.H. (2004). Multi-criteria genetic optimization for distribution network problems. Int J Adv Manuf Technol, 24, 517-532.
11. 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.
12. Diamond, p. & Kloeden, P. (1994). Metric Spaces of fuzzy sets theory and applications, Word Scientific Publishing, Singapore.
13. Gao, J., & Liu, B. (2005). Fuzzy Multilevel Programming with a Hybrid Intelligent Algorithm. Computers and Mathematics with Applications, 49, 1539-1548.
14. 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.
15. 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.
16. Guillén, G., Mele, F.D., Bagajewicz, M.J., Espuña, A., & Puigjaner, L. (2005). Multiobjective supply chain design under uncertainty. Chemical Engineering Science, 60, 1535-1553.
17. 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.
18. 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.
19. 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.
20. Jimenez, M., Arenas, M., Bilbao, A., & Rodrıguez, M.V. (2007). Linear programming with fuzzy parameters:An interactive method resolution. European Journal of Operational Research, 177, 1599-1609.
21. 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.
22. 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.
23. 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.
24. Li, G. (2012). Fuzzy goal programming-A parametric approach. Information Sciences, 195, 287-295.
25. 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.
26. 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.
27. Lu, J., Shi, C., & Zhang, G. (2006). On bilevel multi-follower decision making: General framework and solutions. Information Sciences, 176, 1607-1627.
28. 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.
29. Mishra, S. (2007). Weighting method for bi-level linear fractional programming problems, European Journal of Operational Research, 183, 296-302.
30. Mokashi, S.D. and Kokossis, A.C. (2003). Application of dispersion algorithms to supply chain optimization, Computers and Chemical Engineering, 27, 927-949.
31. 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.
32. 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.
33. 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.
34. Pinto-Varelaa, T., Barbosa-Póvoab, 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.
35. 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.
36. 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.
37. Shi, C., Lu, J., & Zhang, G. (2005-a). An extended Kth-best approach for linear bilevel programming. Applied Mathematics and Computation, 164, 843-855.
38. Shi, C., Lu, J., & Zhang, G. (2005-b). An extended Kuhn-Tucker approach for linear bilevel programming. Applied Mathematics and Computation, 162, 51-63.
39. 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.
40. 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.
41. 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.
42. Wang, G., Wang, X. & Wan, Z. (2009). A fuzzy interactive decision making algorithm for bilevel multifollowers programming with partial shared variables among followers. Expert Systems with Applications, 36, 10471-10474.
43. 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.
44. Wang, F., Lai, X., & Shi, N. (2010). A multi-objective optimization for green supply chain network design. Decision Support Systems, 51, 262-269.
45. 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.
46. Yao, J., & Liu L. (2009). Optimization analysis of supply chain scheduling in mass customization. Int. J. Production Economics, 117, 197-211.
47. Zhang, G., & Lu, J.C. (2010). Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J Glob Optim, 47, 403-419.
48. 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.
49. 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.
50. Zhou, Z., Cheng, S., & Hua, B. (2000). Supply chain optimization of continuous process industries with sustainability considerations. Computers and Chemical Engineering, 24, 1151-1158.