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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 312527, 12 pages
A Class of Expected Value Bilevel Programming Problems with Random Coefficients Based on Rough Approximation and Its Application to a Production-Inventory System
Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, China
Received 1 February 2013; Revised 16 April 2013; Accepted 19 April 2013
Academic Editor: Ryan Loxton
Copyright © 2013 Liming Yao and Jiuping Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- O. E. Emam, “A fuzzy approach for bi-level integer non-linear programming problem,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 62–71, 2006.
- G. B. Dantzig and A. Madansky, “On the solution of two-stage linear programs under uncertainty,” in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Statistical Laboratory, University of California, June 1960.
- C. Liu, Y. Fan, and F. Ordóñez, “A two-stage stochastic programming model for transportation network protection,” Computers & Operations Research, vol. 36, no. 5, pp. 1582–1590, 2009.
- J. Y. Jung, G. Blau, J. F. Pekny, G. V. Reklaitis, and D. Eversdyk, “Integrated safety stock management for multi-stage supply chains under production capacity constraints,” Computers and Chemical Engineering, vol. 32, no. 11, pp. 2570–2581, 2008.
- T. Paksoy and C.-T. Chang, “Revised multi-choice goal programming for multi-period, multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing,” Applied Mathematical Modelling, vol. 34, no. 11, pp. 3586–3598, 2010.
- H. Sun, Z. Gao, and J. Wu, “A bi-level programming model and solution algorithm for the location of logistics distribution centers,” Applied Mathematical Modelling, vol. 32, no. 4, pp. 610–616, 2008.
- E. Roghanian, S. J. Sadjadi, and M. B. Aryanezhad, “A probabilistic bi-level linear multi-objective programming problem to supply chain planning,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 786–800, 2007.
- X. Ji and Z. Shao, “Model and algorithm for bilevel newsboy problem with fuzzy demands and discounts,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 163–174, 2006.
- A. Charnes and W. W. Cooper, “Deterministic equivalents for optimizing and satisficing under chance constraints,” Operations Research, vol. 11, pp. 18–39, 1963.
- J. R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer, New York, NY, USA, 1997.
- Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982.
- Z. Pawlak and R. Sowinski, “Rough set approach to multi-attribute decision analysis,” European Journal of Operational Research, vol. 72, no. 3, pp. 443–459, 1994.
- J. Xu and L. Yao, “A class of multiobjective linear programming models with random rough coefficients,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 189–206, 2009.
- E. A. Youness, “Characterizing solutions of rough programming problems,” European Journal of Operational Research, vol. 168, no. 3, pp. 1019–1029, 2006.
- Y. Shi, L. Yao, and J. Xu, “A probability maximization model based on rough approximation and its application to the inventory problem,” International Journal of Approximate Reasoning, vol. 52, no. 2, pp. 261–280, 2011.
- L. N. Vicente and P. H. Calamai, “Bilevel and multilevel programming: a bibliography review,” Journal of Global Optimization, vol. 5, no. 3, pp. 291–306, 1994.
- J. F. Bard and J. T. Moore, “A branch and bound algorithm for the bilevel programming problem,” Society for Industrial and Applied Mathematics, vol. 11, no. 2, pp. 281–292, 1990.
- O. Ben-Ayed and C. E. Blair, “Computational difficulties of Bi-level Linear Programming,” Operations Research, vol. 38, no. 3, pp. 556–560, 1990.
- W. F. Bialas and M. H. Karwan, “Two-level linear programming,” Management Science, vol. 30, no. 8, pp. 1004–1020, 1984.
- J. Fortuny-Amat and B. McCarl, “A representation and economic interpretation of a two-level programming problem,” The Journal of the Operational Research Society, vol. 32, no. 9, pp. 783–792, 1981.
- S. Sinha and S. B. Sinha, “KKT transformation approach for multi-objective multi-level linear programming problems,” European Journal of Operational Research, vol. 143, no. 1, pp. 19–31, 2002.
- M. Sakawa, I. Nishizaki, and Y. Uemura, “Interactive fuzzy programming for multilevel linear programming problems,” Computers & Mathematics with Applications, vol. 36, no. 2, pp. 71–86, 1998.
- M. Sakawa, “Interactive fuzzy goal programming for nonlinear programming problems and its applications to water quality management,” Control and Cybernetics, vol. 13, pp. 217–228, 1984.
- S. Pramanik and T. K. Roy, “Fuzzy goal programming approach to multilevel programming problems,” European Journal of Operational Research, vol. 176, no. 2, pp. 1151–1166, 2007.
- S. R. Hejazi, A. Memariani, G. Jahanshahloo, and M. M. Sepehri, “Linear bilevel programming solution by genetic algorithm,” Computers and Operations Research, vol. 29, no. 13, pp. 1913–1925, 2002.
- K. H. Sahin and A. R. Ciric, “A dual temperature simulated annealing approach for solving bilevel programming problems,” Computers and Chemical Engineering, vol. 23, no. 1, pp. 11–25, 1998.
- M. Gendreau, P. Marcotte, and G. Savard, “A hybrid tabu-ascent algorithm for the linear bilevel programming problem,” Journal of Global Optimization, vol. 8, no. 3, pp. 217–233, 1996.
- S. F. Woon, V. Rehbock, and R. C. Loxton, “Global optimization method for continuous-time sensor scheduling,” Nonlinear Dynamics and Systems Theory, vol. 10, no. 2, pp. 175–188, 2010.
- S. F. Woon, V. Rehbock, and R. Loxton, “Towards global solutions of optimal discrete-valued control problems,” Optimal Control Applications & Methods, vol. 33, no. 5, pp. 576–594, 2012.
- D. D. Wu, “BiLevel programming data envelopment analysis with constrained resource,” European Journal of Operational Research, vol. 207, no. 2, pp. 856–864, 2010.
- R. Slowinski and D. Vanderpooten, “A generalized definition of rough approximations based on similarity,” IEEE Transactions on Knowledge and Data Engineering, vol. 12, no. 2, pp. 331–336, 2000.
- Y. Yao, “Probabilistic rough set approximations,” International Journal of Approximate Reasoning, vol. 49, no. 2, pp. 255–271, 2008.
- M. Sakawa, I. Nishizaki, and Y. Uemura, “Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters,” Fuzzy Sets and Systems, vol. 109, no. 1, pp. 3–19, 2000.
- J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan, Ann Arbor, Mich, USA, 1975.
- D. B. Fogel, Evolution Computation: Toward a New Philosophy of Machine Intelligence, IEEE Press, Piscataway, NJ, USA, 1995.
- J. R. Koza, Genetic Programming, The MIT Press, Cambridge, Mass, USA, 1992.
- C. Fonseca and P. Fleming, “An overview of evolutionary algorithms in multiobjective optimization,” Evolutionary Computation, vol. 3, pp. 1–16, 1995.
- Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, New York, NY, USA, 1994.
- D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, New York, NY, USA, 1989.
- M. Gen and R. Cheng, Gennetic Algorithms and Engineering Design, Wiley, New York, NY, USA, 1997.
- J. Gao and B. Liu, “Fuzzy multilevel programming with a hybrid intelligent algorithm,” Computers & Mathematics with Applications, vol. 49, no. 9-10, pp. 1539–1548, 2005.