Model, solution concept, and Kth-best algorithm for linear trilevel programming

Information Sciences

Volumn 180, Issue 4, 2010, Pages 481-492

  Zhang, Guangquan ^a   Lu, Jie ^a   Montero, Javier ^b   Zeng, Yi ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Bilevel programming; Decision support systems; Hierarchical decision making; Kth best algorithm; Optimization; Trilevel programming

Indexed keywords

ALGORITHM OPTIMIZATION; BILEVEL PROGRAMMING; COMPLEX PROBLEMS; DECISION SUPPORT TOOLS; HIERARCHICAL OPTIMIZATION; PARTIAL CONTROL; SOLUTION CONCEPTS;

ALGORITHMS; DECISION SUPPORT SYSTEMS; DECISION THEORY; HIERARCHICAL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

DECISION MAKING;

EID: 71149097662     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2009.10.013     Document Type: Article

References (39)

1. Abo-Sinna M.A., and Baky I.A. Interactive balanced space approach for solving multi-level multi-objective programming problems. Information Sciences 177 16 (2007) 3397-3410
2. Amat J., and McCarl B. A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society 32 (1981) 783-792
3. Anandalingam G., and Friesz T. Hierarchical optimization: an introduction. Annals of Operations Research 34 (1992) 1-11
4. Bard J. Optimality conditions for the bilevel programming problem. Naval Research Logistics Quarterly 31 (1984) 13-26
5. Bard J. Practical Bilevel Optimization (1998), Kluwer, Dordrecht
6. Bard J., and Falk J. An explicit solution to the multi-level programming problem. Computer and Operations Research 9 (1982) 77-100
7. J. Bard, J. Falk, Necessary conditions for the linear three-level programming problem, in: Proceedings of the 21st IEEE Conference on Decision and Control, vol. 21, 1982, pp. 642-646.
8. Bard J., and Moore J.T. A branch-and-bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing 11 (1990) 281-292
9. Ben-Ayed O. Bilevel linear programming. Computers and Operations Research 20 (1993) 485-501
10. Bialas W., and Karwan M. Two-level linear programming. Management Science 30 (1984) 1004-1020
11. Blair C. The computational complexity of multi-level linear programs. Annals of Operations Research 34 (1992) 13-19
12. Calvete H.I., Gale C., and Mateo P.M. A new approach for solving linear bilevel problems using genetic algorithms. European Journal of Operational Research 188 (2008) 14-28
13. Cao D., and Leung L.C. A partial cooperation model for non-unique linear two-level decision problems. European Journal of Operational Research 140 (2002) 134-141
14. Cao D., and Chen M. Capacitated plant selection in a decentralized manufacturing environment: a bilevel optimization approach. European Journal of Operational Research 169 (2006) 97-110
15. Chiou S.-W. A bi-level programming for logistics network design with system-optimized flows. Information Sciences 179 14 (2009) 2434-2441
16. Cutello V., and Montero J. Hierarchies of aggregation operators. International Journal of Intelligent Systems 9 (1994) 1025-1045
17. Dempe S. Foundations of Bilevel Programming (2002), Kluwer, Dordrecht
18. Feng C., and Wen C. Bi-level and multi-objective model to control traffic flow into the disaster area post-earthquake. Journal of the Eastern Asia Society for Transportation Studies 6 (2005) 4253-4268
19. Hansen P., Jaumard B., and Savard G. New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical Computing 13 (1992) 1194-1217
20. Hobbs B.F., Metzler B., and Pang J.S. Strategic gaming analysis for electric power systems: an MPEC approach. IEEE Transactions on Power Systems 15 (2000) 637-645
21. Labbé M., Marcotte P., and Savard G. A bilevel model of taxation and its application to optimal highway pricing. Management Science 44 (1999) 1608-1822
22. Lai Y.J. Hierarchical optimization: a satisfactory solution. Fuzzy Sets and Systems 77 (1996) 321-335
23. Liu B. Stackelberg-Nash equilibrium for multilevel programming with multiple followers using genetic algorithms. Computers and Mathematics with Applications 36 (1998) 79-89
24. Lu J., Shi C., and Zhang G. On bilevel multi-follower decision-making: general framework and solutions. Information Sciences 176 (2006) 1607-1627
25. Lu J., Shi C., Zhang G., and Dillon T. Model and extended Kuhn-Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation. International Journal of Global Optimization 38 (2007) 597-608
26. Lu J., Shi C., Zhang G., and Ruan D. An extended branch-and-bound algorithm for bilevel multi-follower decision making in a referential-uncooperative situation. International Journal of Information Technology and Decision Making 6 (2007) 371-388
27. Lukac Z., Soric K., and Rosenzweig V.V. Production planning problem with sequence dependent setups as a bilevel programming problem. European Journal of Operational Research 187 (2008) 1504-1512
28. Montero J., Gomez D., and Bustince H. On the relevance of some families of fuzzy sets. Fuzzy Sets and Systems 158 (2007) 2429-2442
29. Sakawa M., Nishizaki I., and Uemura Y. Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters. Fuzzy Sets and Systems 109 (2000) 3-19
30. Shi X., and Xia H. Interactive bilevel multi-objective decision making. Journal of the Operational Research Society 48 (1997) 943-949
31. Shih H.S., Lai Y.J., and Lee E.S. Fuzzy approach for multi-level programming problems. Computers and Operations Research 23 (1996) 73-91
32. Sinha S., and Sinha S.B. KKT transformation approach for multi-objective multi-level linear programming problems. European Journal of Operational Research 143 (2002) 19-31
33. Taha H.A. Operations Research: An Introduction. eighth ed. (2007), Prentice-Hall
34. Stackelberg H.V. Theory of the Market Economy (1952), Oxford University Press, New York
35. Wen U.P., and Hsu S.T. Linear bilevel programming problems - a review. Journal of the Operational Research Society 42 (1991) 123-133
36. White D. Penalty function approach to linear trilevel programming. Journal of Optimization Theory and Applications 93 (1997) 183-197
37. White D., and Anandalingam G. A penalty function approach for solving bi-level linear programs. Journal of Global Optimization 3 (1993) 397-419
38. Zhang G., and Lu J. Model and approach of fuzzy bilevel decision making for logistics planning problem. Journal of Enterprise Information Management 20 (2007) 178-197
39. Zhang G., Lu J., and Dillon T. Decentralized multi-objective bilevel decision making with fuzzy demands. Knowledge-Based Systems 20 (2007) 495-507