Decentralized multi-objective bilevel decision making with fuzzy demands

Decisions in a decentralized organization often involve two levels. The leader at the upper level attempts to optimize his/her objective but is affected by the follower; the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. When model a real-world bilevel decision problem, it also may involve fuzzy demands which appear either in the parameters of objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously in achieving a solution. This study addresses both fuzzy demands and multi-objective issues and propose a fuzzy multi-objective bilevel programming model. It then develops an approximation branch-and-bound algorithm to solve multi-objective bilevel decision problems with fuzzy demands. Finally, two case-based examples further illustrate the proposed model and algorithm.

[1]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[2]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[3]  Masatoshi Sakawa,et al.  Interactive decision making for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms , 2000, Fuzzy Sets Syst..

[4]  Jie Lu,et al.  An extended Kuhn-Tucker approach for linear bilevel programming , 2005, Appl. Math. Comput..

[5]  Guangquan Zhang,et al.  An Approximation Branch-and-Bound Algorithm for Fuzzy Bilevel Decision Making Problems , 2006 .

[6]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for two-level linear fractional programming problems , 2001, Fuzzy Sets Syst..

[7]  Terry L. Friesz,et al.  Hierarchical optimization: An introduction , 1992, Ann. Oper. Res..

[8]  G. Anandalingam,et al.  A penalty function approach for solving bi-level linear programs , 1993, J. Glob. Optim..

[9]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[10]  Tan HEURISTIC ALGORITHMS FOR DELIVERED PRICE SPATIALLY COMPETITIVE NETWORK FACILITY LOCATION PROBLEMS , .

[11]  Hong Zhou,et al.  An extended branch and bound algorithm for linear bilevel programming , 2006, Appl. Math. Comput..

[12]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters , 2000, Fuzzy Sets Syst..

[13]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

[14]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[15]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters , 2000 .

[16]  Masatoshi Sakawa,et al.  Fuzzy Sets and Interactive Multiobjective Optimization , 1993 .

[17]  Tharam S. Dillon,et al.  Solution Concepts and an Approximation Kuhn–Tucker Approach for Fuzzy Multiobjective Linear Bilevel Programming , 2008 .

[18]  E. Stanley Lee,et al.  Compensatory fuzzy multiple level decision making , 2000, Fuzzy Sets Syst..

[19]  Jie Lu,et al.  The Definition of Optimal Solution and an Extended Kuhn-Tucker Approach for Fuzzy Linear Bilevel Programming , 2005, IEEE Intell. Informatics Bull..

[20]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for two-level nonconvex programming problems with fuzzy parameters through genetic algorithms , 2002, Fuzzy Sets Syst..

[21]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications) , 2006 .

[22]  Guangquan Zhang,et al.  Model and approach of fuzzy bilevel decision making for logistics planning problem , 2007, J. Enterp. Inf. Manag..

[23]  Tharam S. Dillon,et al.  An Approximation Kuhn-Tucker Approach for Fuzzy Linear Bilevel Decision Making , 2008, Intelligent Decision Making: An AI-Based Approach.

[24]  S. Dempe A simple algorithm for the-linear bilevel programming problem , 1987 .

[25]  Yao Chen,et al.  A descent dual approach for linear bilevel programs. Technical Report CRT866 , 1992 .

[26]  Surabhi Sinha,et al.  Fuzzy programming approach to multi-level programming problems , 2003, Fuzzy Sets Syst..

[27]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters , 2000, Fuzzy Sets Syst..

[28]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[29]  Jerome Bracken,et al.  Mathematical Programs with Optimization Problems in the Constraints , 1973, Oper. Res..

[30]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for decentralized two-level linear programming problems , 2002, Fuzzy Sets Syst..

[31]  Da Ruan,et al.  An Extended Branch and Bound Algorithm for bilevel Multi-Follower Decision Making in a Referential-Uncooperative Situation , 2007, Int. J. Inf. Technol. Decis. Mak..

[32]  Fatma Tiryaki,et al.  Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems , 2006, Fuzzy Sets Syst..

[33]  Wilfred Candler,et al.  A linear two-level programming problem, , 1982, Comput. Oper. Res..

[34]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[35]  C. Hwang Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .