Multifollower trilevel decision making models and system

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In a trilevel hierarchical decision problem, the objectives and variables of each decision entity at one level are controlled, in part, by the decision entities at other levels. The choice of values for the decision variables at each level may influence the decisions made at other levels, and may thereby improve/reduce the objective for each level. When multiple decision entities are involved at the middle and bottom levels of a trilevel decision problem, the top-level entity's decision will be affected, not only by these followers' individual reactions, but also by the relationships between them. We call this problem a multifollower trilevel (MFTL) decision. This paper firstly defines and analyzes various kinds of relationships between decision entities in an MFTL decision problem. We then propose an MFTL decision making framework, in which 64 standard MFTL decision situations and their possible combinations are identified. To model these MFTL decision situations, we developed an innovative decision entity-relationship diagram (DERD) approach. We also established a general model for MFTL decision making and a set of standard MFTL decision models using trilevel programming. A trilevel decision support system (TLDSS) software has also been developed to transfer a DERD into a programming model. Finally, a case study illustrates typical MFTL decision making models and their development, using both DERD and programming approaches.
G. Anandalingam and T. Friesz "Hierarchical optimization:An introduction", Ann. Operations Res., vol. 34, pp.1 -11 1992 J. Bard "Optimality conditions for thebilevel programming problem", Naval Res. Log.Quart., vol. 31, pp.13 -26 1984 J. Bard Practical Bilevel Optimization,1998 :KluwerAcademic Publishers J. Bard and J. Falk "Necessary conditions for the linear threelevel programming problem", Proc. 21st IEEEConf. Decision Contr., vol. 21, pp.642 -646 1982 Abstract | Full Text: PDF (424KB) O. Ben-Ayed "Bilevel linear programming", Comput. Operations Res., vol. 20, pp.485 -501 1993 W. Bialas and M. Karwan "Two-level linear programming", Manag. Sci., vol. 30, pp.1004 -1020 1984 C. Blair "The computational complexityof multi-level linear programs", Ann. OperationsRes., vol. 34, pp.13 -19 1992 W. Candler and R. Townsley "A linear two-level programmingproblem", Comput. Operations Res., vol. 9, pp.59 -76 1982 D. Cao and M. Chen "Capacitated plant selection in a decentralized manufacturingenvironment: A bilevel optimization approach", Eur.J. Operational Res., vol. 169, pp.97 -110 2006 S. Chen , J. Zhang , Y. Li and J. Zhang "A hierarchical model incorporating segmented regions andpixel descriptors for video background subtraction", IEEETrans. Ind. Informat., vol. 8, no. 1, pp.118 -127 2012 Abstract | Full Text: PDF (849KB) | Full Text: HTML K. Deb and A. Sinha Y. Shi , S. Wang , Y. Peng , J Li and Y. Zeng Cutting-Edge Research Topics on Multiple Criteria Decision Making, vol. 35, pp.17 -24 2009 :Communicationsin Computer and Information Science S. Dempe Foundations of Bilevel rogramming,2002 :KluwerAcademic Publishers C. Feng and C. Wen "Bi-level and multi-objective model to controltraffic flow into the disaster area post earthquake", J.Eastern Asia Soc. Transportation Stud., vol. 6, pp.4253 -4268 2005 Y. Gao , G. Zhang , J. Ma and J. Lu "A $\lambda$-cut and goal programming based algorithm for fuzzy linear multipleobjective bilevel optimization", IEEE Trans.Fuzzy Syst., vol. 18, no. 1, pp.1 -13 2010 Abstract | Full Text: PDF (1192KB) | Full Text: HTML Y. Gao , G. Zhang , J. Lu and H. Wee "Particle swarm optimization for bi-level pricing problemsin supply chains", J. Global Optimiz., vol. 51, pp.245 -254 2011 B. F. Hobbs , B. Metzler and J. Pang "Strategic gaming analysis for electric powersystem: An MPEC approach", IEEE Trans. PowerSyst., vol. 15, no. 2, pp.637 -645 2000 Abstract | Full Text: PDF (144KB) M. L. Rosa , A. T. Hofstede , P. Wohed , H. Reijers , J. Mendling and W. van der Aalst "Managing process model complexity via concretesyntax modifications", IEEE Trans. Ind. Informat., vol. 7, no. 2, pp.255 -265 2011 Abstract | Full Text: PDF (985KB) | Full Text: HTML M. Labbé , P. Marcotte and G. Savard "A bilevel model of taxationand its application to optimal highway pricing", Manag.Sci., vol. 44, pp.1608 -1822 1999 Y. Lai "Hierarchical optimization:A satisfactory solution", Fuzzy Sets Syst., vol. 77, pp.321 -335 1996 J. Lu , C. Shi and G. Zhang "On bilevel multi-follower decision-making: General frameworkand solutions", Inform. Sci., vol. 176, pp.1607 -1627 2006 J. Lu , C. Shi , G. Zhang and T. Dillon "Model and extended Kuhn-Tucker approach for bilevel multi-followerdecision making in a referential-uncooperative situation", J. Global Optimiz., vol. 38, pp.597 -608 2007a Z. Lukac , K. Soric and V. Rosenzweig "Production planning problem with sequencedependent setups as a bilevel programming problem", Eur.J. Operational Res., vol. 187, pp.1504 -1512 2008 A. Migdalas , P. Pardalos and P.Varbrand Multilevel Optimization: Algorithmsand Applications, 1997 :Kluwer Academic Publishers A. Ning , H. Lau , Y. Zhao and T. Wong "Fulfillment of retailer demand by using the MDL-optimalneural network prediction and decision policy", IEEETrans. Ind. Informat., vol. 5, no. 4, pp.495 -506 2009 Abstract | Full Text: PDF (1654KB) | Full Text: HTML H. Shih , Y. Lai and E. Lee "Fuzzy approach for multi-level programming problems", Comput. Operation Res., vol. 23, pp.73 -91 1996 H. Stackelberg Theory of the Market Economy, 1952 :Oxford Univ. Press U. Wen and S. Hsu "Linear bilevel programming problems—Areview", J. Operational Res. Soc., vol. 42, pp.123 -133 1991 D. White "Penalty function approach tolinear trilevel programming", J. Optimiz. TheoryAppl., vol. 93, pp.183 -197 1997 G. Zhang , G. Zhang , Y. Gao and J. Lu "Competitive strategic bidding optimization in electricitymarkets using bi-level programming and swarm technique", IEEE Trans. Ind. Electron., vol. 58, pp.2138 -2146 2011 Abstract | Full Text: PDF (341KB) | Full Text: HTML G. Zhang , J. Lu , J. Montero and Y. Zeng "Model, Solution concept and the Kth-best algorithm for lineartri-level programming", Inform. Sci., vol. 180, pp.481 -492 2010