Article Outline
Introduction
Formulation
Bilevel Programming
Bilevel Programming with Multi-Followers
Applications
Cases
Global Optimum of a Bilevel Programming Problem
Bilevel Programming Problem
Bilevel Programming Problem with Multi-Followers
Bilevel Programming with Uncertainty
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Acevedo J, Pistikopoulos EN (1997) A multiparametric programming approach for linear process engineering problems under uncertainty. Ind Eng Chem Res 36:717–728
Başar T, Olsder GJ (1982) Dynamic Noncooperative Game Theory. Academic Press, London
Cao D, Chen M (2006) Capacitated plant selection in a decentralized manufacturing environment: a bilevel optimization approach. Eur J Oper Res 169(1):97–110
Clark PA (1990) Bilevel programming for steady-state chemical process design – ii. performance study for nondegenerate problems. Comput Chem Eng 14(1):99–109
Clark PA, Westerberg AW (1990) Bilevel programming for steady-state chemical process design – i. fundamentals and algorithms. Comput Chem Eng 14(1):87–97
Dempe S (2003) Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3):33–359
Dempe S, Kalashnikov V, Ríos-Mercado RZ (2005) Discrete bilevel programming: Application to a natural gas cash-out problem. Eur J Oper Res 166:469–488
Deng X (1998) Complexity issues in bilevel linear programming. In: Multilevel optimization: algorithms and applications. Kluwer, Dordrecht, pp 149–164
Dua V, Bozinis A, Pistikopoulos EN (2002) A multiparametric programming approach for mixed-integer quadratic engineering problems. Comput Chem Eng 26:715–733
Dua V, Pistikopoulos EN (2000) An algorithm for the solution of multiparametric mixed integer linear programming problems. Ann Oper Res 99:123–139
Dua V (2000) Parametric programming techniques for process engineering problems under uncertainty. PhD thesis, Department of Chemical Engineering and Chemical Technology Imperial College of Science, Technology and Medicine London, London
Evans GW (1984) An overview of thecniques for solving multiobjective mathematical programs. Manag Sci 30(11):1268–1282
Faísca NP, Dua V, Saraiva PM, Rustem B, Pistikopoulos EN (2007) Parametric global optimisation for bilevel programming. J Glob Optim 38(4):609–623
Faísca NP, Saraiva PM, Rustem B, Pistikopoulos EN (2007) A multi-parametric programming approach for multi-level hierarchical and decentralised optimisation problems. Comput Manag Sci (in press)
Fiacco AV (1976) Sensitivity analysis for nonlinear programming using penalty methods. Math Program 10:287–311
Fiacco AV (1983) Introduction to sensitivity and stability analysis in nonlinear programming. Academic Press, New York
Floudas CA (2000) Deterministic global optimization. Kluwer, Dordrecht
Floudas CA, Pardalos PM, Adjiman CS, Esposito WR, Gümüş ZH, Harding ST, Klepeis JL, Meyer CA, Schweiger CA (1999) Handbook of test problems in local and global optimization. Kluwer, Dordrecht
Fortuny-Amat J, McCarl B (1981) A representation and economic interpretation of a two-level programming problem. J Oper Res Soc 32(9):783–792
Gümüş ZH, Floudas CA (2001) Global optimization of nonlinear bilevel programming problems. J Glob Optim 20(1):1–31
Hansen P, Jaumard B, Savard G (1992) New brach-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13:1194–1217
Lai Y (1996) Hierarchical optimization: a satisfactory solution. Fuzzy Sets Syst 77:321–335
LeBlanc LJ, Boyce DE (1985) A bilevel programming algorithm for exact solution of network design problem with user-optimal flows. Transp Res B Methodol 20:259–265
Liu B (1998) Stackelberg-nash equilibrium for multilevel programming with multiple followers using genetic algorithms. Comput Math Appl 36(7):79–89
Migdalas A, Pardalos PM, Varbrand P (1997) Multilevel optimization: algorithm and applications. Kluwer, Dordrecht
Ryu J, Dua V, Pistikopoulos EN (2004) A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput Chem Eng 28:1121–1129
Ryu J-H (2003) Design and operation of enterprise-wide process networks under uncertainty. PhD thesis, Department of Chemical Engineering and Chemical Technology Imperial College of Science, Technology and Medicine London, London
Shih H, Lai Y, Lee ES (1996) Fuzzy approach for multi-level programming problems. Comput Oper Res 23(1):73–91
Shimizu K, Ishizuka Y, Bard JF (1997) Nondifferentiable and two-level mathematical programming. Kluwer, Boston
Tabucanon MT (1988) Multiple Criteria Decision Making in Industry. Elsevier, Amsterdam
Vicente LN, Savard G, Júdice J (1994) Descent approaches for quadratic bilevel programming. J Optim Theor Appl 81:379–399
Vicente L (1992) Bilevel programming. Master's thesis, Department of Mathematics, University of Coimbra, Coimbra
Visweswaran V, Floudas MG, Ierapetritou CA, Pistikopoulos EN (1996) A decomposition-based global optimization approach for solving bilevel linear and quadratic programs. In: State of the art in global optimization. Kluwer, Dordrecht, pp 139–162
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Pistikopoulos, E.N., Faísca, N.P., Saraiva, P.M., Rustem, B. (2008). Bilevel Programming Framework for Enterprise-Wide Process Networks Under Uncertainty . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_42
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_42
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering