Bilevel Programming Problems by Stephan Dempe Vyacheslav Kalashnikov Gerardo A. Pérez-Valdés & Nataliya Kalashnykova

Author:Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés & Nataliya Kalashnykova
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5)Department of Industrial Economics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

(6)Facultad Ciencias Físico-Mathemáticas (FCFM), Universidad Autónoma de Nuevo León (UANL), San Nicolás de los Garza, Mexico

Stephan Dempe (Corresponding author)

Email: [email protected]

Vyacheslav Kalashnikov

Email: [email protected]

Gerardo A. Pérez-Valdés

Email: [email protected]

Nataliya Kalashnykova

Email: [email protected]

This chapter discusses several models in which bilevel programming has been applied to the natural gas industry. The analysis of done in the context of the US natural gas markets, in which regulations in the last 20 years have made it so that separations between supply chain agents is compulsory, in order to avoid monopolistic practices. As a result of this, natural gas shippers/traders and pipeline operators engage in business in a way that can be modeled as a bilevel problem.

This chapter is divided as follows: Sect. 6.1 describes the background for the problems, Sect. 6.2 details the formulation of the bilevel model that abstracts the problem, with an approximation to this given in Sect. 6.3. A preliminary direct solution method is sketched in Sect. 6.4, while Sect. 6.5 shows a penalty function approach to the solution of this model using a variational inequality. Section 6.6 presents a way to expand the problem and then solve it by first reformulating both levels with linear problems thus, obtaining a linear bilevel optimization problem. Then, the techniques in this chapter are used to provide numerical results in Sect. 6.7. Finally, in Sect. 6.8, one possible stochastic formulation is suggested, building upon the deterministic models presented before.

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