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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 286083, 17 pages
Research Article

The Natural Gas Cash-Out Problem: A Bilevel Optimal Control Approach

1Departamento de Ingeniería Industrial y de Sistemas, Tecnológico de Monterrey (ITESM), Campus Monterrey, Avenida Eugenio Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico
2Department of Social Modeling, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences (RAS), Nakhimovsky Prospekt 47, Moscow 117418, Russia
3Department of Electronics and Computing, Sumy State University, Rimsky-Korsakov Street 2, Sumy 40007, Ukraine
4Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, Prüferstrasse 9, 09596 Freiberg, Germany

Received 26 March 2015; Revised 10 June 2015; Accepted 18 June 2015

Academic Editor: Ching-Ter Chang

Copyright © 2015 Vyacheslav V. Kalashnikov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is threefold: first, it formulates the natural gas cash-out problem as a bilevel optimal control problem (BOCP); second, it provides interesting theoretical results about Pontryagin-type optimality conditions for a general BOCP where the upper level boasts a Mayer-type cost function and pure state constraints, while the lower level is a finite-dimensional mixed-integer programming problem with exactly one binary variable; and third, it applies these theoretical results in order to find possible local minimizers of the natural gas cash-out problem.