Annals of Operations Research

, Volume 181, Issue 1, pp 423–442 | Cite as

A linearization approach to solve the natural gas cash-out bilevel problem

  • Vyacheslav V. KalashnikovEmail author
  • Gerardo A. Pérez
  • Nataliya I. Kalashnykova


In this article, we discuss a particular imbalance cash-out problem arising in the natural gas supply chain. This problem was created by the liberalization laws that regulate deals between a natural gas shipping company and a pipeline operator. The problem was first modeled as a bilevel nonlinear mixed-integer problem that considers the cash-out penalization for the final imbalance occurring in the system. We extend the original problem’s upper level objective function by including additional terms accounting for the gas shipping company’s daily actions aimed at taking advantage of the price variations. Then we linearize all the constraints at both levels in an equivalent way so as to make easier their numerical solution. The results of numerical experiments are compared with those obtained by the inexact penalization method proposed by the authors in previous papers.


Natural gas cash-out problem Bi-level programming Linearization 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vyacheslav V. Kalashnikov
    • 1
    • 2
    Email author
  • Gerardo A. Pérez
    • 3
  • Nataliya I. Kalashnykova
    • 4
  1. 1.Department of Systems & Industrial EngineeringITESM (Tec de Monterrey)MonterreyMexico
  2. 2.Central Economics & Mathematics Institute (CEMI)Russian Academy of Sciences (RAS)MoscowRussia
  3. 3.Centro de Calidad y ManufacturaITESM (Tec de Monterrey)MonterreyMexico
  4. 4.Facultad de Ciencias Físico-Matemáticas (FCFM)Universidad Autónoma de Nuevo León (UANL)San Nicolás de los GarzaMexico

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