A Bilevel Market Equilibrium Model for Natural Gas Pipeline Network Operations: Convex Relaxations and Single-level Reformulations
Abstract
We propose an integrated market equilibrium model for determining the spot market prices and flow rates in a natural gas pipeline network. The traditional approach solves the market equilibrium model separately from the natural gas network flow allocation problem in a sequential manner. Our proposed framework synthesizes marketing and operations by using a bilevel optimization formulation where the market equilibrium model in the upper level is connected and simultaneously solved with the natural gas network flow model in the lower level. We introduce convex relaxations for the nonconvex Weymouth pipe pressure drop equation and a surrogate for the compressor operating cost. Furthermore, we compare multiple single level reformulations of the bilevel problem based on Karush-Kuhn-Tucker (KKT) optimality conditions, Wolfe duality, and Lagrange duality conditions. Numerical studies on a small 6-node network demonstrates the efficacy and accuracy of our model and the comparison between different duality and optimality based reformulations.
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BibTeX
@misc{dey2026bilevel,
title = {{A Bilevel Market Equilibrium Model for Natural Gas Pipeline Network Operations: Convex Relaxations and Single-level Reformulations}},
author = {Novel Kumar Dey and Afrooz Jalilzadeh and Erfan Yazdandoost Hamedani and Saif R. Kazi and Anatoly Zlotnik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14339},
eprint = {2610.14339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bilevel Market Equilibrium Model for Natural Gas Pipeline Network Operations: Convex Relaxations and Single-level Reformulations
AU - Novel Kumar Dey
AU - Afrooz Jalilzadeh
AU - Erfan Yazdandoost Hamedani
AU - Saif R. Kazi
AU - Anatoly Zlotnik
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14339
UR - https://arxiv.org/abs/2610.14339
AB - We propose an integrated market equilibrium model for determining the spot market prices and flow rates in a natural gas pipeline network. The traditional approach solves the market equilibrium model separately from the natural gas network flow allocation problem in a sequential manner. Our proposed framework synthesizes marketing and operations by using a bilevel optimization formulation where the market equilibrium model in the upper level is connected and simultaneously solved with the natural gas network flow model in the lower level. We introduce convex relaxations for the nonconvex Weymouth pipe pressure drop equation and a surrogate for the compressor operating cost. Furthermore, we compare multiple single level reformulations of the bilevel problem based on Karush-Kuhn-Tucker (KKT) optimality conditions, Wolfe duality, and Lagrange duality conditions. Numerical studies on a small 6-node network demonstrates the efficacy and accuracy of our model and the comparison between different duality and optimality based reformulations.
ER -