We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to the model by using a jointly constrained bilinear programming formulation. We then propose a decomposition branch-and-bound algorithm for globally solving the resulting bilinear problem. The subdivision takes place in one-dimensional intervals that enables solving the problem with relatively large sizes. Numerical experiments and results on randomly generated data show the efficiency of the proposed algorithm.
Mots-clés : Generalized Cournot model, bilinear programming, branch-and-bound, Pareto solution
@article{RO_2015__49_5_845_0,
author = {Van Quy, Nguyen},
title = {A jointly constrained bilinear programming method for solving generalized {Cournot{\textendash}Pareto} models},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {845--864},
publisher = {EDP-Sciences},
volume = {49},
number = {5},
year = {2015},
doi = {10.1051/ro/2015031},
mrnumber = {3549616},
zbl = {1338.91090},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2015031/}
}
TY - JOUR AU - Van Quy, Nguyen TI - A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 845 EP - 864 VL - 49 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015031/ DO - 10.1051/ro/2015031 LA - en ID - RO_2015__49_5_845_0 ER -
%0 Journal Article %A Van Quy, Nguyen %T A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 845-864 %V 49 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015031/ %R 10.1051/ro/2015031 %G en %F RO_2015__49_5_845_0
Van Quy, Nguyen. A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 5, pp. 845-864. doi : 10.1051/ro/2015031. http://www.numdam.org/articles/10.1051/ro/2015031/
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