Geodesic
A bilevel competitive location and pricing model with nonuniform split of demand
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 27-45

Voir la notice de l'article provenant de la source Math-Net.Ru

Under study is the bilevel competitive facility location and pricing problem which is formulated in terms of the Stackelberg game. The problem involves the two producers: the Leader and the Competitor. They consistently place their facilities and set prices. The choice of prices is based on the Bertrand model of price competition and the possibility of dividing a client's demand if this will be profitable for both players. In this case, the demand is divided between the players in a given proportion. The complexity is investigated of finding the optimal solution of the problem and its particular cases. It is shown that the problem is $\Sigma_2^P$-hard. However, under certain conditions on the input parameters, the complexity decreases significantly and in some cases the problem becomes polynomially solvable. Illustr. 3, bibliogr. 25.
Keywords: bilevel problem, Stackelberg game, facility location, pricing, Bertrand model, nonuniform split of demand, complexity, polynomial hierarchy. 
@article{DA_2019_26_3_a1,
     author = {A. V. Kononov and A. A. Panin and A. V. Plyasunov},
     title = {A bilevel competitive location and pricing model with nonuniform split of demand},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {27--45},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_3_a1/}
}
TY  - JOUR
AU  - A. V. Kononov
AU  - A. A. Panin
AU  - A. V. Plyasunov
TI  - A bilevel competitive location and pricing model with nonuniform split of demand
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2019
SP  - 27
EP  - 45
VL  - 26
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2019_26_3_a1/
LA  - ru
ID  - DA_2019_26_3_a1
ER  - 
%0 Journal Article
%A A. V. Kononov
%A A. A. Panin
%A A. V. Plyasunov
%T A bilevel competitive location and pricing model with nonuniform split of demand
%J Diskretnyj analiz i issledovanie operacij
%D 2019
%P 27-45
%V 26
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2019_26_3_a1/
%G ru
%F DA_2019_26_3_a1
A. V. Kononov; A. A. Panin; A. V. Plyasunov. A bilevel competitive location and pricing model with nonuniform split of demand. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 27-45. http://geodesic.mathdoc.fr/item/DA_2019_26_3_a1/