On complexity of the bilevel location and pricing problems - Panin, A. A.; Plyasunov, A. V. (Journal of applied and industrial mathematics, 2014)
We consider the bilevel mixed integer location and pricing problems. Each problem is determined by the optimization problems of the upper and lower levels of which the first describes the choice of location and pricing, while the second models the reaction of the customers on the upper-level solution. The article focuses on studying the computational complexity of bilevel problems with various pricing strategies: uniform, mill, and discriminatory pricing. We show that, for an arbitrary pricing strategy, the corresponding optimization problem is NP-hard in the strong sense, belongs to the class Poly-APX, and is complete in it with respect to AP-reducibility.