Abstract:

We consider an $(r|p)$-centroid problem formulated as a bilevel mathematical programming problem. In the problem, two competing parties open, respectively, $r$ and $p$ facilities aiming to attract customers' demand and maximize the market share. An approach for computing upper bounds for the first player's (Leader) objective function, is proposed based on generating additional constraints (cuts) for the high-point relaxation of the bi-level problem. New types of additional constraints are introduced, which take into account the specific of the $(r|p)$-centroid problem.
A procedure of generating these constraints is discussed, which allows to improve sequentially the upper bound's quality.