  We study a competitive facility location problem (CFLP), in which two firms
sequentially select locations of new facilities, in order to maximize their
market shares of customer demand that follows a probabilistic choice model.
This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear
program (MINLP) formulation. Through integer programming methods, we derive an
equivalent, single-level MINLP reformulation. In addition, we exploit the
problem structures and derive two classes of valid inequalities, one based on
submodularity and the other based on concave overestimation. We apply these
inequalities in a branch-and-cut algorithm to find a globally optimal solution
to CFLP. Furthermore, we propose an approximation algorithm for solving CFLP
that is computationally more effective. Notably, this algorithm admits a
constant approximation guarantee. Extensive numerical studies demonstrate that
the exact algorithm can significantly accelerate the solving of CFLP on problem
instances that have not been solved to optimality by existing methods. The
approximation algorithm can find near-optimal solutions even more quickly.
