  We study a variant of the competitive facility location problem, in which a
company is to locate new facilities in a market where competitor's facilities
already exist. We consider the scenario where only a limited number of possible
attractiveness levels is available, and the company has to select exactly one
level for each open facility. The goal is to decide the facilities' locations
and attractiveness levels that maximize the profit. We apply the gravity-based
rule to model the behavior of the customers and formulate a multi-ratio linear
fractional 0-1 program. Our main contributions are the exact solution
approaches for the problem. These approaches allow for easy implementations
without the need for designing complicated algorithms and are "friendly" to the
users without a solid mathematical background. We conduct computational
experiments on the randomly generated datasets to assess their computational
performance. The results suggest that the mixed-integer quadratic conic
approach outperforms the others in terms of computational time. Besides that,
it is also the most straightforward one that only requires the users to be
familiar with the general form of a conic quadratic inequality. Therefore, we
recommend it as the primary choice for such a problem.
