Sequential Competitive Facility Location: Exact and Approximate Algorithms

We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation … Read more

Maximizing a Class of Submodular Utility Functions

Given a finite ground set N and a value vector a in R^N, we consider optimization problems involving maximization of a submodular set utility function of the form h(S)= f (sum_{i in S} a_i), S subseteq N, where f is a strictly concave, increasing, differentiable function. This function appears frequently in combinatorial optimization problems when … Read more