Efficient formulations and solution methods for discrete facility location and other combinatorial optimization problems
Many integer programming problems, even if linear, are very difficult to solve due to the high number of integer variables involved. Once our solver starts to branch, our hopes for solving the problem fast are highly correlated to how good our formulation is and how good the solution method of our choice is. Therefore, two elements are key: to have a very good formulation as a starting point, and then to make the best possible use of it by having an efficient solution algorithm. This presentation will show some particular very successful methods (formulations and algorithms), like the radius formulation for the classical p-median problem, but whose core idea has also been applied successfully to a problem very different such as airport slot allocation. Time permitting, other successful techniques used in facility location with preferences or location of ellipses will be discussed.