We investigate the polyhedral structure of an integer program with a single functional constraint: the integer capacity-cover polyhedron. Such constraints arise in telecommunications planning and facility location applications, and feature the use of general integer (rather than just binary) variables. We derive a large class of facet-defining inequalities by using an augmenting technique that builds … Read more
The $p$-Center problem consists in locating $p$ facilities among a set of $M$ possible locations and assigning $N$ clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. We present a new integer linear programming formulation for this Min-Max problem with a polynomial number … Read more
Inspired by an algorithm due to Minieka, we develop a simple and yet very efficient exact algorithm for the problem of locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility it is assigned to. After a lower bounding phase, the algorithm iteratively sets … Read more
We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x … Read more
We present a nontrivial family of facet-defining inequalities for the p-median polytope. We incorporate the inequalities in a branch-and-cut scheme, and we report computational results that demonstrate their effectiveness. CitationDepartment of Industrial Engineering, State University of New York at Buffalo, submittedArticleDownload View PDF