We present an application of the MaxCut problem in statistical physics. We design a branch-and-bound algorithm for MaxCut and use it to nd all ground states in three dimensional 5 5 5 Ising spin glass systems.

We analyze the facial structure of the polytope associated to the GMSTP with the aim of nding \good" inequalities to strengthen our previous linear formulations. Several families of inequalities which are facet-inducing for the polytope of the GMSTP are investigated. Our proofs of \facetness" for valid inequalities of the GMSTP polytope use tools developped in [3] and also classical results fro...

We study the product assortment problem of a retail operation that faces a stream of customers who are heterogeneous with respect to preferences. Each customer belongs to a market segment characterized by a consideration set that includes the alternatives viewed as options, and by the preference weights that the segment assigns to each of those alternatives. Upon arrival, he checks the offer se...

 In spite of the many special purpose heuristics for specific classes of integer programming (IP) problems, there are few developments that focus on general purpose integer programming heuristics. This stems partly from the perception that general purpose methods are likely to be less effective than specialized procedures for specific problems, and partly from the perception that there is no u...

We present computational experience with a branch-and-cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in nancial applications. The algorithm solves the largest real-life problems in a few minutes of run-time.

Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. Following a proof that clique pricing is NP-hard, we propose strong valid inequalities, some of which define facets of the 2-commodity polyhedron. The numerical efficiency of these inequalities is assessed by embe...

Bran h-and-Cut Matteo Fis hetti DEI, University of Padova, 35131 Padova, Italy; Email: s h dei.unipd.it Juan Jos e Salazar Gonz alez DEIOC, University of La Laguna, 38271 Tenerife, Spain; Email: jjsalaza ull.es Paolo Toth DEIS, University of Bologna, 40136 Bologna, Italy; Email: ptoth deis.unibo.it Abstra t In the Orienteering Problem (OP) we are given an undire ted graph with edge weights and ...

The Single Row Facility Layout Problem (SRFLP) is the NP -hard problem of arranging facilities on a line, while minimizing a weighted sum of the distances between facility pairs. In this paper, a detailed polyhedral study of the SRFLP is performed, and several huge classes of valid and facet-inducing inequalities are derived. Some separation heuristics are presented, along with a primal heurist...

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint. In this paper we...

We propose a branch-and-cut algorithm for the VRPSPD where the constraints that assure that the capacities are not exceeded in the middle of a route are applied in a lazy fashion. The algorithm was tested in 87 instances with 50-200 customers, finding improved lower bounds and several new optimal solutions.