We extend the Sherali-Adams, Lovász-Schrijver, Balas-Ceria-Cornuéjols and Lasserre lift-and-project methods for 0-1 optimization by considering liftings to subset algebras. Our methods yield polynomialtime algorithms for solving a relaxation of a set-covering problem at least as strong as that given by the set of all valid inequalities with small coefficients, and, more generally, all valid ine...

We introduce the interval order polytope of a digraph D as the convex hull of interval order inducing arc subsets of D. Two general schemes for producing valid inequalities are presented. These schemes have been used implicitly for several polytopes and they are applied here to the interval order polytope. It is shown that almost all known classes of valid inequalities of the linear ordering po...

The paper investigates connections between linear inequalities that are valid for Shannon entropies and for Kolmogorov complexities.

The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities for Sn to obtain a valid inequalities for Pn. As an application, we describe a surprising relations...

We study the polyhedral structure of a new model for various bottleneck resource allocation problems in which the resource consumption is determined by the activity with the maximum usage. The model, called the mixed vertex packing problem, is a generalization of the vertex packing problem having both binary and bounded continuous variables. We give valid inequalities and separation algorithms ...

In this paper, we present a new frequency reassignment problem (FP) arising from the installation of new base stations for capacity expansion of a mobile telecommunication network, and develop two mathematical formulations along with some valid inequalities. Also, we develop a novel decomposition based heuristic procedure for solving large size problems. Computational results show that the deve...

In this paper we describe some results on the linear integer programming formulation of the Probabilistic Minimum Power Multicast (PMPM) problem for wireless networks. The PMPM problem consists in optimally assigning transmission powers to the nodes of a given network in order to establish a multihop connection between a source node and a set of destination nodes. The nodes are subject to failu...

We consider the problem of maximizing the revenue raised from tolls set on the links of a multicommodity transportation network. Since an optimal policy must balance toll levels against utilization rates, this problem lends itself naturally to a bilevel formulation, where network users assign themselves to shortest paths with respect to a disutility defined as the sum of travel time and out-of-...

Bus transit network planning is a complex process that is divided into several phases such as: line planning, timetable generation, vehicle scheduling, and crew scheduling. In this work, we address the timetable generation which consists in scheduling the departure times for all trips of each bus line. We focus on the Synchronization Bus Timetabling Problem (SBTP) that favors passenger transfer...

In this paper, we develop a convexification tool that enables the construction of convex hulls for orthogonal disjunctive sets using convex extensions and disjunctive programming techniques. A distinguishing feature of our technique is that, unlike most applications of disjunctive programming, it does not require the introduction of new variables in the relaxation. We develop and apply a toolbo...