Odile Marcotte

A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem

We consider the multiple depot vehicle scheduling problem (MDVSP) and propose a branch-and-bound algorithm for solving it that combines column generation, variable fixing, and cutting planes. We show that the solutions of the linear relaxation of the MDVSP contain many odd cycles. We derive a class of valid inequalities by extending the notion of odd cycle and describe a lifting procedure for these inequalities. We prove that the lifted inequalities represent, under certain conditions, facets of the underlying polytope. Finally, we present the results of a computational study comparing several strategies (variable fixing, cutting planes, mixed branching, and tree search) for solving the MDVSP.

An instance of the cutting stock problem for which the rounding property does not hold

We say that an instance of the cutting stock problem has the integer rounding property if its optimal value is the least integer greater than or equal to the optimal value of its linear programming relaxation. In this note we give an instance of the cutting stock problem for which the rounding property does not hold, and show that it is NP-hard to decide whether the rounding holds or not.

Mathematical Models and Exact Methods For Channel Assignment in Cellular Networks

The continuous growth in traffic and the number of subscribers (4 million worldwide in 1988 vs 123 million in 1995, while about 400 million are expected in 2001), as well as the emergence of new technologies, are forcing telecommunication companies to optimize further the channel assignment of their cellular networks. A few years ago, the channel assignment problem wets formulated as an optimization problem with the objective of minimizing the order (i.e., the number of channels) or the channel span, subject to various interference constraints. Today, because of the rapid growth of cellular networks, all possible channels are used and it is usually impossible to assign channels with the guarantee that the networks (especially in urban areas) contain no interferences.

Fast matching algorithms for points on a polygon

Given a set P of

Extending an edge-coloring

2n

Optimizing the Design of a Wind Farm Collection Network

points on the boundary of a polygon, consider the complete graph whose vertex set is P, and whose edges are assigned weights equal to the Euclidean distance between their endpoints if the endpoints see each other in the polygon and

On the chromatic index of multigraphs and a conjecture of seymour (I)

+ \infty

Dispatching Buses in a Depot Using Block Patterns

otherwise. The problem of finding a minimum-weightperfect matching is investigated in this graph, and an

On the joint topological, dimensioning and location problem for broadband networks

O(n\log (n))

Optimal optode montage on electroencephalography/functional near-infrared spectroscopy caps dedicated to study epileptic discharges

time algorithm is obtained if the polygon is convex; an