Improved Lagrangean Decomposition: An Application to the Generalized Assignment Problem

Recently two new ways of obtaining improved Lagrangean bounds have been suggested: Lagrangean decomposition and bound improving sequences. In this work we will obtain a Lagrangean approach combining the two ideas mentioned above. We provide theoretical results about the sharpness of the bounds obtained by the combined approach for the general case and an application to the generalized assignment problem. Computational experience is reported.N/

Variable Spliting and Constructive Duality: A Method for Structured Integer Programming Problems

In this paper we will present a method for structured pure integer programming problems based on the ideas of variable splitting and bound improving sequences i.e., we will combine a special type of Lagrangean relaxation with a constructive duality scheme in order to make use of the inherent structure of the studied problem. As an example of the usefulness of the method we will present an application of the technique to the generalised assignment problem.N/

Overcoming the (apparent) problem of inconsistency in O-D matrix estimations

Recently a number of models for the estimation of origin-destination trip matrices from traffic counts have been presented. One class of models assumes knowledge of the proportional usage of each link by the interzonal traffic. These models result in an underspecified, and often inconsistent, system of linear equations. Several authors have addressed the problem of inconsistency by, in different ways, changing the traffic count data so as to achieve consistency. We argue that, modeling-wise, this is not a sound approach because inconsistent data is a natural part of any origin-destination matrix estimation problem. By using a stochastic programming approach the inconsistent input data becomes a natural part of the estimation process. This is done by viewing the traffic counts as realizations of some unknown underlying distribution of traffic flows