An abstract view of symmetric gaussian elimination is presented. Problems are viewed as an assembly of computational entities whose interdependence is modeled by a graph. An algorithmic transformation on the entities which can be associated withvertex removal, is assumed to exist. The...

We consider the cutting of rectangular order pieces into stock pieces of specified width and length. The cutting process involves three stages of orthogonal guillotine cutting: Stock pieces are cut into sections that are cut into slits that are cut into order pieces. Restrictions imposed on the...

Recently Beltrán-Royo, Vial & Alonso-Ayuso (2012) presented a semi-Lagrangean relaxation for the classical p-median location problem and for the incapacitated facility location problem. The results, obtained using the semi-Lagrangean relaxation approach, were quite impressive. In this paper we...

Recently Beltran-Royo et.al presented a Semi-Lagrangean relaxation for the classical p-median location problem. The results obtained using the Semi-Lagrangean relaxation approach were quite impressive. In this paper we use a reformulation of the p-median problem in order to start from a...

In this paper, we use a reformulation of the symmetric and the asymmetric travelling salesman problem more suitable for Lagrangean relaxation and analyse the new approach on examples from TSP Lib. Furthermore the Lagrangean relaxed subproblems are travelling salesman alike which means that...

Fuelwood is one of the main fuels for heating in many countries. As the price of fuelwood is relative low, comparing to oil or gas, demand for fuelwood rises over the years. A supply chain is considered by different nodes that are essential for some operations concerning transportation and...

This paper proposes a column generation approach based on the Lagrangean relaxation with clusters to solve the unconstrained binary quadratic programming problem that consists of maximizing a quadratic objective function by the choice of suitable values for binary decision variables. The...

Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master...

The aim of this paper is to solve p-median problems with an additional coverage constraint. These problems arise in location applications, when the trade-off between distance and coverage is being calculated. Three kinds of heuristic algorithms are developed. First, local search procedures are...