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Given an integer polyhedron , an integer point , and a point , the primal separation problem is the problem of finding a linear inequality which is valid for PI, violated by x*, and satisfied at equality by . The primal separation problem plays a key role in the primal approach to integer programming. In this paper...
We review the recent three-volume monograph authored by Alexander Schrijver, Combinatorial Optimization - Polyhedra and Efficiency, Springer-Verlag, 2003, ISBN 3-540-44389-4, 1881 pages (in a slip-case), price: 89,95 .
This is a summary of the main results presented in the author’s PhD thesis. This thesis, written in English, was supervised by Frits Spieksma and defended on September 23, 2005 at the Katholieke Universiteit Leuven. A copy of the thesis is available from the authors website (http://www.econ. kuleuven.be/linda.moonen/public/). The thesis can be roughly split into two parts. The first part is dedicated...
The paper summarizes the main results of the author’s Ph.D. thesis presented in December 2006 at the École des Mines de Saint Étienne. The work was supervised by Alexandre Dolgui and Xavier Delorme. The thesis is written in French and is available upon request from the author. Its purpose is to provide decision support in the design and reconfiguration of modular machining lines with multi-spindle...
This is a summary of the author’s Ph.D. thesis supervised by Federico Malucelli and defended on 15 May 2008 at the Politecnico di Milano. The thesis is written in English and is available from the author upon request. This work presents new methods for enhancing the Column Generation approach based on Constraint Programming when it is used for solving combinatorial optimization problems. The methods...
We survey the main results of the PhD Thesis presented by the author in January 2009 at the University of Padova. This work was supervised by Giacomo Zambelli. The thesis is written in English and is available from the author upon request. In this work we consider the Edmonds–Johnson property and we survey some related results. Next we present our contributions, that consist into two classes of matrices...
This a summary of the author’s PhD thesis supervised by Leo Liberti, Philippe Baptiste and Daniel Krob and defended on 18 June 2009 at Ecole Polytechnique, Palaiseau, France. The thesis is written in English and is available at http://pastel.paristech.org/5275/ . The computation of point-to-point shortest paths in road networks has many practical applications that require very fast solution times,...
In this paper, a supply chain management problem from a real case study is modeled and solved. A company in Pakistan wanted to outsource part of its warehousing activity to a third party logistics (3PL) provider. Consequently, the company had to decide on where to rent space in the 3PL warehouses. Knowing that such a strategic decision is affected by tactical and operational decisions, the problem...
This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled Some continuous functions related to corner polyhedra I, II (Math Program 3:23–85, 359–389, 1972a, b). The survey presents the infinite group problem in the modern context of cut generating functions...
This is the second part of a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled Some continuous functions related to corner polyhedra I, II (Math Program 3:23–85, 1972a; Math Program 3:359–389, 1972b). The survey presents the infinite group problem in the...
Based on an application in the field of server consolidation, we consider the one-dimensional cutting stock problem with nondeterministic item lengths. After a short introduction to the general topic we investigate the case of normally distributed item lengths in more detail. Within this framework, we present two lower bounds as well as two heuristics to obtain upper bounds, where the latter are either...
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