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Efficient Management of Multiple Sets to Extract Complex Structures from Mathematical Programs

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Abstract

Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the algebraic formulation is usually sufficient to retrieve different block structures from mathematical programs. These structured problems can then be solved by adequate solution techniques. To illustrate this idea we focus on stochastic programming problems with recourse. Taking into account both time and uncertainty dimensions of these problems, we are able to retrieve different customized structures in their constraint matrices. We applied the Structure Exploiting Tool to retrieve the structure from models built with the GAMS modeling language. The underlying mathematical programs are solved with the decomposition algorithm that applies interior point methods. The optimization algorithm is run in a sequential and in a parallel computing environment.

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Authors and Affiliations

  1. The School of Management, University of Bath, Bath, BA2 7AY, England

    Emmanuel Fragnière

  2. Department of Mathematics and Statistics, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

    Jacek Gondzio

  3. Judge Institute of Management Studies, Cambridge University, Trumpington Street, Cambridge, CB2 1AG, England

    Robert Sarkissian

Authors
  1. Emmanuel Fragnière
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  2. Jacek Gondzio
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  3. Robert Sarkissian
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Fragnière, E., Gondzio, J. & Sarkissian, R. Efficient Management of Multiple Sets to Extract Complex Structures from Mathematical Programs. Annals of Operations Research 104, 67–87 (2001). https://doi.org/10.1023/A:1013134818537

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