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The Robust Shortest Path Problem by Means of Robust Linear Optimization

In: Operations Research Proceedings 2004

Author

Listed:
  • D. Chaerani

    (Delft University of Technology)

  • C. Roos

    (Delft University of Technology)

  • A. Aman

    (Department Mathematics Institut Pertanian Bogor Indonesia)

Abstract

We investigate the robust shortest path problem using the robust linear optimization methodology as proposed by Ben-Tal and Nemirovski. We discuss two types of uncertainty, namely, box uncertainty and ellipsoidal uncertainty. In case of box uncertainty, the robust counterpart is simple. It is a shortest path problem with the original arc lengths replaced by their upper bounds. When dealing with ellipsoidal uncertainty, we obtain a conic quadratic optimization problem with binary variables. We present an example to show that a subpath of a robust shortest path is not necessarily a robust shortest path.

Suggested Citation

  • D. Chaerani & C. Roos & A. Aman, 2005. "The Robust Shortest Path Problem by Means of Robust Linear Optimization," Operations Research Proceedings, in: Hein Fleuren & Dick Hertog & Peter Kort (ed.), Operations Research Proceedings 2004, pages 335-342, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-27679-1_42
    DOI: 10.1007/3-540-27679-3_42
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    Cited by:

    1. Changhyun Kwon & Taehan Lee & Paul Berglund, 2013. "Robust shortest path problems with two uncertain multiplicative cost coefficients," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(5), pages 375-394, August.

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