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The Weighted Linear Ordering Problem

In: Operations Research Proceedings 2019

Author

Listed:
  • Jessica Hautz

    (Alpen-Adria-Universität Klagenfurt)

  • Philipp Hungerländer

    (Alpen-Adria-Universität Klagenfurt)

  • Tobias Lechner

    (Alpen-Adria-Universität Klagenfurt)

  • Kerstin Maier

    (Alpen-Adria-Universität Klagenfurt)

  • Peter Rescher

    (Alpen-Adria-Universität Klagenfurt)

Abstract

In this work, we introduce and analyze an extension of the Linear Ordering Problem ( LOP) . The LOP aims to find a simultaneous permutation of rows and columns of a given weight matrix such that the sum of the weights in the upper triangle is maximized. We propose the weighted Linear Ordering Problem ( wLOP) that additionally considers individual node weights. First, we argue that in several applications of the LOP the optimal ordering obtained by the wLOP is a worthwhile alternative to the optimal solution of the LOP. Additionally, we show that the wLOP constitutes a generalization of the well-known Single Row Facility Layout Problem. We introduce an Integer Linear Programming formulation as well as a Variable Neighborhood Search for solving the wLOP. Finally, we provide a benchmark library and examine the efficiency of our exact and heuristic approaches on the proposed instances in a computational study.

Suggested Citation

  • Jessica Hautz & Philipp Hungerländer & Tobias Lechner & Kerstin Maier & Peter Rescher, 2020. "The Weighted Linear Ordering Problem," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 223-229, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_27
    DOI: 10.1007/978-3-030-48439-2_27
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