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On discrete optimization with ordering

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Abstract

This paper studies discrete optimization problems with ordering requirements. These problems are formulated on general discrete sets in which there exists an ordering on their elements together with a cost function that evaluates each element of a given subset depending on its ordering relative to the remaining elements in the set. It is proven that ordered sequences over the original ground set define an independence system. The simplest such ordering problem, that consists of finding the ordered sequence of maximum weight, and its restriction to sets of a fixed cardinality are studied. In both cases, the polyhedral structure of the corresponding feasible sets is analyzed.

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Acknowledgements

The authors would like to acknowledge the suggestions received by a referee that have led to a shorter proof of Theorem 3.1. This research has been partially supported by Spanish Ministry of Science and Innovation/FEDER grants numbers MTM2009-14039-C06-05, MTM2007-67433-C02-(01,02), MTM2010-19576-C02-(01,02), DE2009-0057, Fundación Séneca (08716/PI/08), and Junta de Andalucía/FEDER, grant number FQM-5849.

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Authors and Affiliations

  1. Dpt. d’Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, Barcelona, Spain

    Elena Fernández

  2. Dpt. Estadística e Investigación Operativa, Universidad de Sevilla, Sevilla, Spain

    Justo Puerto

  3. Dpt. Estadística e Investigación Operativa, Universidad de Cádiz, Cadiz, Spain

    Antonio M. Rodríguez-Chía

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  1. Elena Fernández
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Correspondence to Antonio M. Rodríguez-Chía.

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Fernández, E., Puerto, J. & Rodríguez-Chía, A.M. On discrete optimization with ordering. Ann Oper Res 207, 83–96 (2013). https://doi.org/10.1007/s10479-011-1044-7

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