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On discrete optimization with ordering

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  • Elena Fernández
  • Justo Puerto
  • Antonio Rodríguez-Chía

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. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Elena Fernández & Justo Puerto & Antonio Rodríguez-Chía, 2013. "On discrete optimization with ordering," Annals of Operations Research, Springer, vol. 207(1), pages 83-96, August.
    • Handle: RePEc:spr:annopr:v:207:y:2013:i:1:p:83-96:10.1007/s10479-011-1044-7
    DOI: 10.1007/s10479-011-1044-7
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    References listed on IDEAS

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    1. Pierre Hansen & Martine Labbé, 1988. "Algorithms for Voting and Competitive Location on a Network," Transportation Science, INFORMS, vol. 22(4), pages 278-288, November.
    2. Jörg Kalcsics & Stefan Nickel & Justo Puerto & Antonio Rodríguez-Chía, 2010. "The ordered capacitated facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 203-222, July.
    3. HANSEN, Pierre & LABBE, Martine & THISSE, Jacques-François, 1991. "From the median to the generalized center," LIDAM Reprints CORE 937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Lara Turner & Abraham Punnen & Yash Aneja & Horst Hamacher, 2011. "On generalized balanced optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 19-27, February.
    5. Egon Balas & Manfred W. Padberg, 1972. "On the Set-Covering Problem," Operations Research, INFORMS, vol. 20(6), pages 1152-1161, December.
    6. Eugene L. Lawler, 1972. "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem," Management Science, INFORMS, vol. 18(7), pages 401-405, March.
    7. Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1984. "A Cutting Plane Algorithm for the Linear Ordering Problem," Operations Research, INFORMS, vol. 32(6), pages 1195-1220, December.
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    Cited by:

    1. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    2. Arpita Roy & Shib Sankar Sana & Kripasindhu Chaudhuri, 2018. "Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model," Annals of Operations Research, Springer, vol. 260(1), pages 481-500, January.
    3. Samuel Deleplanque & Martine Labbé & Diego Ponce & Justo Puerto, 2020. "A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 582-599, July.

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    Keywords

    Discrete optimization; Ordering problems;

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