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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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    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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