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On the multicriteria allocation problem

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Abstract

We consider multicriteria allocation problems with linear sum objectives. Despite the fact that the single objective allocation problem is easily solvable, we show that already in the bicriteria case the problem becomes intractable, is NP-hard and has a non-connected efficient set in general. Using the equivalence to appropriately defined multiple criteria multiple-choice knapsack problems, an algorithm is suggested that uses partial dominance conditions to save computational time. Different types of enumeration schemes are discussed, for example, with respect to the number of necessary filtering operations and with regard to possible parallelizations of the procedure.

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Acknowledgements

We like to thank Britta Schulze, who constructed the counterexample in the proof of Lemma 13. We acknowledge the financial support of the LORIA grant “Multiple Criteria on ROAD”, the support of the DAAD project RepSys and the support of the DFG through the HBFG program.

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Authors and Affiliations

  1. Department of Mathematics, University of Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany

    Michael Stiglmayr & Kathrin Klamroth

  2. CEG-IST Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    José Rui Figueira

  3. LORIA Laboratory, Nancy, France

    José Rui Figueira

Authors
  1. Michael Stiglmayr
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  2. José Rui Figueira
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  3. Kathrin Klamroth
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Correspondence to Michael Stiglmayr.

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Stiglmayr, M., Figueira, J.R. & Klamroth, K. On the multicriteria allocation problem. Ann Oper Res 222, 535–549 (2014). https://doi.org/10.1007/s10479-013-1356-x

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