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Complexity of the Object Allocation Problem with Minimum Number of Changes

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  • Umutcan Salman

    (University of Padova)

Abstract

This paper studies the problem of reallocating objects to agents while taking into account agents’ endowments, object capacities and agents’ preferences. The goal is to find a Pareto efficient and individually rational allocation that minimizes the number of individuals who need to change from their initial allocation to the final one. We call this problem as MINDIST. We establish NP-completeness result for MINDIST. We also show that MINDIST remains NP-complete when we restrict individual preferences to be binary, meaning that each individual can rank at most two objects in the preferences. Finally, we present an integer programming formulation to solve small to moderately sized instances of the NP-hard problems.

Suggested Citation

  • Umutcan Salman, "undated". "Complexity of the Object Allocation Problem with Minimum Number of Changes," "Marco Fanno" Working Papers 0323, Dipartimento di Scienze Economiche "Marco Fanno".
    • Handle: RePEc:pad:wpaper:0323
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    References listed on IDEAS

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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
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