The Fair OWA One-to-One Assignment Problem: NP-Hardness and Polynomial Time Special Cases
We consider a one-to-one assignment problem consisting of matching n objects with n agents. Any matching leads to a utility vector whose n components measure the satisfaction of the various agents. We want to find an assignment maximizing a global utility defined as an ordered weighted average (OWA) of the n individual utilities. OWA weights are assumed to be non-increasing with ranks of satisfaction so as to include an idea of fairness in the definition of social utility. We first prove that the problem is NP-hard; then we propose a polynomial algorithm under some restrictions on the set of admissible weight vectors, proving that the problem belongs to XP.
KeywordsAssignment problem Fairness Ordered weighted average Complexity
The referees are gratefully acknowledged for their constructive comments and suggestions which resulted in an improved presentation of the paper.
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