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The Fair Periodic Assignment Problem

Authors Rolf Nelson van Lieshout , Bartholomeüs Theodorus Cornelis van Rossum

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Graph algorithms
  • Applied computing → Transportation
Keywords
  • Cyclic scheduling
  • Fairness
  • Traveling Salesman Problem

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Abstract

We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a 𝒪(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always be found using the Nearest Neighbor heuristic. We characterize all instances that admit a solution that is both fair and efficient, and use this result to develop a 𝒪(n log n) exact algorithm for the fair periodic assignment problem. Finally, we show that allowing aperiodic schedules never reduces the price of fairness.

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Rolf Nelson van Lieshout and Bartholomeüs Theodorus Cornelis van Rossum. The Fair Periodic Assignment Problem. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.ATMOS.2025.1

Author Details

Rolf Nelson van Lieshout
  • Eindhoven University of Technology, The Netherlands
Bartholomeüs Theodorus Cornelis van Rossum
  • Eindhoven University of Technology, The Netherlands

References

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