Optimizing Fairness over Time with Homogeneous Workers (Short Paper)

Authors Bart van Rossum, Rui Chen, Andrea Lodi

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Author Details

Bart van Rossum
  • Econometric Institute, Erasmus University Rotterdam, The Netherlands
Rui Chen
  • Cornell Tech, New York City, NY, USA
Andrea Lodi
  • Cornell Tech, New York City, NY, USA

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Bart van Rossum, Rui Chen, and Andrea Lodi. Optimizing Fairness over Time with Homogeneous Workers (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


There is growing interest in including fairness in optimization models. In particular, the concept of fairness over time, or, long-term fairness, is gaining attention. In this paper, we focus on fairness over time in online optimization problems involving the assignment of work to multiple homogeneous workers. This encompasses many real-life problems, including variants of the vehicle routing problem and the crew scheduling problem. The online assignment problem with fairness over time is formally defined. We propose a simple and interpretable assignment policy with some desirable properties. In addition, we perform a case study on the capacitated vehicle routing problem. Empirically, we show that the most cost-efficient solution usually results in unfair assignments while much more fair solutions can be attained with minor efficiency loss using our policy.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Fairness
  • Online Optimization
  • Combinatorial Optimization
  • Vehicle Routing


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  2. Andrea Lodi, Sriram Sankaranarayanan, and Guanyi Wang. A framework for fair decision-making over time with time-invariant utilities, 2022. URL: https://arxiv.org/abs/2212.10070.
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  6. Man Yiu Tsang and Karmel S. Shehadeh. A unified framework for analyzing and optimizing a class of convex inequity measures, 2022. URL: https://arxiv.org/abs/2211.13427.
  7. Eduardo Uchoa, Diego Pecin, Artur Pessoa, Marcus Poggi, Thibaut Vidal, and Anand Subramanian. New benchmark instances for the capacitated vehicle routing problem. European Journal of Operational Research, 257(3):845-858, 2017. Google Scholar
  8. Bart van Rossum, Twan Dollevoet, and Dennis Huisman. Dynamic railway crew planning with fairness over time. Technical Report EI 2022-10, Economometric Institute, Erasmus University Rotterdam, 2022. Google Scholar
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