A Quadratic Programming Model for Fair Resource Allocation

Yanmeng Tao, Bo Jiang (), Qixiu Cheng and Shuaian Wang
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Yanmeng Tao: School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
Bo Jiang: Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China
Qixiu Cheng: Business School, University of Bristol, Bristol BS8 1PY, UK
Shuaian Wang: Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China

Mathematics, 2025, vol. 13, issue 16, 1-21

Abstract: In collaborative projects, traditional resource allocation methods often rely on company-assigned contribution rates, which can be subjective and lead to unfair outcomes. To address this, we propose a quadratic programming model that integrates participants’ self-reported rankings of their contributions across projects with company evaluations. The model aims to minimize deviations from company-assigned rates while ensuring consistency with participants’ perceived contribution rankings. Extensive simulations demonstrate that the proposed method reduces allocation errors by an average of 50.8% compared to the traditional approach and 21.4% against the method considering only individual estimation tendencies. Additionally, the average loss reduction in individual resource allocation ranges from 40% to 70% compared to the traditional method and 10% to 50% against the estimation-based method, with our approach outperforming both. Sensitivity analyses further reveal the model’s robustness and its particular value in flawed systems; the error is reduced by approximately 75% in scenarios where company evaluations are highly inaccurate. While its effectiveness is affected by factors such as team size variability and self-assessment errors, the approach consistently provides more equitable allocation of resources that better reflects actual individual contributions, offering valuable insights for improving fairness in team projects.

Keywords: resource allocation fairness; contribution rate evaluation; quadratic programming model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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