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A Mathematical Model of a Fair Blood Allocation Framework for the Transfusion Haematology System of Bulgaria

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  • Vassia Atanassova

    (Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Peter Vassilev

    (Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Ivo Umlenski

    (Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Nikolay Andreev

    (ImunoChem SMDL, 1784 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Krassimir Atanassov

    (Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    These authors contributed equally to this work.)

Abstract

Efficient and fair allocation of donated blood depends on multiple factors, like medical urgency, donor/recipient compatibility, blood availability, geographic location, limited shelf life, etc. Due to the limited supply of blood and its critical role in healthcare, fair distribution protocols are essential. This study builds upon previous authors’ research that proposed a general mathematical model for fair blood allocation, taking as inputs the universal blood compatibility chart and the assumption of allocating equal shares of the donated blood from each blood type to recipients with respectively compatible blood types. The sum normalization technique was performed (twice, first per recipients and then per donors) for the purpose of balancing between donation needs and options. The result was an indicative blood allocation reference framework in support of the decision making in transfusion haematology. In the present paper, we tailor that general model by introducing as model variables the actual blood group frequencies of a given population. Additional customization is proposed by adding weight coefficients to the values along the framework’s main diagonal that represent ABO-identical transfusions, preferred to non-identical transfusions for minimizing the risks of hemolytic reactions. The model is further elaborated via intervalization of the estimations in the resultant blood allocation framework, thus making the model more flexible and usable. While demonstrated with Bulgarian blood group distributions from 2023, the model can be adapted to other populations and contexts.

Suggested Citation

  • Vassia Atanassova & Peter Vassilev & Ivo Umlenski & Nikolay Andreev & Krassimir Atanassov, 2025. "A Mathematical Model of a Fair Blood Allocation Framework for the Transfusion Haematology System of Bulgaria," Mathematics, MDPI, vol. 13(7), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1062-:d:1619963
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    References listed on IDEAS

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    1. Karsu, Özlem & Morton, Alec, 2014. "Incorporating balance concerns in resource allocation decisions: A bi-criteria modelling approach," Omega, Elsevier, vol. 44(C), pages 70-82.
    2. Özlem Karsu & Hale Erkan, 2020. "Balance in resource allocation problems: a changing reference approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 297-326, March.
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