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Robust Additive Value-Based Efficiency Analysis with a Hierarchical Structure of Inputs and Outputs


[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee | [ SzD ] doctoral school student

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication


Published in

Applied Sciences

Journal year: 2023 | Journal volume: vol. 13 | Journal number: iss. 11

Article type

scientific article

Publication language


  • data envelopment analysis
  • value-based efficiency
  • hierarchical structure
  • robustness analysis
  • healthcare

EN We introduce a novel methodological framework based on additive value-based efficiency analysis. It considers inputs and outputs organized in a hierarchical structure. Such an approach allows us to decompose the problem into manageable pieces and determine the analyzed units’ strengths and weaknesses. We provide robust outcomes by analyzing all feasible weight vectors at different hierarchy levels. The analysis concerns three complementary points of view: distances to the efficient unit, ranks, and pairwise preference relations. For each of them, we determine the exact extreme results and the distribution of probabilistic results. We apply the proposed method to a case study concerning the performance of healthcare systems in sixteen Polish voivodeships (provinces). We discuss the results based on the entire set of factors (the root of the hierarchy) and three subcategories. They concern health improvement of inhabitants, efficient financial management, and consumer satisfaction. Finally, we show the practical conclusions that can be derived from the hierarchical decomposition of the problem and robustness analysis.

Date of online publication


Pages (from - to)

6406-1 - 6406-33





Article Number: 6406

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Ministry points / journal


Impact Factor

2,7 [List 2022]

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