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Combinatorial efficiency evaluation: the knapsack problem in data envelopment analysis.

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This study introduces a novel combinatorial efficiency evaluation model for selecting multiple decision-making units (DMUs), addressing limitations of traditional methods. The enhanced model provides a unique best combination, improving practical decision-making in efficiency analysis.

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Area of Science:

  • Operations Research
  • Management Science
  • Decision Analysis

Background:

  • Traditional Data Envelopment Analysis (DEA) focuses on single Decision Making Unit (DMU) efficiency.
  • Practical scenarios often require selecting multiple DMUs, a problem not adequately addressed by existing DEA literature.
  • Existing combinatorial efficiency models may present drawbacks in practical application.

Purpose of the Study:

  • To develop a modified combinatorial efficiency evaluation model for selecting multiple DMUs.
  • To address the limitations of the basic model proposed by Cook and Green.
  • To provide decision-makers with a unique and persuasive best combination of DMUs.

Main Methods:

  • Formulating the combinatorial efficiency evaluation problem as a knapsack problem.
  • Integrating the super-efficiency model with a modified DEA framework.
  • Developing an adapted local search algorithm to solve the combinatorial optimization problem.

Main Results:

  • The proposed modified model overcomes drawbacks of previous approaches.
  • The model successfully identifies a unique best combination of DMUs.
  • Numerical examples validate the effectiveness of the proposed model and algorithm.

Conclusions:

  • The novel combinatorial efficiency model offers a more robust approach for selecting multiple DMUs.
  • The integrated super-efficiency and modified DEA model provides a unique optimal solution.
  • The adapted local search algorithm efficiently solves the complex combinatorial problem, enhancing practical decision-making.