Comprehensive DEA Evaluation Method Implemented in MATLAB

Data Envelopment Analysis (DEA) is a comprehensive evaluation method used to assess the relative efficiency of Decision Making Units (DMUs), widely applied in economics, management, energy, and other fields. MATLAB serves as an ideal programming tool for implementing DEA models due to its powerful matrix operations and optimization toolbox capabilities.

The core implementation of DEA comprehensive evaluation method in MATLAB involves constructing linear programming models. Common DEA models include CCR (Constant Returns to Scale) and BCC (Variable Returns to Scale) formulations. In MATLAB implementation, the computational process primarily consists of three key steps: standardization of input-output data using matrix normalization functions, construction of efficiency frontiers through mathematical programming, and linear optimization solving using MATLAB's optimization algorithms.

MATLAB's advantage lies in its ability to rapidly process large-scale data matrices and solve linear programming problems through built-in functions like linprog(). The linprog function efficiently handles the optimization constraints and objective functions required for DEA calculations. For complex multi-input, multi-output systems, the DEA method effectively avoids subjective weight setting and objectively evaluates the relative efficiency values of each decision-making unit through mathematical programming techniques.

In practical applications, beyond basic efficiency scoring, MATLAB enables extended functionality including scale efficiency analysis through additional mathematical modeling, slack variable calculations using optimization results, and efficiency improvement direction analysis. These advanced features provide more comprehensive decision support references by implementing additional analytical modules in the MATLAB codebase.