MATLAB Implementation of Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a mathematical programming approach for evaluating the relative efficiency of decision-making units with multiple inputs and outputs. This method helps users assess various decision alternatives and identify optimal solutions through frontier analysis. The DEA program typically includes detailed inline comments that explain the mathematical formulation and computational steps, making it particularly suitable for beginners studying operations research and efficiency analysis. During implementation, users need to input data matrices containing input and output indicators, which can be structured as tables or arrays in MATLAB. The core algorithm involves solving linear programming problems to construct an efficiency frontier and calculate efficiency scores for each decision unit. Key functions may include data normalization, constraint matrix generation, and linear optimization using MATLAB's linprog function or optimization toolbox. The program processes these data inputs through mathematical optimization routines and outputs efficiency scores for each alternative, typically ranging from 0 to 1. These scores help users understand the relative strengths and weaknesses of each option, where units on the frontier (score = 1) are considered efficient. The implementation may include visualization components to display efficiency frontiers using MATLAB's plotting capabilities, showing efficient units versus inefficient ones. Therefore, the Data Envelopment Analysis program is highly valuable for users requiring multi-objective decision support, particularly in fields like performance evaluation, resource allocation, and comparative efficiency studies across organizations or processes.