Data Envelopment Analysis (DEA) is a linear programming technique for evaluating the relative efficiency of similar decision making units (DMUs). Each DMU consumes inputs to produce outputs, and DEA determines whether a DMU is efficient relative to others. Efficiency is measured as the ratio of weighted outputs to weighted inputs. DEA allows for different weights for each DMU and handles incommensurable inputs and outputs. A process is output-efficient if no other process produces higher outputs with the same or smaller inputs, and input-efficient if no other process uses smaller inputs to produce the same or higher outputs. DEA models include constant, variable, increasing, and decreasing returns to scale. The production possibility set includes all DMUs and virtual DMUs derived from linear combinations of original data. The efficient frontier is a subset of the boundary of this set. DEA aims to determine if a DMU lies on the efficient frontier and to assign a score based on its distance from it. The 'constant returns, input oriented' model minimizes the ratio of inputs to outputs, while the 'constant returns, output oriented' model maximizes the ratio of outputs to inputs. The dual problems for these models are presented, with constraints defining variable, increasing, and decreasing returns. The efficiency of a DMU is determined by whether it is inefficient or efficient, with extreme efficiency defined by unique solutions. The optimal objective function values lie in specific intervals depending on the orientation. The linear programs can be interpreted as comparing a reference DMU with a virtual DMU derived from linear combinations of other DMUs.Data Envelopment Analysis (DEA) is a linear programming technique for evaluating the relative efficiency of similar decision making units (DMUs). Each DMU consumes inputs to produce outputs, and DEA determines whether a DMU is efficient relative to others. Efficiency is measured as the ratio of weighted outputs to weighted inputs. DEA allows for different weights for each DMU and handles incommensurable inputs and outputs. A process is output-efficient if no other process produces higher outputs with the same or smaller inputs, and input-efficient if no other process uses smaller inputs to produce the same or higher outputs. DEA models include constant, variable, increasing, and decreasing returns to scale. The production possibility set includes all DMUs and virtual DMUs derived from linear combinations of original data. The efficient frontier is a subset of the boundary of this set. DEA aims to determine if a DMU lies on the efficient frontier and to assign a score based on its distance from it. The 'constant returns, input oriented' model minimizes the ratio of inputs to outputs, while the 'constant returns, output oriented' model maximizes the ratio of outputs to inputs. The dual problems for these models are presented, with constraints defining variable, increasing, and decreasing returns. The efficiency of a DMU is determined by whether it is inefficient or efficient, with extreme efficiency defined by unique solutions. The optimal objective function values lie in specific intervals depending on the orientation. The linear programs can be interpreted as comparing a reference DMU with a virtual DMU derived from linear combinations of other DMUs.