Data Envelopment Analysis (DEA) is a linear programming technique used to evaluate the relative performance of decision-making units (DMUs). Each DMU consumes varying amounts of inputs and produces different outputs. The goal of DEA is to determine whether a DMU is operating efficiently, given its inputs and outputs, compared to other DMUs. Efficiency is measured by the ratio of a weighted sum of outputs to a weighted sum of inputs, with weights specific to each DMU. DEA models include four orientations: constant returns, variable returns, increasing returns, and decreasing returns. Each model is defined by specific economic assumptions about the relationship between inputs and outputs. The production possibility set, which includes all possible inputs and outputs for the system, is used to determine the efficient frontier. DEA aims to identify if a DMU lies on this frontier and assigns an efficiency score based on its distance from the frontier. The linear programming problems for each orientation are detailed, including the constraints and objective functions. For example, the 'constant returns, input-oriented' model involves minimizing a variable \(\theta\) subject to constraints comparing the DMU's inputs and outputs to a virtual DMU formed from the original DMUs. The optimal value of this problem is always less than or equal to 1, indicating efficiency if it is strictly less than 1. The efficiency of a DMU can be classified as extreme-efficient (unique solution) or nonextreme efficient (multiple optimal solutions). The conditions for efficiency are consistent across different models, and the optimal objective function values lie within specific intervals based on the orientation.Data Envelopment Analysis (DEA) is a linear programming technique used to evaluate the relative performance of decision-making units (DMUs). Each DMU consumes varying amounts of inputs and produces different outputs. The goal of DEA is to determine whether a DMU is operating efficiently, given its inputs and outputs, compared to other DMUs. Efficiency is measured by the ratio of a weighted sum of outputs to a weighted sum of inputs, with weights specific to each DMU. DEA models include four orientations: constant returns, variable returns, increasing returns, and decreasing returns. Each model is defined by specific economic assumptions about the relationship between inputs and outputs. The production possibility set, which includes all possible inputs and outputs for the system, is used to determine the efficient frontier. DEA aims to identify if a DMU lies on this frontier and assigns an efficiency score based on its distance from the frontier. The linear programming problems for each orientation are detailed, including the constraints and objective functions. For example, the 'constant returns, input-oriented' model involves minimizing a variable \(\theta\) subject to constraints comparing the DMU's inputs and outputs to a virtual DMU formed from the original DMUs. The optimal value of this problem is always less than or equal to 1, indicating efficiency if it is strictly less than 1. The efficiency of a DMU can be classified as extreme-efficient (unique solution) or nonextreme efficient (multiple optimal solutions). The conditions for efficiency are consistent across different models, and the optimal objective function values lie within specific intervals based on the orientation.