An extended inequality approach for evaluating decision making units with a single output

Area of Science:

• Operations Research
• Management Science
• Economics

Background:

• Evaluating decision-making units (DMUs) is crucial for optimizing performance.
• Existing methods may not adequately capture efficiency nuances for single-output DMUs.
• A need exists for extended evaluation approaches in performance analysis.

Purpose of the Study:

• To propose an extended evaluation approach for decision-making units (DMUs) with a single output.
• To develop a method for distinguishing between weak efficiency and full efficiency.
• To provide a practical example illustrating the proposed evaluation technique.

Main Methods:

• Data normalization: Input and output data are proportionally adjusted until all outputs are equal.
• Coordinate system establishment: A system is created with input variables as coordinate axes.
• Production possibility set definition: The set is defined by inequalities using DMUs excluding the evaluated one.
• Efficiency measure calculation: Derived from the geometric relationship between the production possibility set and the DMU's data line segment.
• Distinguishing efficiency levels: Introduction of partially ordered sets and minimal elements to differentiate weak and full efficiency.

Main Results:

• A novel geometric approach for evaluating single-output DMUs is presented.
• The method provides a clear distinction between weak and full efficiency.
• The proposed technique is demonstrated through a practical example, showing its applicability.

Conclusions:

• The extended evaluation approach offers a robust framework for assessing single-output DMU efficiency.
• The method enhances the precision of efficiency measurement by incorporating geometric principles.
• This work contributes to the field of performance evaluation by providing a refined analytical tool.