Directional slack-based measure for the inverse data envelopment analysis.

Area of Science:

• Operations Research
• Management Science

Background:

• Data Envelopment Analysis (DEA) is widely used for efficiency measurement.
• Inverse DEA models are crucial for understanding efficiency improvements.
• Existing methods may not fully capture modifications within production possibility sets.

Purpose of the Study:

• To introduce and elucidate a novel inverse directional slack-based measure (DSBM).
• To develop a model for modifying efficient decision-making units (DMUs) within a new production possibility set.
• To demonstrate the application and benefits of the proposed model in resource allocation problems.

Main Methods:

• Development of an inverse directional slack-based measure model.
• Modification of efficient DMUs by substituting and adjusting input/output quantities.
• Retaining overall DMU efficiency scores while allowing for improvements.
• Application to a resource allocation problem with simultaneous output/input adjustments.

Main Results:

• The proposed model successfully retains efficiency scores of all DMUs.
• The method demonstrates potential for improving efficiency scores.
• Numerical examples confirm the model's applicability and significance in resource allocation.
• The approach allows for simultaneous consideration of output upsurges or declines.

Conclusions:

• The novel inverse directional slack-based measure offers a refined approach to efficiency analysis.
• The method provides a flexible framework for analyzing modified production possibility sets.
• The technique is valuable for resource allocation and understanding efficiency dynamics.