Optimal scale sizes and average-profit efficiency under uncertainty: A chance-constrained DEA approach

Area of Science:

• Operations Research
• Econometrics
• Management Science

Background:

• Profit efficiency evaluation is crucial for understanding unit performance when input/output costs are known.
• Existing efficiency measures may lack the precision needed for complex, real-world scenarios.

Purpose of the Study:

• To present a novel definition of optimal scale size based on maximizing average profit efficiency.
• To introduce a more accurate measure of economic efficiency compared to existing methods.
• To develop models for calculating profit efficiency in stochastic environments.

Main Methods:

• Definition of optimal scale size via maximization of average profit efficiency.
• Development of the average measure of profit efficiency.
• Formulation of stochastic models for profit efficiency calculation.
• Empirical application to Iranian postal areas.

Main Results:

• The average measure of profit efficiency is shown to be equivalent to profit efficiency in constant returns to scale technology within convex spaces.
• Stochastic models enhance the applicability of profit models by addressing input/output calculation errors.
• The proposed method successfully calculated average profit efficiency for Iranian postal areas.

Conclusions:

• The novel average profit efficiency measure provides a more accurate assessment of unit performance.
• The developed stochastic models improve the robustness of profit efficiency evaluations in practical settings.
• The empirical study demonstrates the utility of the proposed methodology in a real-world context.