Input redistribution in DEA models: A two-stage approach via mixture design optimization
DOI:
https://doi.org/10.15675/gepros.3053Keywords:
Data envelopment analysis, Resource allocation, Fixed inputs, Mixture design, Efficiency optimizationAbstract
Objective: This study develops a novel approach to address a fundamental limitation in efficiency analysis using Data Envelopment Analysis (DEA). While traditional DEA models provide valuable insights into organizational efficiency, they typically assume that decision-making units can freely adjust their input quantities. The present work introduces an innovative two-stage methodology that combines DEA with mixture design optimization to redistribute fixed-sum inputs while maximizing overall system efficiency. Methodology/Approach: The proposed methodology begins with a standard DEA assessment to identify technical efficiencies and input slacks across all decision-making units. This initial stage provides the foundation for understanding current performance levels and potential improvement areas. The second stage implements a constrained optimization framework using Mixture Design Experiment, where the fixed input is treated as a mixture component with strict composition boundaries. Research, practical and Social Implications: From a research perspective, this work makes significant contributions to both efficiency analysis and operations research by developing a formal framework for constrained resource redistribution. For practitioners, the approach offers a tool for optimizing resource allocation in various sectors, including public administration, healthcare systems, and industrial operations, where fixed budgets or quotas are common constraints. Socially, the method provides a systematic way to improve resource distribution fairness and effectiveness, particularly in scenarios involving public goods or services where equitable allocation is crucial. Originality/Value: The principal innovation of this research lies in its unique integration of DEA with mixture design optimization to solve the fixed-input redistribution problem. The study advances the field by demonstrating how experimental design principles can be adapted for efficiency optimization problems, opening new possibilities for hybrid analytical approaches.
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Copyright (c) 2025 Gustavo dos Santos Leal, Pedro Paulo Balestrassi, João Batista Turrioni, Lupércio França Bessegato
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