Endogenous Aggregation of Multiple Data Envelopment Analysis Scores for Large Data Sets

2025-10-22

AI Summary

To address the dynamic evaluation of multi-dimensional organizational efficiency under large-scale data, this paper proposes a regularized Data Envelopment Analysis (DEA) framework integrating both desirable and undesirable outputs. Methodologically, it introduces two complementary models: the Slacks-Based Measure (SBM), which allocates overall efficiency top-down, and the Goal Programming–SBM (GP-SBM), which aggregates dimensional efficiencies bottom-up; both employ slack variables for efficiency measurement and incorporate ℓ₂ regularization to mitigate interference from high-dimensional correlated inputs. GP-SBM further ensures computational tractability via linearization of the goal programming formulation. The key contribution lies in the first endogenous integration and bidirectional calibration of multi-dimensional efficiency, markedly enhancing discriminatory power. Empirical validation across multiple heterogeneous datasets and a hospital case study demonstrates superior modeling consistency and enhanced capability in capturing variable correlations compared to conventional stepwise DEA approaches.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Evaluation and Analysis
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We propose an approach for dynamic efficiency evaluation across multiple organizational dimensions using data envelopment analysis (DEA). The method generates both dimension-specific and aggregate efficiency scores, incorporates desirable and undesirable outputs, and is suitable for large-scale problem settings. Two regularized DEA models are introduced: a slack-based measure (SBM) and a linearized version of a nonlinear goal programming model (GP-SBM). While SBM estimates an aggregate efficiency score and then distributes it across dimensions, GP-SBM first estimates dimension-level efficiencies and then derives an aggregate score. Both models utilize a regularization parameter to enhance discriminatory power while also directly integrating both desirable and undesirable outputs. We demonstrate the computational efficiency and validity of our approach on multiple datasets and apply it to a case study of twelve hospitals in Ontario, Canada, evaluating three theoretically grounded dimensions of organizational effectiveness over a 24-month period from January 2018 to December 2019: technical efficiency, clinical efficiency, and patient experience. Our numerical results show that SBM and GP-SBM better capture correlations among input/output variables and outperform conventional benchmarking methods that separately evaluate dimensions before aggregation.

Problem

• Dynamic efficiency evaluation across multiple organizational dimensions using DEA
• Generating dimension-specific and aggregate efficiency scores for large datasets
• Incorporating both desirable and undesirable outputs in efficiency measurement

Innovation

• Regularized DEA models with slack-based measures
• Integrated desirable and undesirable outputs directly
• Dynamic efficiency evaluation across multiple organizational dimensions