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

TL;DR

This paper introduces two regularized DEA models for dynamic, large-scale efficiency evaluation across multiple organizational dimensions, effectively integrating desirable and undesirable outputs.

Contribution

It presents novel slack-based and goal programming DEA models that improve discrimination and aggregate efficiency assessment in large datasets.

Findings

Models outperform conventional methods in capturing input-output correlations.

Both models demonstrate computational efficiency and validity on real datasets.

Application to hospital data shows improved evaluation of organizational effectiveness.

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.