Document Type : Applied Article
Authors
1 Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran
2 Department of Mathematics, Ne.C., Islamic Azad University, Neyshabur, Iran
Abstract
Two-stage network Data Envelopment Analysis (DEA) models under variable returns to scale (VRS) suffer from a well-known pitfall: efficiency score decomposition and frontier projection can be mutually inconsistent, undermining both the theoretical foundations and practical interpretability of the results. A further limitation is the universal assumption of strong disposability for all inputs and outputs, which is unrealistic when variables are structurally or statistically interdependent—as is common in healthcare settings. This paper addresses both issues simultaneously by developing a novel two-stage network DEA model under hybrid disposability (HD) technology, which allows selective strong or weak disposability for subsets of closely related inputs, intermediate measures, and outputs. We formally derive the efficiency decomposition and frontier projection under HD technology, establish theoretical consistency between the envelopment and multiplier forms, and prove that the proposed model yields Pareto-efficient targets. The model captures synergistic scale effects across stages and preserves structural dependencies between them, thereby providing a more realistic representation of multi-stage production systems. The practical relevance and advantages of the proposed framework are demonstrated through an empirical case study involving 32 Iranian healthcare centers operating under a two-stage network structure with interdependent variables.
Highlights
- A novel two-stage network DEA model under hybrid disposability (HD) technology is developed, allowing selective strong and weak disposability for subsets of interdependent inputs, intermediate measures, and outputs simultaneously.
- Theoretical consistency between efficiency score decomposition and frontier projection is established within the HD framework, resolving the well-known pitfall identified in two-stage network DEA under variable returns to scale.
- Dual equivalence between the envelopment and multiplier forms of the proposed model is formally proved, guaranteeing Pareto-efficient target projections under hybrid disposability assumptions.
- A corrective algorithm is proposed and validated to handle cases where stage-level efficiency scores exceed unity, ensuring theoretically admissible and practically meaningful decompositions.
- An empirical application to 32 Iranian healthcare centers demonstrates the model's enhanced discriminatory power, revealing stage-specific inefficiencies and providing actionable improvement targets that respect structural interdependencies among clinical and operational variables.
Keywords
- Data envelopment analysis
- Two-stage network DEA
- Hybrid disposability
- Variable returns to scale
- Efficiency decomposition
- Frontier projection
- Healthcare performance evaluation
Main Subjects
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