Uncertain Data Envelopment Analysis
| Autor: | Matthias Ehrgott, Omid Nohadani, Allen Holder |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
021103 operations research Information Systems and Management Leverage (finance) General Computer Science Linear programming Uncertain data Computer science 0211 other engineering and technologies Nonparametric statistics Robust optimization Monotonic function 02 engineering and technology Management Science and Operations Research Industrial and Manufacturing Engineering Data-driven 03 medical and health sciences 0302 clinical medicine 030220 oncology & carcinogenesis Modeling and Simulation Data envelopment analysis Leverage (statistics) |
| Zdroj: | European Journal of Operational Research. 268:231-242 |
| ISSN: | 0377-2217 |
| Popis: | Data Envelopment Analysis (DEA) is a nonparametric, data driven method to conduct relative performance measurements among a set of decision making units (DMUs). Efficiency scores are computed based on assessing input and output data for each DMU by means of linear programming. Traditionally, these data are assumed to be known precisely. We instead consider the situation in which data is uncertain, and in this case, we demonstrate that efficiency scores increase monotonically with uncertainty. This enables inefficient DMUs to leverage uncertainty to counter their assessment of being inefficient. Using the framework of robust optimization, we propose an uncertain DEA (uDEA) model for which an optimal solution determines (1) the maximum possible efficiency score of a DMU over all permissible uncertainties, and (2) the minimal amount of uncertainty that is required to achieve this efficiency score. We show that the uDEA model is a proper generalization of traditional DEA and provide a first-order algorithm to solve the uDEA model with ellipsoidal uncertainty sets. Finally, we present a case study applying uDEA to the problem of deciding efficiency of radiotherapy treatments. |
| Databáze: | OpenAIRE |
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