Uncertain Data Envelopment Analysis

Matthias Ehrgott*, Allen Holder, Omid Nohadani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)231-242
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - Jul 1 2018


  • Data Envelopment Analysis
  • Radiotherapy design
  • Robust optimization
  • Uncertain DEA problem
  • Uncertain data

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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