Uncertain Data Envelopment Analysis

Ehrgott, Matthias and Holder, Allen and Nohadani, Omid (2018) Uncertain Data Envelopment Analysis. European Journal of Operational Research, 268 (1). pp. 231-242. ISSN 0377-2217

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Abstract

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.

Item Type: Journal Article
Journal or Publication Title: European Journal of Operational Research
Additional Information: This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 268, 1, 2018 DOI: 10.1016/j.ejor.2018.01.005
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/1800/1802
Subjects:
Departments: Lancaster University Management School > Management Science
ID Code: 90174
Deposited By: ep_importer_pure
Deposited On: 06 Feb 2018 17:00
Refereed?: Yes
Published?: Published
Last Modified: 22 Feb 2020 04:23
URI: https://eprints.lancs.ac.uk/id/eprint/90174

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