Uncertain data envelopment analysis with box uncertainty

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• Emma Stubington (Lancaster University)
• Wednesday 13 November 2019, 12:00-13:00
• Strathcona, SR5.

If you have a question about this talk, please contact Sergey Sergeev.

Data envelopment analysis (DEA) is a nonparametric, data driven technique to perform relative performance analysis among a group of comparable “decision-making units” (DMUs). Efficiency is assessed by comparing input and output data for each DMU via linear programming. Traditionally in DEA the data are considered to be exact. However, it is likely that the values for the variables used in the analysis are imprecise. To account for the inherent uncertainty present in many real-world data instances we assume that the variables are in fact realisations from a range, called an uncertainty set and consider the uncertain DEA problem (uDEA). We wish to determine the minimum amount of uncertainty required for an inefficient DMU to be evaluated as efficient. That is, we leverage the uncertainty present in the data such that inefficient DMUs may improve. We develop the uDEA problem for the case of box uncertainty and show that for small problems this can be solved exactly. We explore the relationship between the amount of uncertainty required for an inefficient DMU to be deemed efficient and how this efficiency is achieved. We determine the minimum amount of uncertainty required for a DMU to be deemed efficient. For small problems, this value can be easily calculated but for larger instances, this becomes computationally intensive as it requires the facets of the Production Possibility Set to be known. This study of uncertainty is motivated by the inherently uncertain nature of the radiotherapy treatment planning process.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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• Optimisation and Numerical Analysis Seminars
• School of Mathematics events
• Strathcona, SR5

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