Robust DEA efficiency scores: A probabilistic/combinatorial approach

TL;DR

This paper introduces a probabilistic and combinatorial method to compute robust efficiency scores in Data Envelopment Analysis, accounting for input/output uncertainty and enabling large-scale computations.

Contribution

It develops a novel approach to calculate three types of robust DEA efficiency scores using probabilistic modeling and efficient algorithms for large datasets.

Findings

Able to compute over 200 million linear problems efficiently

Provides three robust efficiency scores based on probability distributions

Demonstrates application in assessing professional tennis players

Abstract

In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This proba- bilistic approach allows us to obtain three different robust efficiency scores: the Conditional Expected Score, the Unconditional Expected Score and the Expected score under the assumption of Maximum Entropy principle. The calculation of the three efficiency scores involves the resolution of an exponential number of linear problems. The algorithm presented in this paper allows to solve over 200 millions of linear problems in an affordable time when considering up 20 inputs/outputs and 200 DMUs. The approach proposed is illustrated with an application to the assessment of professional tennis players.