Stochastic ranking and dominance in DEA

AuthorsM. Davtalab Olyaie, M. Asgharian and V. Partovi Nia
JournalInternational Journal of Production Economics
Paper TypeFull Paper
Published At2019
Journal GradeISI
Journal TypeTypographic
Journal CountryNetherlands

Abstract

Data Envelopment Analysis (DEA) requires deterministic input/output data for efficiency evaluation of a set of
Decision Making Units (DMUs). When there are more than one set of input/output data for each DMU, however,
such requirement is infeasible. Stochastic DEA (SDEA), where input/output data are assumed to be stochastic, is
a natural approach for such applications. Performance evaluation of DMUs in SDEA naturally calls for ranking
methods that can account for stochastic fluctuations of the input/output, and hence the efficiency score. None of
the proposed methods in the current literature incorporates all the information in the efficiency score distributions
for ranking DMUs. To fill this gap, we introduce two ranking methods, a partial and a linear, for
performance evaluation in SDEA using the reliability function of the efficiency scores. Our proposed partial
ranking is based on the notion of stochastic ordering, while our linear ordering is a weighted average of the
reliability function of the efficiency scores. Special cases of our proposed linear ranking method include mean
and median ordering in SDEA. Our proposed partial ordering provides a notion for stochastic dominance using
which one can define a natural notion of admissibility as a minimal performance requirement. We demonstrate
how the proposed ranking methods can be implemented and illustrate the methods using the Grundfeld data,
analyzed using both parametric and non-parametric approaches.