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Π2.7β D.K. Despotis, G. Koronakos, D. Sotiros (2014). Composition versus decomposition in two-stage network DEA: a reverse approach. Journal of Productivity Analysis

Abstract A two-stage production process assumes that
the first stage transforms external inputs to a number of
intermediate measures, which then are used as inputs to the
second stage that produces the final outputs. The fundamental
approaches to two-stage network data envelopment
analysis are the multiplicative and the additive efficiencydecomposition
approaches. Both they assume a series
relationship between the two stages but they differ in the
definition of the overall system efficiency as well as in the
way they conceptualize the decomposition of the overall
efficiency to the efficiencies of the individual stages. In this
paper, we first show that the efficiency estimates obtained
by the additive decomposition method are biased, by
unduly favouring one stage against the other, while those
obtained by the multiplicative method are not unique.
Then, we present a novel approach to estimate unique and
unbiased efficiency scores for the individual stages, which
are then composed to obtain the efficiency of the overall
system, by selecting the aggregation method a posteriori.
Within the particularity of two-stage processes emerging
from the conflicting role of the intermediate measures, we
develop an envelopment model to locate the efficient
frontier whose derivation from our primal multiplier efficiency
assessment model is effectively justified. The results
derived from our approach are compared with those
obtained by the aforementioned basic methods on experimental
data as well as on test data drawn from the literature.
Similarities and dissimilarities in the results are
rigorously justified.