Composition versus decomposition in two-stage network DEA: a reverse approach

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 efficiency-decomposition 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.