Analiza DEA procesów dwuetapowych: Podejście alternatywne (niekonwencjonalne)
[Data Envelopment Analysis of two-stage processes: An alternative (non-conventional) approach]

Dimitris Despotis (Department of Informatics, University of Piraeus, Greece)


Network data envelopment analysis (NDEA) is an extension of standard data envelopment analysis 
(DEA) that models the efficiency assessment of DMUs by considering their internal structure. 
While in standard DEA the DMU is regarded as a single process, in NDEA the DMU is viewed as a 
network of interconnected sub-processes (stages, divisions), where the flow of the 
intermediate products (measures) is essential in the efficiency assessment. In the prevalent 
conventional methodological approach to NDEA, the sub-processes are assumed as distinct 
entities with distinct inputs and outputs. Thus, each sub-process has its own production 
possibility set (PPS), which can be derived axiomatically from a set of assumptions using the 
minimum extrapolation principle. The PPS of the overall system is defined as the composition 
of the individual PPSs. 

The conventional approach comprises all the methods, in which the system and the divisional 
efficiencies are computed jointly in a single mathematical program. A fundamental property 
connecting the system with the divisional efficiencies is that a system is overall efficient 
if and only if its divisions are all efficient. In NDEA, regardless of the method used, there 
are cases where none of the observed DMUs is rendered overall efficient, as corroborated by 
real-world case studies. This is the main issue we discuss in this paper and the motivation 
to propose an alternative, non-conventional, approach to address it in the frame of two-stage 
processes. 

We consider the two-stage process as a system that can be viewed in two perspectives depending 
on the role of the intermediate measures: the system as producer and as consumer of the 
intermediates. As our approach is based on standard DEA, it satisfies the basic desirable 
properties. The fundamental NDEA property, that the overall system is efficient if and only 
if both perspectives are efficient, is met. The efficient frontier of the system is 
explicitly defined by the overall efficient observed DMUs and the inefficient DMUs are 
projected on the efficient frontier of the system.