Sieciowe DEA: podejście "bottom up" a podejście "top down"
[Network DEA: Bottom-up versus top-down approach]

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


Data Envelopment Analysis (DEA) is a non-parametric technique based on linear
programming for the efficiency assessment of Decision-Making Units (DMUs), which use
multiple inputs to produce multiple outputs. Network DEA is an extension of the
conventional DEA, which considers the DMU as a network of sub-DMUs (stages, divisions,
sub-processes, etc.). In network DEA, the efficiency is a multi-dimensional (vector) 
measure, as one has to account for the efficiency of the divisions encountered in the 
process as well as the overall system efficiency. Assessing the efficiency of the 
individual divisions and the overall efficiency of the system independently of each 
other constitutes the so-called independent efficiency assessments approach. The 
holistic approach, on the other hand, requires that the efficiencies of the individual 
divisions and the overall system efficiency are estimated jointly by considering the 
interdependencies of the divisions by means of the flow of intermediate measures. The 
series and the parallel production processes are two characteristic process 
configurations studied extensively in the literature. Generally, there are two main 
paradigms in the holistic approach of network DEA for series processes, namely the 
non- cooperative and the cooperative. In both paradigms, the efficiency of each
division is commonly defined as the ratio of the implied aggregate value of its 
outputs to the implied aggregate value of its inputs. Focusing on two-stage processes, 
the non-cooperative paradigm assumes that pre-emptive priority is given to one of the 
two stages (leader stage), whose efficiency is assessed first. Then, the efficiency of 
the other stage (follower) is assessed in a manner that the optimal efficiency of the 
leader is maintained. In the cooperative paradigm, two broad approaches can be 
identified, namely the top-down approach and the bottom-up approach. This 
classification reflects how the different methods select the driver of the assessment, 
i.e. whether the system (top-down) or the divisional efficiencies (bottom-up) is given 
priority for optimization. We critically outline representative methods of the two 
approaches and discuss their compliance with some required properties.

Based on:
[1] G Koronakos, D Sotiros, DK Despotis (2019). Reformulation of Network Data 
Envelopment Analysis models using a common modelling framework. European Journal of 
Operational Research , 278 (2), 472-480.
[2] D Sotiros, G Koronakos, DK Despotis (2019). Dominance at the divisional 
efficiencies level in network DEA: The case of two-stage processes. Omega 85, 144-155.
[3] DK Despotis, G Koronakos, D Sotiros (2016). The "weak-link" approach to 
network DEA for two-stage processes. European Journal of Operational Research 254(2), 
481-492.
[4] DK Despotis, D Sotiros, G Koronakos (2016). A network DEA approach for series 
multi-stage processes. Omega 61, 35-48.
[5] DK Despotis, G Koronakos, D Sotiros (2016). Composition versus decomposition in 
two-stage network DEA: a reverse approach. Journal of Productivity Analysis 45(1) 71-87.