# Data Envelopment Analysis of two-stage processes: An alternative (non-conventional) approach

Network data envelopment analysis (NDEA) is an extension of standard data envelopment analysis 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, where the common characteristic is that 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. However, real-word case studies have shown that there are cases where none of the DMUs is rendered overall efficient regardless of the NDEA method used. This is the main issue we discuss in this paper and our 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 acquires 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 overall efficient observed DMUs. The inefficient DMUs are projected on the efficient frontier of the system. The models are equivalently expressed in both the multiplier and the envelopment forms due to strict primal-dual correspondence and are able to operate under both constant and variable returns-to-scale assumptions. We use the case of twenty-two automotive manufactures for the fiscal year 2019 as an example to illustrate our approach. Comparison with other NDEA methods is also provided.

## Citation

University of Piraeus, Department of Informatics, Karaoli and Dimitriou 80, 18534, May/2022