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

Network data envelopment analysis (NDEA) is an extension of standard data envelopmentanalysis (DEA) that models the efficiency assessment of DMUs by considering their internalstructure. While in standard DEA the DMU is regarded as a single process, in NDEA the DMUis viewed as a network of interconnected sub-processes (stages, divisions), where the flow ofthe intermediate products (measures) is essential in the efficiency assessment. In the prevalentconventional methodological approach to NDEA, the sub-processes are assumed as distinctentities with distinct inputs and outputs. Thus, each sub-process has its own productionpossibility set (PPS), which can be derived axiomatically from a set of assumptions using theminimum extrapolation principle. The PPS of the overall system is defined as the compositionof the individual PPSs. The conventional approach comprises all the methods, in which thesystem 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 systemis overall efficient if and only if its divisions are all efficient. In NDEA, regardless of themethod 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 andthe motivation to propose an alternative, non-conventional, approach to address it in the frameof two-stage processes. We consider the two-stage process as a system that can be viewed intwo perspectives depending on the role of the intermediate measures: the system as producerand as consumer of the intermediates. As our approach is based on standard DEA, it satisfiesthe basic desirable properties. The fundamental NDEA property, that the overall system isefficient if and only if both perspectives are efficient, is met. The efficient frontier of the systemis explicitly defined by the overall efficient observed DMUs and the inefficient DMUs areprojected on the efficient frontier of the system. A convergent procedure is presented for thispurpose. The proposed models are equivalently expressed in both the multiplier and theenvelopment forms due to strict primal-dual correspondence and are able to operate under bothconstant and variable returns-to-scale assumptions. We use the case of twenty-two automotivemanufactures for the fiscal year 2019 as an example to illustrate our approach. Comparisonwith other NDEA methods is also provided