Data envelopment analysis of two‐stage processes: an alternative (non‐conventional) approach

Abstract

AbstractNetwork data envelopment analysis (NDEA) is an extension of standard DEA that models the efficiency assessment of decision‐making units (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 from 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. A convergent procedure is presented for this purpose. The proposed models are equivalently expressed in both the multiplier and the envelopment forms due to strict primal‐dual correspondence and can operate under both constant and variable returns‐to‐scale assumptions. We use the case of 22 automotive manufacturers for the fiscal year 2019 as an example to illustrate our approach. Comparison with other NDEA methods is also provided.