Efficiency stability region for two-stage production processes with intermediate products

Abstract Network data envelopment analysis (NDEA) is used to evaluate the performance of a set of multi-stage decision-making units (DMUs) (or multi-stage production processes) taking into account the internal structure of these DMUs. Finding efficiency stability regions (ESRs) for efficient DMUs is one of the most important issues in DEA because it can provide useful information for their managers (or decision-makers) from the managerial and economic viewpoints. ESR of an efficient DMU is the region that this DMU will remain efficient if and only if after changing its inputs and its outputs it stays in this region. Hitherto, there exist many DEA approaches in the context of finding the ESRs of DMUs however, none of them take into account the internal structures of DMUs to find their ESRs. They only consider the inputs and the (final) outputs of DMUs to find their ESRs. This problem is the drawback of all existing approaches in this context. Hence, this study contributes to network DEA by proposing a novel approach to tackle this problem. To do this, we first define the three concepts of ‘network-efficient’, ‘extreme network-efficient’, and ‘ESR’ in network DEA and then introduce a linear DEA model to specify the extreme network-efficient two-stage production processes. Second, we propose a DEA approach to find the ESRs of these two-stage production processes. The proposed approach finds the ESR of an extreme network-efficient two-stage production process when its inputs increase, its intermediate products and (final) outputs decrease, and the data of the other two-stage production processes remain unchanged. This research also clarifies the managerial and economic implications of finding the ESRs. Finally, three numerical examples and an empirical application are given to show the use of the proposed approach. Proofs of the theorems are also presented in the appendix.