Shared and unsplittable performance links in network DEA

Data envelopment analysis (DEA) is a broadly used non-parametric technique for performance evaluation and data analytics. While conventional single-stage DEA models overlook the internal interactions of decision making units (DMUs), network DEA opens this black box to investigate the internal structure of DMUs. Practically, many network DEA models involve shared performance measures that are not easily divisible among individual components of a network. Based upon a two-stage network DEA model, the current study treats such performance measures as inseparable links, implying that no proportions are optimized and allocated to the two stages of the network. The shared and unsplittable links in the proposed two-stage DEA model manifest integrality while both ends of the link are maximized or minimized simultaneously, and this setting has not been modeled in any existing DEA studies. The shared and unsplittable links in our model can be considered intermediate measures, but they are different from the two existing types of dual-role intermediate measures, which are traditional intermediate measures and feedback measures. Our performance link is a new type of intermediate measure that is minimized or maximized in both stages of the network. The resulting network DEA model is highly non-linear. To address the non-linearity, a parametric linear model is adopted. The proposed approach is construed in four variants, and then illustrated using a set of 100 banks in the United States.