Two-stage network DEA: Who is the leader?

The non-cooperative two-stage network DEA approach requires the assumption as to whether the first or second stage is the leader or follower. In many real-world situations such as evaluating sustainable design performances, however, information about the leader (dominant) stage is often unavailable as a firm׳s internal decision process may not be observable for outsiders. In the current study, we extend the work by Despotis, Sotiros and Koronakos (2016) [9] to generate a Pareto solution and identify the leader stage. We show that the optimal solution for the extended model is also a leader-follower solution and that the global optimal solution can be identified by comparing the efficiency score difference for the upper and lower bounds of the two stages. We also perform empirical tests with data from the insurance industry and automobile industry to demonstrate the applications of the proposed model in identifying the leader stage in two-stage DEA. It is shown that, in the absence of a priori knowledge, our analytical results can be used to uncover the dominant decision stage in a two-stage decision making process with interesting implications in performance evaluation in the two selected industries.