Ranking intervals for two-stage production systems

Traditional Data Envelopment Analysis (DEA) models find the most desirable weights for each Decision Making Unit (DMU) in order to estimate the highest efficiency score as possible. Usually, decision-makers are using these efficiency scores for ranking the DMUs. The main drawback in this process is that the ranking based on weights obtained from the standard DEA models ignore other feasible weights, this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black box” and developed a mix-integer model to obtain the ranking intervals for each DMU over sets of all its feasible weights. In many real-world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka (2011)’s model to more common and practical applications considering the two-stage production structure. The proposed approach calculates each DMU’s ranking interval for the overall system as well as for each subsystem/sub-stage. An application for non-life insurance companies is given to illustrate the applicability of the proposed approach. A real application in Chinese commercial banks shows how this approach can be used by policy makers.