A mixed-integer slacks-based measure data envelopment analysis for efficiency measuring of German university hospitals.

Standard Data Envelopment Analysis (DEA) models consider continuous-valued and known input and output statuses for measures. This paper proposes an extended Slacks-Based Measure (SBM) DEA model to accommodate flexible (a measure that can play the role of input and output) and integer measures simultaneously. A flexible measure's most appropriate role (designation) is determined by maximizing the technical efficiency of each unit. The main advantage of the proposed model is that all inputs, outputs, and flexible measures can be expressed in integer values without inflation of efficiency scores since they are directly calculated by modifying input and output inefficiencies. Furthermore, we illustrate and examine the application of the proposed models with 28 university hospitals in Germany. We investigate the differences and common properties of the proposed models with the literature to shed light on both teaching and general inefficiencies. Results of inefficiency decomposition indicate that "Third-party funding income" that university hospitals receive from the research-granting agencies dominates the other inefficiencies sources. The study of the efficiency scores is then followed up with a second-stage regression analysis based on efficiency scores and environmental factors. The result of the regression analysis confirms the conclusion derived from the inefficiency decomposition analysis.