Extensions On Non-radial Data Envelopment Analysis And Their Applications

Traditional data envelop analysis (DEA) uses radial measures to calculate the efficiency of peer decision making units (DMUs). Radial measures assume that inputs and outputs change proportionally. However, there are some cases that inputs and outputs may change non-proportionally. For example, they do not change proportionally if we regard market share and revenues as outputs. As a result, there is a need for non-radial measures. Moreover, the results based on non-radial measures may be totally different from those based on radial measures. Compared with radial measures, non-radial measures successfully reflect the slacks associated with input excesses and output shortfalls. In this dissertation, we study several issues related to non-radial DEA.First and generally, DEA uses radial efficiency measures in existing DEA applications on player performance. Namely, the inputs or outputs of a player change proportionally. However, it is usually impossible. For example, it is impossible to require a player’s score and assist to change proportionally. Hence, non-radial measures are more appropriate in improving a player’s performance. Moreover, DEA usually assumes that data are continuous in existing literature. However, there are situations where data are integers and bounded. For example, in basketball games, the total number of points that a player has scored is an integer and cannot exceed three times of the number of point field goals that a player has attempted. Without modeling the correct data type, the DEA results can be biased and erroneous. The current study applies a non-radial bounded integer DEA model to evaluating the performance of NBA players when bounded integer data exist. As a result, we properly consider non-radial measure and correctly capture the data type. The current study also develops a non-radial super-efficiency measure under the bounded integer data. The problem for the application of non-radial measures is illustrated with data involving a set of NBA shooting guards in the 2013-2014 season.Second, a slacks-based version of the super slacks-based measure (S-SBM) is developed and a novel two-stage approach is proposed recently to calculate both super-efficiency score by the S-SBM model and efficiency score by the slacks-based measure (SBM) model. In this study, we extend the approach to consider continuity of efficiency scores. We illustrate the discontinuity of efficiency measure, then define a continuous slacks-based measure (CSBM) which is proved continuous and directly calculated. An interesting efficiency zone category is also provided. In addition, this study has investigated the relationship among the super-efficiency measures of the proposed approach in this study and some existing approaches under variable returns to scale (VRS).Third, in the prior literature on measuring the efficiency of two-stage processes, there are both radial and non-radial methods of efficiency measurement. In some cases, non-radial methods which allow all inputs, intermediate measures and outputs to change non-proportionally are more appropriate than radial methods, but they do not ensure stage efficiency or allow for the efficiency decomposition of two-stage processes. Based on SBM, this study develops both envelopment-based and multiplier-based models to obtain simultaneously both the frontier projection and the efficiency decomposition. Specifically, we propose the variable intermediate measures SBM (VSBM) model to evaluate the system efficiency of two-stage processes and consider the following three properties of the VSBM model:1) we derive the efficient DEA frontier projection based on the VSBM model; 2) we address potential conflicts in this model with respect to the intermediate measures; 3) we prove that the system inefficiency is equivalent to the sum of inefficiencies of the two stages. Furthermore, we derive the efficiency decomposition of two-stage processes based on the dual of the VSBM model. Finally, we apply our proposed approach to real data of US commercial banks, and extend our approach to settings in which the assumption of variable returns to scale (VRS) holds or there are more general network structures.