Integer-valued DEA super-efficiency based on directional distance function with an application of evaluating mood and its impact on performance

The conventional data envelopment analysis (DEA) assumes that the inputs and outputs are real values. However, in many real world instances, some inputs and outputs must be in integer values. While integer-valued DEA models have been proposed, the current paper develops an integer-valued DEA super-efficiency model. Super-efficiency DEA models are known to have the problem of infeasibility. Recent studies have shown that directional distance function (DDF) based super-efficiency does not seem to have the infeasibility issue. However, the existing DDF DEA approach cannot be directly modified to incorporate integer values under the concept of super-efficiency. The current paper thus modifies the DDF approach so that integer values can be incorporated under the concept of super-efficiency. Our proposed approach is then applied to evaluating mood and its impact on performance. We use both traditional methods as well as the new DEA model to calculate a set of scores for the constructs under the investigation. These analyses extend the application of the DEA method to judgment and decision making. In particular, the results show that the new DEA model is able to reveal subtle nuances such as the impact of mood on performance with a decision support system.