Undesirable factors in integer-valued DEA: Evaluating the operational efficiencies of city bus systems considering safety records

In conventional data envelopment analysis (DEA) methods, all inputs and outputs are assumed to be continuous. However, in many practical situations, firms may generate both desirable and undesirable outputs, and some of which may only take integer values (e.g., the number of traffic accidents and deaths in a transportation system). The efficiency evaluation results can be inaccurate if these conditions are not incorporated in the model. In this paper we propose an integer DEA model with undesirable inputs and outputs. The proposed model is developed based on the additive DEA model, in which input and output slacks are used to compute efficiency scores. We also develop an integer super-efficiency model to discriminate the performance of efficient firms. As an illustration, we apply the proposed models to the longitudinal data from a city bus company in Taiwan. ► We propose an additive DEA model dealing with integer undesirable inputs and outputs. ► We further present its related super-efficiency model to distinguish efficient units. ► Both additive models can cope with undesirable factors and integer constraints. ► Models are illustrated by an empirical efficiency evaluation of city bus operation. ► Safety record, an integer undesirable output, is considered in the empirical study.