Development of a multiple layer DEA model with applications in road safety performance evaluation

Abstract

Data envelopment analysis (DEA) developed by Charnes, Cooper and Rhodes (CCR) is a mathematical programming methodology to measure the relative efficiency of a homogeneous set of decision making units (DMUs) by estimating the relations between multiple inputs and multiple outputs related to the DMUs. Since its first introduction in 1978, DEA has been quickly recognized as a powerful analytical research tool for modeling operational processes in terms of performance evaluations, benchmarking, and decision making, and it has been successfully applied to a host of different types of entities engaged in a wide variety of activities in many contexts. However, since performance management becomes more and more complex nowadays, a structural weakness has also arisen in the applications of the basic DEA models. Specifically, there are a great number of performance evaluation activities which not only need to be represented by a set of performance indicators, but these indicators might also belong to different categories and further be linked to one another constituting a multilayer structure, such as in the road safety performance evaluation, relevant factors determining the occurrence of crashes or the severity of casualties are usually quantified by means of safety performance indicators (SPIs). Given the high number of factors (e.g., the use of protective systems) and corresponding SPIs (e.g., seat belt wearing rate in front seats, seat belt wearing rate in rear seats, helmet wearing, …), these indicators are best presented as a layered hierarchy. Therefore, simply treating all the indicators to be in the same layer of the DEA model obviously ignores the information on their hierarchical structure and further leads up to weak discriminating power and unrealistic weight allocations. To this end, the concept of multiple layer DEA (MLDEA) model is proposed in this study. Starting from the input‐oriented CCR model, we elaborate the mathematical deduction process of the MLDEA model, formulate the weights in each layer of the hierarchy, and indicate different types of possible weight restrictions for each category of each layer. Meanwhile, its linear transformation is realized and further extended to the dual formulation. To demonstrate the proposed MLDEA model, applications to the road safety performance evaluation for a set of European countries are carried out. A comparison of the results with the ones from the one layer DEA model clearly indicates the usefulness and effectiveness of this improvement in dealing with a great number of performance evaluation activities with hierarchical structures.