A generalized multiple layer data envelopment analysis model for hierarchical structure assessment: A case study in road safety performance evaluation

Data envelopment analysis (DEA) is a powerful analytical research tool for measuring the relative efficiency of a homogeneous set of decision making units (DMUs) by obtaining empirical estimates of relations between multiple inputs and multiple outputs related to the DMUs. To further embody multilayer hierarchical structures of these inputs and outputs in the DEA framework, which are prevalent in today's performance evaluation activities, we propose a generalized multiple layer DEA (MLDEA) model. 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. Meanwhile, its linear transformation is realized and further extended to the BCC form. To demonstrate the proposed MLDEA model, a case study in evaluating the road safety performance of a set of 19 European countries is carried out. By using 13 hierarchical safety performance indicators in terms of road user behavior (e.g., inappropriate or excessive speed) as the model's input and 4 layered road safety final outcomes (e.g., road fatalities) as the output, we compute the most optimal road safety efficiency score for the set of European countries, and further analyze the weights assigned to each layer of the hierarchy. 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.