The overall efficiency of the dynamic DEA models

This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA models with time series that, compute the overall efficiency of the units with respect to all their inputs and outputs in all periods. The proposed models are compared with those previously set forth by Park and Park (Eur J Oper Res 193(2):567-580, 2009). We introduce six new dynamic DEA models with the quadratic objective function and nonlinear constraints; they differ in time weights of the units in every year. The first proposed model has a decreasing vector of the weights; for the second model, this vector is convex, and the third model uses the weights' ratio scale. These models are alternatives to already known models. The proposed models give quick results in one stage. We cannot rank the efficiency units by the efficiency scores obtained within the proposed models, three super-efficiency models are therefore proposed. The super-efficiency models compute the super-efficiency scores, greater for the efficient units, which can thus be ranked according to this score. All models are illustrated on a selected dataset, and then their results are discussed. The dataset contains 38 German NUTS 2 (Nomenclature of Units for Territorial Statistics) regions. The aim is to find the most efficient regions and their ranking between the years 2008 and 2016. Two inputs are used- employment (in thousands of hours worked) and gross fixed capital formation (in millions EUR) and one output-gross domestic product (in millions EUR). All calculations are carried out using our original procedures written in the LINGO modelling language.