Measuring Spatio-temporal Efficiency: An R Implementation for Time-Evolving Units

Classical data envelopment analysis models have been applied to extract efficiency when time series data are used. However, these models do not always yield realistic results, especially when the purpose of the study is to identify the peers of the decision making unit (DMU) under investigation. This is due to the fact that apart from the spatial distance of DMUs, which is the basis on which efficiency is extracted, the distance in time between DMUs is also important in identifying the most suitable peer that could serve as a benchmark for the DMU under investigation. Based on these two dimensions, i.e. the spatial and the temporal, the concept of spatio-temporal efficiency is introduced and a mixed integer linear programming model is proposed to obtain its value. This model yields a unique past peer for benchmarking purposes based on both dimensions. The implementation has been performed in the R language, where the user can provide, through a graphical interface, the data (inputs and outputs for successive versions of a DMU) for which the spatio-temporal efficiency is measured. Applications to the real world and particularly from the discipline of software engineering are provided to show the applicability of the model to temporally arranged data. Profiling results of the code in the R language are also provided showing the effectiveness of the implementation.