Skip to main content

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

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Notes

  1. http://www.r-project.org/about.html.

  2. Lang ML and DT. RGtk2: R bindings for Gtk 2.8.0 and above. 2014.

References

  • Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.

    Article  Google Scholar 

  • Banker, R. D., & Slaughter, S. A. (1997). A field study of scale economies in software maintenance. Management Science, 43, 1709–1725.

    Article  Google Scholar 

  • Berkelaar, M., et al. (2007). lpSolve: Interface to Lp solve v. 5.5 to solve linear or integer programs. R Package Version 5.

  • Bogetoft, P., & Otto, L. (2011). Benchmarking with DEA, SFA, and R. New York: Springer.

    Book  Google Scholar 

  • Borchers, S. T., & H.W. (2014). CRAN task view: Optimization and mathematical programming.

  • Canty, A., & Ripley, B. (2012). boot: Bootstrap R (S-Plus) functions. R Package Version 1.

  • Charnes, A., Cooper, W. W., Golany, B., Seiford, L., & Stutz, J. (1985). Foundations of data envelopment analysis for Pareto–Koopmans efficient empirical production functions. Journal of Economics, 30, 91–107.

    Article  Google Scholar 

  • Chidamber, S. R., & Kemerer, C. F. (1994). A metrics suite for object oriented design. IEEE Transactions on Software Engineering, 20, 476–493. https://doi.org/10.1109/32.295895.

    Article  Google Scholar 

  • Emrouznejad, A., Rostami-Tabar, B., & Petridis, K. (2016). A novel ranking procedure for forecasting approaches using data envelopment analysis. Technological Forecasting and Social Change, 111, 235–243.

    Article  Google Scholar 

  • Emrouznejad, A., & Thanassoulis, E. (2010). Measurement of productivity index with dynamic DEA. International Journal of Operational Research, 8, 247–260.

    Article  Google Scholar 

  • Färe, R., & Grosskopf, S. (1996). Dynamic production models. In Intertemporal production frontiers: With dynamic DEA (pp. 151–188). New York: Springer.

  • Geyer, C. J., & Meeden, G. D. (2008). R package rcdd (C double description for R), version 1.1. Incorporates code from (4). http://www.stat.umn.edu/geyer/rcdd.

  • Grigoroudis, E., Petridis, K., & Arabatzis, G. (2014). RDEA: A recursive DEA based algorithm for the optimal design of biomass supply chain networks. Renewable Energy, 71, 113–122.

    Article  Google Scholar 

  • Hayfield, T., & Racine, J. S. (2008). Nonparametric econometrics: The np package. Journal of Statistical Software, 27, 1–32.

    Article  Google Scholar 

  • Henningsen, A. (2010). linprog: Linear programming. Optim. R Package Version 09-0.

  • Hornik, K., Meyer, D., & Theussl, S. (2013). ROI: R optimization infrastructure.

  • Inman, O. L., Anderson, T. R., & Harmon, R. R. (2006). Predicting US jet fighter aircraft introductions from 1944 to 1982: A dogfight between regression and TFDEA. Technological Forecasting and Social Change, 73, 1178–1187. https://doi.org/10.1016/j.techfore.2006.05.013.

    Article  Google Scholar 

  • Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2005). kernlab—Kernel methods. R Package Version 06-2 URL HttpCRAN R-Proj. Org.

  • Konis, K., et al. (2011). lpSolveAPI: R Interface for lp_solve Version 5.5. 2.0. R package version 5.5. 2.0-5.

  • Lang, M. L., & D.T. (2014). RGtk2: R bindings for Gtk 2.8.0 and above.

  • Nemoto, J., & Goto, M. (2003). Measurement of dynamic efficiency in production: An application of data envelopment analysis to Japanese electric utilities. Journal of Product Analysis, 19, 191–210.

    Article  Google Scholar 

  • Oh, D., & Oh, M. D. (2013). Packagenonparaeff’.

  • Ouellette, P., & Vierstraete, V. (2004). Technological change and efficiency in the presence of quasi-fixed inputs: A DEA application to the hospital sector. European Journal of Operational Research, 154, 755–763. https://doi.org/10.1016/S0377-2217(02)00712-9.

    Article  Google Scholar 

  • Petridis, K., Chatzigeorgiou, A., & Stiakakis, E. (2016). A spatiotemporal Data Envelopment Analysis (ST DEA) approach: The need to assess evolving units. Annals of Operations Research, 238(1–2), 475–496.

    Article  Google Scholar 

  • Petridis, K., Dey, P. K., & Emrouznejad, A. (2017). A branch and efficiency algorithm for the optimal design of supply chain networks. Annals of Operations Research, 253, 545–571.

    Article  Google Scholar 

  • Prior, D. (2006). Efficiency and total quality management in health care organizations: A dynamic frontier approach. Annals of Operations Research, 145, 281–299.

    Article  Google Scholar 

  • Rudy, J., Rudy, M. J., Liu, S., & Matrix, D., n.d. PackageCLSOCP’.

  • Shott, T., & Lim, D.-J. (2015). TFDEA: Technology forecasting using DEA.

  • Simm, J., Besstremyannaya, G., & Simm, M. J. (2014). PackagerDEA’.

  • Soetaert, K., Van den Meersche, K., & van Oevelen, D. (2009). limSolve: Solving linear inverse models. R Package Version 1.

  • Team, R. C., et al. (2012). R: A language and environment for statistical computing.

  • The R Project for Statistical Computing (WWW Document), n.d. http://www.r-project.org/. Accessed 26 February 15.

  • Turlach, B. A., & Weingessel, A. (2010). quadprog: Functions to solve quadratic programming problems. R Package Version 1.5-3.

  • Varadhan, R., & Gilbert, P. (2009). BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. Journal of Statistical Software, 32, 1–26.

    Article  Google Scholar 

  • Wilson, P. W. (2008). FEAR: A software package for frontier efficiency analysis with R. Socio-Economic Planning Sciences, 42, 247–254.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Konstantinos Petridis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Digkas, G., Petridis, K., Chatzigeorgiou, A. et al. Measuring Spatio-temporal Efficiency: An R Implementation for Time-Evolving Units. Comput Econ 56, 843–864 (2020). https://doi.org/10.1007/s10614-019-09945-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-019-09945-4

Keywords

  • DEA
  • LP
  • MILP
  • R platform
  • Spatio-temporal efficiency
  • Computational economics