Improving the Analytical Power of Dynamic DEA Models, by the Consideration of the Shape of the Distribution of Inputs/Outputs Data: A Linear Piecewise Decomposition Approach

Authors: Elias K. Maragos, Petros E. Maravelakis

Abstract:

In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.

Keywords: Data envelopment analysis, Dynamic DEA, Piecewise linear inputs, Piecewise linear outputs.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316871

References:

[1] Charnes, A., Cooper, W. and Rhodes, E., (1978). Measuring the efficiency of decision making units. European Journal of Operational Research. 2(1). pp:429-444.
[2] Despotis, D., Stamati, L. and Smirlis, J., (2009). Data envelopment analysis with nonlinear virtual inputs and outputs. European Journal of Operational Research. 202(2), pp.604-613.
[3] Färe, R., Grosskopf, S. and Roos, P., (1989). Productivity developments in Swedish hospitals: A Malmquist output index approach, in: A. Charnes, W. W. Cooper, A. Y. Lewin and L. M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Academic Publishers, Boston.
[4] Färe, R., Grosskopf, S., (1996). Intertemporal Production Frontiers: With Dynamic DEA. Kluwer Academic Publishers, Boston.
[5] Färe, R., Grosskopf, S., (2000). Network DEA. Socio-economic Planning Sciences. 34(1), pp.35-49.
[6] Imanirad, R., Cook, W. and Zhu, J., (2013). Partial input to output impacts in DEA: Production considerations and resource sharing among business subunits. Naval Research Logistics 60(3), pp.190-207.
[7] Kao, C., (2013). Dynamic data envelopment analysis: A relational analysis. European Journal of Operational Research 227, pp. 325-330.
[8] Kao, C., Hwang, S.N., 2010. Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems 48, 437–446.
[9] Maragos, E., Despotis, D., (2003). Evaluation of High School Performance: A Data Envelopment Analysis Approach. Proceedings of Apors 2003 Conference. New Delhi, India, pp.435-442.
[10] Maragos, E., Despotis, D., (2004). Evaluating School Performance over time in the frame of Regional Socio-Economic Specificities. WSEAS Transactions on Mathematics 3(3), pp.664-670.
[11] Mariz, F., Almeida, M. and Aloisie, D., (2018). A review of Dynamic Data Envelopment Analysis: state of the art and applications. International Transactions in Operational Research. 25. Pp.469-505.
[12] Sahoo, B., Tone, K., (2013). Non-parametric measurement of economies of scale and scope in non-competitive environment with price uncertainty, Omega 41, pp.97-111.
[13] Skevas, T., Oude Lansink, A., Stefanou, S.E., 2012. Measuring technical efficiency in the presence of pesticide spillovers and production uncertainty: the case of Dutch arable farms. European Journal of Operational Research 223(2), pp.550–559.
[14] Tone, K., Tsutsui, M., (2010). Dynamic DEA: a slacks-based measure approach. Omega 38(3), pp.145–156.
[15] Tone, K., Tsutsui, M., (2014). Dynamic DEA with network structure. Omega 42(1), pp. 124–131.