Measuring and decomposing the overall efficiency of multi-period and -division systems associated with DEA

Chen, Kaihua (2014): Measuring and decomposing the overall efficiency of multi-period and -division systems associated with DEA.

Abstract

The combination way of component efficiencies into the overall efficiency is a central topic in the efficiency modeling of network systems based on data envelopment analysis (DEA). In terms of the feature and advantage of DEA modeling as the multiplier generation on inputs/outputs, it is desirable that the combination weights are derived from the data and self-generated in calculation process. The prior weights choice makes DEA modeling lose the objectivity and generalization in efficiency measures. This study proposes a new formulating approach of dynamic network DEA (DN-DEA) models to measure and decompose the overall efficiency of multi-period and -division systems without the pre-specified weights to combine component efficiencies into the overall efficiency. In our formulating approach, the double identities of carry-overs connecting consecutive periods and linkers connecting consecutive divisions are fully accounted for. This approach is applicable for the formulations of both radial measures (DN-CCR and DN-BCC) and non-radial measures (DN-SBM). This study extends Kao’s (in press) relational approach of dynamic DEA to dynamic network systems for empirical comparison. In contrast to Kao’s (in press) approach, our approach can present a weighted average decomposition of the overall (in)efficiency score into components ones by a set of endogenous weight sets which are the most favorable for the tested multi-period and -division system. This makes sense of the comparison between overall and component (in)efficiency scores. In this context, the overall efficiency score is less or more than all component ones. We applied our models to evaluate the innovation efficiency of OECD (Organization for Economic Co-operation and Development) countries.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic network DEA; Multi-period and -division systems; Efficiency measurement and decomposition; Innovation efficiency; OECD countries
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O31 - Innovation and Invention: Processes and Incentives; P - Economic Systems > P5 - Comparative Economic Systems > P51 - Comparative Analysis of Economic Systems

References

Avkiran, N.K., McCrystal, A., 2013. Dynamic network range-adjusted measure vs. dynamic network slacks-based measure. Workshop on Dynamic and Network DEA 2013, January 29-30, National Graduate Institute for Policy Studies, Tokyo.

Avkiran, N.K., McCrystal, A., In press. Intertemporal Analysis of Organizational Productivity in Residential Aged Care Networks: Scenario Analyses for Setting Policy Targets. Health Care Management Science, doi: 10.1007/s10729-013-9259-6.

Banker, R.D., Charnes, A., Cooper, W.W., 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30(9), 1078-1092.

Bogetoft, P., Färe, R., Grosskopf, S., Hayes, K., Taylor, L., 2009. Dynamic network DEA: an illustration. Journal of the Operations Research Society of Japan 52(2), 147-162.

Charnes, A., Cooper, W.W., 1962. Programming with Linear Fractional Functionals. Naval Research Logistics Quarterly 9(3), 181-196.

Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2(6), 429-444

Chen, K.H., 2013. Measurement of innovation process performance. China Science and Technology Press, Beijing. (In Chinese)

Chen, K.H., Guan, J.C., 2012. Measuring China's Regional Innovation Systems: An Application of A Relational Network DEA. Regional Studies 46(3), 355-37.

Chen, K.H., Guan, J.C., Kou, M.T., Kang, X.M., 2013. An applied study of network DEA model to the efficiency measurement of scientific an d technologic innovation investment. Management Review 25(12), 3-16. (In Chinese)

Chen, Y., Cook, W.D. Li, N., Zhu, J., 2009. Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research 196(3), 1170-1176.

Cook, W.D., Zhu, J., Bi, G.B., Yang, F., 2010. Network DEA: Additive efficiency decomposition. European Journal of Operational Research 207(2), 1122-1129.

Cooper, W.W., Park, K.S., Pastor, J.T., 2001. The Range Adjusted Measure (RAM) in DEA: A response to the comment by Steinmann and Zweifel. Journal of Productivity Analysis 15(2), 145-152.

Guan J.C., Chen, K.H., 2010. Measuring the innovation production process: A cross-region empirical study of China’s high-tech innovations. Technovation 30(5), 348-358. Guan, J.C., Chen, K.H., 2012. Modeling the relative efficiency of national innovation systems. Research Policy 41(1), 102-115.

Hollanders, H., Celikel-Esser, F., 2007. Measuring innovation efficiency. INNO Metrics 2007 report, European Commission, DG Enterprise, Brussels.

Kao, C., 2009. Efficiency decomposition in network data envelopment analysis: a relational model. European Journal of Operational Research 192(3), 949-962.

Kao, C., Hwang, S.-N., 2008. Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. European Journal of Operational Research1 85(1), 418-429.

Kao, C., in press. Dynamic data envelopment analysis: A relational analysis. European Journal of Operational Research, doi: 10.1016/j.ejor. 2012.12.012.

Tone, K., 2001. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 130(3), 498-509.

Kao, C., 2014. Efficiency decomposition in network data envelopment analysis with slacks-based measures. Omega 45, 1–6.

Tone, K., Tsutsui, M., 2010. Dynamic DEA: a slacks-based measure approach. Omega 38(3), 145-156.

Tone, K., Tsutsui, M., 2014. Dynamic DEA with network structure: A slacks-based measure approach. Omega 42(1), 124-131.

Wang, E.C., Huang W.C. 2007. Relative efficiency of R&D activities: a cross-country study accounting for environmental factors in the DEA approach. Research Policy 36(2), 260-273.