Abstract
Data envelopment analysis (DEA) is a method for identifying best practices among peer decision making units (DMUs). An important area of development in recent years has been that devoted to applications wherein DMUs represent network processes. One particular subset of such processes is those in which all the outputs from the first stage become inputs to the second stage. We call these types of DMU structures “two-stage networks”. Existing approaches in modeling efficiency of two-stage networks can be categorized as using either Stackelberg (leader-follower), or cooperative game concepts. There are two types of efficiency decomposition; multiplicative and additive. In multiplicative efficiency decomposition, the overall efficiency is defined as a product of the two individual stages’ efficiency scores, whereas in additive efficiency decomposition, the overall efficiency is defined as a weighted average of the two individual stages’ efficiency scores. We discuss modeling techniques used for solving two-stage network DEA models in linear programs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Avkiran, N. K. (2009). Opening the black box of efficiency analysis: An illustration with UAE banks. Omega, 37, 930–941.
Castelli, L., Pesenti, R., & Ukovich, W. (2004). DEA-like models for the efficiency evaluation of hierarchically structured units. European Journal of Operational Research, 154(2), 465–476.
Charnes, A., & Cooper, W.W. (1962). Programming with linear fractional functionals, Naval Research Logistics Quarterly, 9, 181–186.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Chen, C.-M. (2009). A network-DEA model with new efficiency measures to incorporate the dynamic effect in production networks. European Journal of Operational Research, 194(3), 687–699.
Chen, Y., & Zhu, J. (2004). Measuring information technology’s indirect impact on firm performance. Information Technology & Management Journal, 5(1–2), 9–22.
Chen, Y., Liang, L., Yang, F., & Zhu, J. (2006). Evaluation of information technology investment: A data envelopment analysis approach. Computers & Operations Research, 33(5), 1368–1379.
Chen, Y., Liang, L., & Zhu, J. (2009a). Equivalence in two-stage DEA approaches. European Journal of Operational Research, 193(2), 600–604.
Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009b). Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research, 196, 1170–1176.
Chen, Y., Cook, W. D., & Zhu, J. (2010a). Deriving the DEA frontier for two-stage processes. European Journal of Operational Research, 202, 138–142.
Chen, Y., Du, J., Sherman, H. D., & Zhu, J. (2010b). DEA model with shared resources and efficiency decomposition. European Journal of Operational Research, 207, 339–349.
Chen, C.-L., Zhu, J., Yu, J.-Y., & Noori, H. (2012). A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis. European Journal of Operational Research, 221(2), 348–359.
Chen, Y., Cook, W. D., Kao, C., & Zhu, J. (2013). Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures. European Journal of Operational Research, 226, 507–515.
Chilingerian, J., & Sherman, H. D. (2004). Health care applications: From Hospitals to Physician, from productive efficiency to quality frontiers. In W. W. Cooper, L. M. Seiford, & J. Zhu (Eds.), Handbook on data envelopment analysis. Boston: Springer.
Cook, W. D., & Hababou, M. (2001). Sales performance measurement in bank branches. Omega, 29, 299–307.
Cook, W. D., & Zhu, J. (2007). Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research, 180(2), 692–699.
Cook, W. D., Green, R., & Zhu, J. (2006). Dual-role factors in data envelopment analysis. IIE Transactions, 38(2), 105–115.
Cook, W. D., Zhu, J., Yang, F., & Bi, G.-B. (2010). Network DEA: Additive efficiency decomposition. European Journal of Operational Research, 207(2), 1122–1129.
Du, J., Liang, L., Chen, Y., Cook, W. D., & Zhu, J. (2011). A bargaining game model for measuring performance of two-stage network structures. European Journal of Operational Research, 210(2), 390–397.
Färe, R., & Grosskopf, S. (1996). Productivity and intermediate products: A frontier approach. Economics Letters, 50, 65–70.
Färe, R., & Whittaker, G. (1995). An intermediate input model of dairy production using complex survey data. Journal of Agricultural Economics, 46(2), 201–213.
Fukuyama, H., & Weber, W. L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega 38(5), 398–409.
Huang, Z. M., & Li, S. X. (2001). Co-op advertising models in a manufacturing-retailing supply chain: A game theory approach. European Journal of Operational Research, 135, 527–544.
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 Research, 185(1), 418–429.
Li, Y., Chen, Y., Liang, L., & Xie, J. (2012). DEA models for extended two-stage network structures. Omega, 40(5), 611–618.
Liang, L., Yang, F., Cook, W. D., & Zhu, J. (2006). DEA models for supply chain efficiency evaluation. Annals of Operations Research, 145(1), 35–49.
Liang, L., Cook, W. D., & Zhu, J. (2008). DEA models for two-stage processes: Game approach and efficiency decomposition. Naval Research Logistics, 55, 643–653.
Liang, L., Li, Z.-Q., Cook, W. D., & Zhu, J. (2011). DEA Efficiency in two-stage networks with feed back. IIE Transactions, 43, 309–322.
Lim, S., & Zhu, J. (2013). Integrated data envelopment analysis: Global vs local optimum. European Journal of Operational Research, 229(1), 276–278.
Premachandra, I. M., Zhu, J., Watson, J., & Galagedera, D. U. A. (2012). Best-performing US mutual fund families from 1993 to 2008: Evidence from a novel two-stage DEA model for efficiency decomposition. Journal of Banking and Finance, 36(12), 3302–3317.
Seiford, L. M., & Zhu, J. (1999). Profitability and marketability of the top 55 US commercial banks. Management Science, 45(9), 1270–1288.
Sexton, T. R., & Lewis, H. F. (2003). Two-stage DEA: An application to major league baseball. Journal of Productivity Analysis, 19(2–3), 227–249.
Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operational Research, 197(1), 243–252.
Tone, K., & Tsutsui, M. (2010). Dynamic DEA: A slacks-based measure approach. Omega, 38(3–4), 145–156.
Wang, C. H., Gopal, R., & Zionts, S. (1997). Use of data envelopment analysis in assessing information technology impact on firm performance. Annals of Operations Research, 73, 191–213.
Yu, M.-M., & Lin, E. T. J. (2008). Efficiency and effectiveness in railway performance using a multi-activity network DEA model. Omega, 36, 1005–1017.
Zhu, J. (2000). Multi-factor performance measure model with an application to Fortune 500 companies. European Journal of Operational Research, 123(1), 105–124.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cook, W.D., Zhu, J. (2014). DEA for Two-Stage Networks: Efficiency Decompositions and Modeling Techniques. In: Cook, W., Zhu, J. (eds) Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 208. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-8068-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4899-8068-7_1
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-8067-0
Online ISBN: 978-1-4899-8068-7
eBook Packages: Business and EconomicsBusiness and Management (R0)