DEA model with shared resources and efficiency decomposition. (English) Zbl 1205.90146

Summary: Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.


90B50 Management decision making, including multiple objectives
91B06 Decision theory
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
Full Text: DOI


[1] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[2] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444 (1978) · Zbl 0416.90080
[3] Chen, Y.; Zhu, J., Measuring information technology’s indirect impact on firm performance, Information Technology & Management Journal, 5, 1-2, 9-22 (2004)
[4] Chilingerian, J.; Sherman, H. D., Health care applications: From Hospitals to Physician, from productive efficiency to quality frontiers, (Cooper, W. W.; Seiford, L. M.; Zhu, J., Handbook on Data Envelopment Analysis (2004), Springer: Springer Boston) · Zbl 1090.90525
[5] Cook, W. D.; Hababou, M., Sales performance measurement in bank branches, OMEGA, 29, 299-307 (2001)
[6] Cook, W. D.; Hababou, M.; Tuenter, H., Multicomponent efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches, Journal of Productivity Analysis, 14, 3, 209-224 (2000)
[7] Cooper, W. W.; Seiford, L. M.; Zhu, J., Handbook on Data Envelopment Analysis (2004), Springer: Springer Boston · Zbl 1050.90002
[8] Färe, R.; Grosskopf, S., Productivity and intermediate products: A frontier approach, Economics Letters, 50, 65-70 (1996) · Zbl 0900.90164
[9] Huang, Z. M.; Li, S. X., Co-Op advertising models in a manufacturing-retailing supply chain: A game theory approach, European Journal of Operational Research, 135, 527-544 (2001) · Zbl 0989.90083
[10] Kao, C.; Hwang, S. N., 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 (2008) · Zbl 1137.91497
[11] Liang, L.; Cook, W. D.; Zhu, J., DEA models for two-stage processes: Game approach and efficiency decomposition, Naval Research Logistics, 55, 643-653 (2008) · Zbl 1160.90528
[12] Seiford, L. M.; Zhu, J., Profitability and marketability of the top 55 US commercial banks, Management Science, 45, 9, 1270-1288 (1999)
[13] Sexton, T. R.; Lewis, H. F., Two-Stage DEA: An application to major league baseball, Journal of Productivity Analysis, 19, 2-3, 227-249 (2003)
[14] Wang, C. H.; Gopal, R.; Zionts, S., Use of data envelopment analysis in assessing information technology impact on firm performance, Annals of Operations Research, 73, 191-213 (1997) · Zbl 0891.90018
[15] Zhu, J., Multi-factor performance measure model with an application to Fortune 500 companies, European Journal of Operational Research, 123, 1, 105-124 (2000) · Zbl 1059.90515
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.