Congestion Status Identification Using Slack Based Models in Data Envelopment Analysis

Subject Areas : Statistics

M. Abbasi ¹ , M. Rostamy-Malkhlifeh ²

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Corresponding Author

Received: 2015-09-01 Accepted : 2015-11-01 Published : 2015-10-01

Keywords: تحلیل پوششی داده ها- تراکم ضعی, &amp, emsp, ,

Abstract :

Congestion is a wasteful stage of the production process where outputs are reduced due to excessive amount of inputs. There are several approaches in data envelopment analysis (DEA) literatures to treat congestion. The concept of strong and weak congestion first developed by Tone and Sahoo [Tone, K., Sahoo, B.K., 2004. Degree of scale economies and congestion: A unified DEA approach. European Journal of Operational Research 158, 755–772]. Evidence of strong congestion occurs whenever reducing proportionally all inputs can increase all outputs. Tone and Sahoo extended the relationship between congestion and other economic concept such as marginal productivity. They proved that existence of strong congestion is hinged to negative marginal productivity. Nonetheless the definition of strong congestion is too restrictive, since it has severe condition of “proportionate’’ reduction in all inputs causes an augmentation in all outputs. So the number of strongly congested DMUs appeared to be limited. In this paper we define a new less restrictive definition of congestion namely “ strict congestion’’ which is identified if and only if a reduction in all inputs causes an increase in all outputs. Therewith this study first proposes a new approach for the congestion recognition. Then another scheme is presented to determine the status of congestion (weak or strict). The validity of the proposed approach is demonstrated using numerical examples.

References:

[1] 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.

[2] Brockett,P.L., Cooper,W.W., Shin,H.C., Wang, Y.(1998). Inefficiency and congestion in Chinese production before and after the 1978 economic reforms.SocioEconomic Planning Sciences, 32,1-20.

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

[4] Cooper WW, Thompson RG, Thrall RM.(1996). Introduction: extensions and new developments in DEA. Annals of Operations Research ,66,3-45.

[5] Cooper, W. W., Seiford, L. M., Zhu, J.(2000). A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA. SocioEconomic Planning Sciences,34,1-25.

[6] Cooper WW, Deng H, Huang ZM, Li SL. (2002). A one-model approach to congestion in data envelopment analysis. European Journal of Operational Research , 36,231–8. ng Sciences, 34,1-25.