A new approach to computing congestion with linear weak disposability assumption of undesirable outputs

Document Type : Original Article

Authors

1 Ph.D. Student, Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Rasht Branch, Rasht, Iran

2 Professor, Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Rasht Branch, Rasht, Iran

3 Professor, Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Lahijan Branch, Lahijan, Iran

Abstract

In recent years, the concept of congestion has been interested to researchers. Congestion has occurred when an increase in one or more inputs reduces one or more outputs, while other inputs and outputs are unchanged (or vice versa). This concept is important in economics, which means that eliminating congestion reduces costs and increases outputs. On the other hand, in production process or the provision of services, in addition to producing the desirable output, undesirable outputs are produced, too. The concept of congestion in the presence of undesirable factors is different because we desire to increase the desirable outputs and reduce undesirable outputs; therefore, in the presence of undesirable factors, the common definitions and theories to measure congestion cannot be used. In this paper, some of the congestion models using data envelopment analysis are reviewed then a new method for measuring the congestion in presence of undesirable outputs with linear weak disposability assumption is presented. The application of this method has been shown to analyze the effect of congestion in the presence of undesirable outputs on the college faculties’ efficiency. The results show that all inefficient units have congestion in input.

Keywords

References

[1]      Fouladvand, m., Undesirable Outputs in production process with weak disposability assumption in data envelopment analysis, Ph.D. thesis in Mathematics, Faculty of Science, Islamic Azad University, Science and Research Branch of Tehran (Giulan), 2017.
[2]       Azar, A., Khosravani, F., Jalali, R., The Application of DEA in Selecting a Portfolio Consisting of the Most Efficient and the Most Inefficient Companies Now Present in Tehran Stock Market, Management Research in Iran,17 )1),2013, 1-19.
[3]      Mirghafoori, H., Shafiee Roodposht, M., Naddafi, G., Financial Performance Evaluating with Grey Theory and Data Envelopment Analysis Technique Two Step approach (Case Study: Province Telecommunication Companies), Management Research in Iran,16 (4),2013, 189-205.
[4]       Mohallati Rayeni, m., Study of the effect of congestion on undesired output using data envelopment analysis. Case Study: University Performance Evaluation, Quarterly Journal of Production and Operations,6(1), 2015,99-112.
[5]      Kuosmanen, T., Weak Disposability in Nonparametric Production analysis with Undesirable Outputs, American Journal of Agricultural Economics, 87,2005,1077-1082.
[6]      Amirteimoori, A., Fouladvand., M., Kordrostami, S., Efficiency measurement using nonparametric production analysis in the presence of undesirable outputs .Application to power plants, Operation Research and Decisions,3,2017, 5-20.
[7]      Charnes, A., Cooper, W., Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2,1978,429-444.
[8]      Färe, R.,  Pasurka , Jr. C. A., Pollution Abatement activities and traditional productivity, Ecological Economics,62,2007,673-682.
[9]      Hailu, A., Veeman,T., Non parametric Productivity Analysis with undesirable outputs: An allpication to the Canadian Pulp and Paper Industry, American Journal of Agricultural Economics,83,2001,605-616.
[10]   Hailu, A., Nonparametric Productivity Analysis with Undesirable Outputs: Reply, American Journal of Agricultural Economics,85,2003,1075-1077.
[11]   Seiford, L.M., Zhu, J., Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research,142,2002,16-20.
[12]   Färe, R., Grooskopf, S., A Comment on Weak Disposability in Nonparametric productivity with Undesirable Outputs,American Journal of Agricultural Economics, 91,2008,535-538.
[13]   Färe, R., Grooskopf, S., Non-parametric Productivity Analysis with undesirable outputs, American Gournal of Agricultural Economics,85,2003,1070-1074.
[14]   Kuosmanen, T., Podinovski, V.,  Weak Disposability in Production Analysis: Reply, American Journal of Agricultural Economics,91,2009,539-545.
[15]   Podinovski, V.,  Kuosmanen, T., Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions,European Journal of Operational Research, 211,2011, 577-585.
[16]   Azizi, H., Amirteimoori, A.,  Kordrostami, S., Measurement of the worst practice of decision-making units: Incorporating both undesirable outputs and non-discretionary inputs into imprecise DEA, Modern Researches in Decision Making,3(2),2018,197-222.
[17]   Azizi, H., Amirteimoori, A.,  Kordrostami, S., A data envelopment analysis approach with efficient and inefficient frontiers for supplier selection in the presence of both undesirable outputs and imprecise data, Modern Researches in Decision Making,1 (2),2016,139-170.
[18]   Kalhor A., Kazemi Matin R. Study the effects of abatement factors of weak disposability in network data envelopment analysis with undesirable outputs, Journal of operational reearch and its applications,15(1),2018,103-121.        
[19]   Färe, R., Svensson, L., Congestion of production factors, Econometrica,48,1980, 1745–1752.
[20]   Färe, R., Grosskopf, S., Lovell, C.A.K., The Measurement of Efficiency of Production, Kluwer- Nijhoff Publishing, Boston,1985.
[21]   Färe, R., Grooskopf, S., Lovell, C.A.K., Pasurka,  Jr. C. A.,  Multilateral productivity comparisons when some outputs are undesirable : a nonparametric approach, The Review of Economics and Statistics,71,1989,90– 98.
[22]   Byrnes, P., Fare, R., Grosskopf , S., Measuring productive efficiency: an application to Illinois strip mines, Management Science, 30,1984, 671–681.
[23]   Byrnes, P., Fare, R., Grosskopf, S., Lovell, C. A. K., The effect of unions on  productivity: US surface mining of coal, Management Science,9,1988,1037–1053.

[24]   Cooper, W.W., Deng, H., Gu, B., Li, S, Thrall, R.M., Using DEA to improve the management of congestion in Chinese industries (1981-1997), Socio-Economic Planning Sciences,35,2001,227-242.

[25]   Scheel, H., Undesirable outputs in efficiency valuations, European Journal of Operational Research,132,2001,400–410.
[26]   Tone, K. , Sahoo, B. K. , Degree of scale economies and congestion: a unified DEA approach, European Journal of Operational Research,158,2004,755–772.
[27]   Khodabakhshi, M., A one model approach based on relaxed combinations of inputs for evaluating input congestion in DEA, Journal of Computational and Applied Mathematics,230,2009,443-450.
[28]    Fang, L., Congestion measurement in nonparametric analysis under the weakly disposable technology, European Journal of Operational Research, 245,2015, 203-208.
[29]    Rastgoo, R., Rostami Malkhalifeh, M., Congestion  measurment in data envelopment analysis under weak disposability of desirable and desirable  outputs in a two-phase network, Jornal of new reserches in athematics,2,2016,91-100.
[30]   Khodadadi‎, M., Zare Haghighi, H.,Environmental Assessment and Congestion for DMUs With Undesirable Outputs,International ournal ofIndustrial Mathematics,9,2017,  307-318.
[31]   Shephard,R., Theory of cost Production Function, Princeton University Press,1970.
[32]   Wei, Q.L., Yan, H., Congestion and returns to scale in data envelopment analysis,European Journal of Operational Research,153,2004,641–660.

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