Estimating multi-period global cost efficiency and productivity change of systems with network structures
محورهای موضوعی : Mathematical Optimization
S. Tohidnia
1
(Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
G. Tohidi
2
(Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
کلید واژه: Network DEA . Global cost efficiency . Multi, period . Malmquist productivity index . Circularity,
چکیده مقاله :
The current paper develops three different ways to measure the multi-period global cost efficiency for homogeneous networks of processes when the prices of exogenous inputs are known at all time periods. A multi-period network data envelopment analysis model is presented to measure the minimum cost of the network system based on the global production possibility set. We show that there is a relationship between the multi-period global cost efficiency of network system and its subsystems, and also its processes. The proposed model is applied to compute the global cost Malmquist productivity index for measuring the productivity changes of network system and each of its process between two time periods. This index is circular. Furthermore, we show that the productivity changes of network system can be defined as a weighted average of the process productivity changes. Finally, a numerical example will be presented to illustrate the proposed approach.
Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50:1393–1414
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Chen Y, Cook WD, Li N, Zhu J (2009) Additive efficiency decomposition in two-stage DEA. Eur J Oper Res 196:1170–1176
Cooper WW, Seiford LM, Tone K (2006) Introduction to data envelopment analysis and its uses. Springer, New York
Esmaeilzadeh A, Hadi-Vencheh A (2013) A super-efficiency model for measuring aggregative efficiency of multi-period production systems. Measurement 46:3988–3993
Fare R, Grosskopf S (2000) Network DEA. Socio Econ Plan Sci 34:35–49
Fare R, Grosskopf S, Lindgren B, Roos P (1989) Productivity developments in Swedish hospitals: a Malmquist output index
approach. Discussion Paper No. 89-3. Southern Illinois University, Illinois
Fare R, Grosskopf S, Whittaker G (2007) Network DEA. In: Zhu J, Cook WW (eds) Modelling data irregularities and structural complexities. Data envelopment analysis. Springer, New York, pp 209–240
Fukuyama H, Matousek R (2011) Efficiency of Turkish banking: twostage network system. Variable returns to scale model. J Int Financ Mark Inst Money 21:75–91
Kao C (2009a) Efficiency measurement for parallel production systems. Eur J Oper Res 196:1107–1112
Kao C (2009b) Efficiency decomposition in network data envelopment analysis: a relational model. Eur J Oper Res 192:949–962
Kao C, Hwang SN (2010) Efficiency measurement for network systems: IT impact on firm performance. Decis Support Syst
48(3):437–446
Kao C, Hwang SN (2014) Multi-period efficiency and Malmquist productivity index in two-stage production systems. Eur J Oper Res 232:512–521
Kao C, Liu ST (2013) Multi-period efficiency measurement in data envelopment analysis: the case of Taiwanese commercial banks. Omega 47:90–98
Khalili-Damghani K, Hosseinzadeh Lotfi F (2012) Performance measurement of police traffic centres using fuzzy DEA-based Malmquist productivity index. Int J Multicriteria Decis Mak 2(1):94–110
Khalili-Damghani K, Taghavi-Fard M, Abtahi AR (2012) A fuzzy two-stage DEA approach for performance measurement: real case of agility performance in dairy supply chains. Int J Appl Decis Sci 5(4):293–317
Li Y, Chen Y, Liang L, Xie J (2012) DEA models for extended twostage network structures. Omega 40:611–618
Liang L, Cook WD, Zhu J (2008) DEA models for two-stage processes: game approach and efficiency decomposition. Nav
Res Logist 55:643–653
Lin YH, Fu TT, Chen CL, Juo JC (2017) Non-radial cost Luenberger productivity indicator. Eur J Oper Res 256:629–639
Lozano S (2011) Scale and cost efficiency analysis of networks of processes. Expert Syst Appl 38:6612–6661
Lozano S, Gutie´rrez E, Moreno P (2013) Network DEA approach to airports performance assessment considering undesirable outputs. Appl Math Model 37:1665–1676
Maniadakis N, Thanassoulis E (2004) A cost Malmquist productivity index. Eur J Oper Res 154:396–409
Pastor JT, Lovell CAK (2005) A global Malmquist productivity index. Econ Lett 88:266–271
Shafiee M, Hosseinzadeh Lotfi F, Saleh H, Ghaderi M (2016) A mixed integer bi-level DEA model for bank branch performance evaluation by Stackelberg approach. J Ind Eng Int 12:81–91
Shokrollahpour E, Hosseinzadeh Lotfi F, Zandieh M (2016) An integrated data envelopment analysis–artificial neural network approach for benchmarking of bank branches. J Ind Eng Int 12:137–143
Tohidi G, Khodadadi M (2013) Allocation models for DMUs with negative data. J Ind Eng Int 9(1):1–6
Tohidi G, Razavyan S (2010) Non-discretionary imprecise data in efficiency measurement. J Ind Eng Int 7(12):45–51
Tohidi G, Razavyan S (2013) A circular global profit Malmquist productivity index in data envelopment analysis. Appl Math
Model 37:216–227
Tohidi G, Razavyan S, Tohidnia S (2008) A profit Malmquist productivity index. J Ind Eng Int 6(20):23–30
Tohidi G, Razavyan S, Tohidnia S (2012) A global cost Malmquist productivity index using data envelopment analysis. J Oper Res Soc 63:72–78
Tone K (2002) A strange case of the cost and allocative efficiency in DEA. J Oper Res Soc 53:1225–1231
Yu MM (2010) Assessment of airport performance using the SBMNDEA model. Omega 38:440–452
Yu Y, Qinfen S (2014) Two-stage DEA model with additional input in the second stage and part of intermediate products as final output. Expert Syst Appl 41:6570–6574
Zhu J (2011) Airlines performance via two-stage network DEA approach. J Cent Cathedra 4(2):260–269
