A Chance-Constrained DEA Model with Random Input and Output Data:Considering Maintenance Groups of Iranian Aluminum Company

Subject Areas : Applied Mathematics

Mohammad Izadikhah ¹ (Department of Mathematics, College of Science, Arak-Branch, Islamic Azad University, Arak, Iran)
Mohammad Ehsanifar ² (Department of Industrial engineering, Arak Branch, Islamic Azad University, Arak, Iran)
Saman Malekian ³ (Department of Industrial engineering, Arak Branch, Islamic Azad University, Arak, Iran)

Received: 2017-06-15 Accepted : 2018-01-08 Published : 2018-05-01

Keywords: Data envelopment analysis, Chance constraints, Random variables, Quadratic constraints, Super-efficiency,

Abstract :

In this paper, we use an input oriented chance-constrained DEA model withrandom inputs and outputs. A super-eciency model with chance constraintsis used for ranking. However, for convenience in calculations a non-linear deterministicequivalent model is obtained to solve the models. The non-linearmodel is converted into a model with quadratic constraints to solve the nonlineardeterministic model. Finally, data related to twenty-eight maintenancegroups of Iranian Aluminum Company (IRALCO) is used to demonstrate theapplicability of the used Models in this paper.

References:

[1]Adler N., Friedman L., Sinuany-Stern Z., Review of ranking methods in
the data envelopment analysis context, European Journal of Operational
Research, 2002, 140(2), P.249-265.

[2]Andersen P., Petersen N.C., A procedure for ranking ecient units in data
envelopment analysis, Management Science, 1993, 39(10), P.1261-1294.

[3]Azadi M., Farzipoor Saen R., A new chance-constrained data envelopment
analysis for selecting third party reverse logistics providers in the existence
of dual-role factors, Expert Systems with Applications, 2011, 38(10),
P.12231-12236.

[4]Aliakbarpoor Z., Izadikhah M., Evaluation and ranking DMUs in the
presence of both undesirable and ordinal factors in data envelopment
analysis. International Journal of Automation and Computing, 2012, 9(6),
P. 609-615.

[5]Izadikhah M., Farzipoor Saen R., A new data envelopment analysis
method for ranking decision making units: an application in industrial
parks. Expert Systems, 2015, 32(5),P. 598-608.

[6]Izadikhah M., Farzipoor Saen R., Evaluating sustainability of supply
chains by two-stage range directional measure in the presence of negative
data. Transportation Research Part D: Transport and Environment, 2016,
49, P.110-126.

[7]Banker R.D., Maximum likelihood, consistency and data envelopment
analysis: A statistical foundation, Management Science, 1993, 39(10), P.
1265-1273.

[8]Banker R.D., Hypothesis tests using data envelopment analysis, Journal
of Productivity Analysis,, 1996, 7(2), P.139-159.

[9]Banker R.D., Charnes A., Cooper W.W., Some method for estimating
technical and scale ineciencies in data envelopment analysis,
Management Science, 1984, 30(9), P.1078-1092.

[10]Charnes A., Cooper W.W., Rhodes E., Measuring the eciency of decision
making units, European Journal of Operational Research, 1978, 2(6),
P.429-444.

[11]Cooper W.W., Deng H., Huang Z., Li Susan X., Chance constrained
programming approaches to technical efficiencies and inefficiencies in
stochastic data envelopment analysis, Journal of the Operational Research
Society, 2002, 53(12), P.1347-1356.

[12]Cooper W.W., Deng H., Huang Z.M., Li S.X., Chance constrained
programming approaches to congestion in stochastic data envelopment
analysis, European Journal of Operational Research, 2004, 155(2), P.487-
501.

[13]Dibachi, H., Behzadi, M. H., Izadikhah, M., Stochastic multiplicative
DEA model for measuring the eciency and ranking of DMUs under
VRS technology, Indian Journal of Science and Technology, 2014, 7(11),
P.1765-1773.

[14]Dibachi, H., Behzadi, M. H., Izadikhah, M., Stochastic Modied MAJ
Model for Measuring the Eciency and Ranking of DMUs. Indian Journal
of Science and Technology, 2015, 8(8), P.549-555.

[15]Izadikhah M., Farzipoor Saen R., A new preference voting method for
sustainable location planning using geographic information system and
data envelopment analysis. Journal of Cleaner Production, 2016 137,
P.1347-1367. (Doi:http://dx.doi.org/10.1016/j.jclepro.2016.08.021)

[16]Izadikhah M., Farzipoor Saen R., Assessing sustainability of supply
chains by chance-constrained two-stage DEA model in the presence
of undesirable factors. Computers and Operations Research, 2017(Doi:
https://doi.org/10.1016/j.cor.2017.10.002)

[17]Khodabakhshi M., An output oriented super-efficiency measure in
stochastic data envelopment analysis: Considering Iranian electricity
distribution companies, Computers and Industrial Engineering, 2010,
58(4), P.663-671.

[18]Khodabakhshi M., Asgharian M., Gregoriou G.N., An inputoriented
super-eciency measure in stochastic data envelopment analysis:
Evaluating chief executive ocers of US public banks and thrifts, Expert
Systems with Applications, 2010, 37(3), P.2092-2097.

[19]Li S., Jahanshahloo G.R., Khodabakhshi M., A super-efficiency model for
ranking ecient units in data envelopment analysis, Applied Mathematics
and Computation, 2007, 184, (2), 638-648.

[20]Morita H., Seiford L.M., Characteristics on stochastic DEA eciency
Reliability and probability being ecient, Journal of Operational Research
Society of Japan, 1999, 42(4), P.389-404.

[21]Izadikhah M., Farzipoor Saen R., Ahmadi, K., How to Assess
Sustainability of Suppliers in the Presence of Dual-Role Factor and Volume
Discounts? A Data Envelopment Analysis Approach. Asia-Pacic Journal
of Operational Research, 2005, 34(3), P.1-25.

[22]Izadikhah M., Farzipoor Saen R., Ahmadi, K., How to assess sustainability
of suppliers in volume discount context? A new data envelopment analysis
approach. Transportation Research Part D: Transport and Environment,
2017, 51, P.102-121.

[23]Tavana M., Khanjani Shiraz R., Hatami A., A new chance constrained
DEA model with birandom input and output data, Operational Research
Society, 2014, 12, P.1824-1839.

[24]Mehrabian S., Alirezaee A., Jahanshahloo G.R., A complete eciency
ranking of decision making units in DEA, Computational Optimization
and Applications (COAP), 1999, 14, P.261-266.

[25]Tone K., A slakes-based measure of super-eciency in data envelopment
analysis, European Journal of Operational Research, 2002, 143(1), P.32-
41.

[26]Hosseinzadeh Lot F., Nematollahi, N., Behzadi, M.H., Mirbolouki, M.,
Moghaddas, Z., Centralized resource allocation with stochastic data,
Computational and Applied Mathematics, 2012, 24, P.1783-1788.

[27]Izadikhah M., Saeidifar A., Roostaee R., Extending TOPSIS in fuzzy
environment by using the nearest weighted interval approximation of fuzzy
numbers. Journal of Intelligent and Fuzzy Systems, 2014, 27, P.2725-2736.

[28]Zare R., Izadikhah M., Multi-Criteria Decision Making Methods for
Comparing three Models of Aluminum Ingot Production through Life
Cycle Assessment. Applied Ecology and Environmet Research, 2017, 15(3),
P.1697-1715.

[29]Khodabakhshi, M., A super-eciency model based on improved outputs in
data envelopment analysis, Applied Mathematics and Computation, 2007,
184(2), P.695-703.

[30]Land K.C., Lovell C.A.K., Thore S., Chance constrained data envelopment
analysis, Managerial and Decission Economics, 1988, 14, P.541-554.

[31]Olesen O.B., Petersen N.C., Chance constrained efficiency evaluation,
Manaegement Science, 1995, 41, P.442-457.

[32]Izadikhah M., Khoshroo A., Energy management in crop production using
a novel Fuzzy Data Envelopment Analysis model, RAIRO - Operations
Research, In Press, 2017.

[33]Izadikhah M., Tavana M., Di Caprio D., Javier Santos Arteaga F., A Novel
Two-Stage DEA Production Model with Freely Distributed Initial Inputs
and Shared Intermediate Outputs, Expert Systems with Applications, In
Press, 2017.

[34]Khodabakhshi M., Asgharian M., An input relaxation measure of
eciency in stochastic data envelopment analysis, Applied Mathematical
Modelling, 2009, 33, P.2010-2023.

[35]Khodabakhshi M., Estimating most productive scale size in stochastic
data envelopment analysis, Economic Modelling, 2009, 26, 968-973.

[36]Jahanshahloo, G. R., Khodabakhshi, M., Suitable combination of inputs
for improving outputs in DEA with determining input congestion, Applied
Mathematics and Computation, 2004, 151(1), P.263-273.