no. 1
Chance-constrained data envelopment analysis modeling with random-rough data
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 259-284.

Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.

DOI : 10.1051/ro/2016076
Classification : 90B50, 90C29, 90C31, 90C90
Mots clés : Data envelopment analysis, chance-constrained programming, random and rough data, alpha-optimistic, alpha-pessimistic
Shiraz, Rashed Khanjani 1 ; Tavana, Madjid 1 ; Di Caprio, Debora 1

1 
@article{RO_2018__52_1_259_0,
     author = {Shiraz, Rashed Khanjani and Tavana, Madjid and Di Caprio, Debora},
     title = {Chance-constrained data envelopment analysis modeling with random-rough data},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {259--284},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {1},
     year = {2018},
     doi = {10.1051/ro/2016076},
     mrnumber = {3812480},
     zbl = {1397.90222},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2016076/}
}
TY  - JOUR
AU  - Shiraz, Rashed Khanjani
AU  - Tavana, Madjid
AU  - Di Caprio, Debora
TI  - Chance-constrained data envelopment analysis modeling with random-rough data
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2018
SP  - 259
EP  - 284
VL  - 52
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2016076/
DO  - 10.1051/ro/2016076
LA  - en
ID  - RO_2018__52_1_259_0
ER  - 
%0 Journal Article
%A Shiraz, Rashed Khanjani
%A Tavana, Madjid
%A Di Caprio, Debora
%T Chance-constrained data envelopment analysis modeling with random-rough data
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2018
%P 259-284
%V 52
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2016076/
%R 10.1051/ro/2016076
%G en
%F RO_2018__52_1_259_0
Shiraz, Rashed Khanjani; Tavana, Madjid; Di Caprio, Debora. Chance-constrained data envelopment analysis modeling with random-rough data. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 259-284. doi : 10.1051/ro/2016076. http://www.numdam.org/articles/10.1051/ro/2016076/

[1] M.E. Bruni, D. Conforti, P. Beraldi and E. Tundis, Probabilistically constrained models for efficiency and dominance in DEA. Inter. J. Produ. Econ. 117 (2009) 219–228 | DOI

[2] A. Charnes and W.W. Cooper, Chance-Constrained Programming. Manag. Sci. 6 (1959) 73–79 | DOI | MR | Zbl

[3] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units. Europ. J. Oper. Res. 2 (1978) 429–444 | DOI | MR | Zbl

[4] W.W. Cooper, Z. Huang and S. Li, Satisficing DEA models under chance constraints. Ann. Oper. Res. 66 (1996) 279–295 | DOI | MR | Zbl

[5] W.W. Cooper, H. Deng, Z.M. Huang, Z. Li and X. Susan, Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis. J. Oper. Res. Soc. 53 (2002) 1347–1356 | DOI | Zbl

[6] W.W. Cooper, H. Deng, Z.M. Huang and S.X. Li, Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Europ. J. Oper. Res. 155 (2004) 487–501 | DOI | MR | Zbl

[7] W.W. Cooper, Z.M. Huang, V. Lelas, S.X. Li and O.B. Olesen, Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J. Prod. Anal. 9 (1998) 530–579 | DOI

[8] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets. Inter. J. General Syst. 17 (1990) 191–209 | DOI | Zbl

[9] P. Halmos, Naive set theory. Springer (1974) | DOI | MR | Zbl

[10] Z. Huang and S.X. Li, Dominance stochastic models in data envelopment analysis. Eur. J. Oper. Res. 95 (1996) 390–403 | DOI | Zbl

[11] Z. Huangand S.X. Li, Stochastic DEA models with different types of input-output disturbances. J. Product. Anal. 15 (2001) 95–113 | DOI

[12] R. Khanjani Shiraz, V. Charles and L. Jalalzadeh, Fuzzy Rough DEA Model: a possibility and expected value approaches. Expert Syst. Appl. 41 (2014) 43–444

[13] K.C. Land, C.A.K. Lovell and S.Thore, Chance constrained data envelopment analysis. Manag. Decision Econ. 14 (1993) 541–554 | DOI

[14] S.X. Li, Stochastic models and variable returns to scales in data envelopment analysis. Eur. J. Oper. Res. 104 (1998) 532–548 | DOI | Zbl

[15] R. Lempel, S. Moran, The stochastic approach for link-structure analysis (SALSA) and the TKC effect1. Comput. Networks 33 (2000) 387–401 | DOI

[16] B. Liu, Dependent-chance programming: A class of stochastic programming. Comput. Math. Appl. 34 (1997) 89–104 | DOI | MR | Zbl

[17] B. Liu, Theory and Practice of Uncertain Programming 1st edition. Physica Verlag, Heidelberg (2002) | DOI | Zbl

[18] B. Liu, Uncertainty theory: an introduction to its axiomatic foundations. Springer Verlag (2004) | DOI | MR | Zbl

[19] H. Morita and L.M. Seiford, Characteristics on stochastic DEA efficiency- Reliability and probability being efficient. J. Oper. Res. Soc.Jpn 42 (1999) 389–404 | MR | Zbl

[20] H.S. Nguyen, Approximate boolean reasoning: foundations and applications in data mining, Transactions on Rough Sets V. Lect. Notes Comput. Sci. 4100 (2006) 344–523 | MR | Zbl

[21] O.B. Olesen, Comparing and combining two approaches for chance constrained DEA. J. Product. Anal. 26 (2006) 103–119 | DOI

[22] O.B. Olesen and N.C. Petersen, Chance constrained efficiency evaluation. Manag. Sci. 41 (1995) 442–457 | DOI | Zbl

[23] K. Paryab, R. Khanjani Shiraz, L. Jalalzadeh and H. Fukuyama, Imprecise data envelopment analysis model with bifuzzy variables. J. Int. Fuzzy Syst. 27 (2014) 37–48 | MR | Zbl

[24] Z. Pawlak, Rough sets. Inter. J. Infor. Comput. Sci. 11 (1982) 341–356 | DOI | MR | Zbl

[25] Z. Pawlak, Rough set theory and its applications to data analysis. Cybernetics and Systems: An Inter. J. 29 (1998) 661–688 | DOI | Zbl

[26] Z. Pawlak and A. Skowron, Rudiments of rough sets. Infor. Sci. 177 (2007a) 3–27 | DOI | MR | Zbl

[27] Z. Pawlak and A. Skowron, Rough sets: Some extensions. Infor. Sci. 177 (2007b) 28–40 | DOI | MR | Zbl

[28] Z. Pawlak and A. Skowron, Rough sets and Boolean reasoning. Infor. Sci. 177 (2007c) 41–73 | DOI | MR | Zbl

[29] Y.H. Qian, J.Y. Liang, W. Pedrycz and C.Y. Dang, Positive approximation: an accelerator for attribute reduction in rough set theory. Artificial Intelligence 174 (2010) 597–618 | DOI | MR | Zbl

[30] T. Sueyoshi, Stochastic DEA for restructure strategy: an application to a Japanese petroleum company. Omega 28 (2000) 385–98 | DOI

[31] Z. Tao and J. Xu, A class of rough multiple objective programming and its application to solid transportation problem. Infor. Sci. 188 (2012) 215–235 | DOI | MR | Zbl

[32] S. Talluri and R. Narasimhana and A. Nairb, Vendor performance with supply risk: a chance-constrained DEA approach. Inter. J. Production Econ. 100 (2006) 212–222 | DOI

[33] M. Tavana, R. Khanjani Shiraz, A. Hatami-Marbini, P. Agrell and K. Paryab, Fuzzy stochastic data envelopment analysis with application to Base Realignment and Closure (BRAC). Expert Syst. Appl. 39 (2012) 12247–12259 | DOI

[34] M. Tavana, R. Khanjani, A. Shiraz, P. Hatami-Marbini, P. Agrell and K. Paryab, Chance-constrained DEA models with random fuzzy inputs and outputs. Knowledge-Based Syst. 52 (2013a) 32–52 | DOI

[35] M. Tavana, R. Khanjani Shiraz and A. Hatami-Marbini, A New Chance-Constrained DEA Model with Birandom Input and Output Data. J. Operat. Res. Soc. 65 (2014) 1824–1839 | DOI

[36] E.G. Tsionas and E.N. Papadakis, A Bayesian approach to statistical inference in stochastic DEA. Omega 38 (2010) 309–314 | DOI

[37] A. Udhayakumar, V. Charles and M. Kumar, Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems. Omega 39 (2011) 387–397 | DOI

[38] C. Wu, Y. Li, Q. Liu and K. Wang, A stochastic DEA model considering undesirable outputs with weak disposability. Math. Comput. Model. 58 (2013) 980–989 | DOI | MR

[39] Y.M. Wang, K.S. Chin and J.B. Yang, Measuring the performances of decision making units using geometric average efficiency. J. Operat. Res. Soc. 58 (2007) 929–937 | DOI | Zbl

[40] J. Xu and L. Yao, A class of expected value multi-objective programming problems with random rough coefficients. Math. Comput. Model. 50 (2009a) 141–158 | DOI | MR | Zbl

[41] J. Xu and L. Yao, A class of multi-objective linear programming models with random rough coefficients. Math. Comput. Model. 49 (2009b) 189–206 | DOI | MR | Zbl

[42] J. Xu and L. Yao, A class of bi-level expected value programming with random rough coefficients and its application to production-inventory problem. Sichuan University Research Report (2010a)

[43] J. Xu and L. Yao, Random rough variable and random rough programming. Sichuan University Research Report (2010b)

[44] J. Xu, B.Li and D. Wu, Rough data envelopment analysis and its application to supply chain Performance evaluation. Inter. J. Production Econ. 122 (2009) 638–628

Cité par Sources :