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Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

  • Rashed Khanjani Shiraz
  • Adel Hatami-Marbini
  • Ali Emrouznejad
  • Hirofumi Fukuyama
Original Paper
  • 148 Downloads

Abstract

Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework.

Keywords

Data envelopment analysis Weight restrictions Random input–output Cost efficiency Quadratic programming 

References

  1. Amirteimoori A, Kordrostami S, Rezaitabar A (2006) An improvement to the cost efficiency interval: a DEA-based approach. Appl Math Comput 181:775–781Google Scholar
  2. Bagherzadeh Valami H (2009) Cost efficiency with triangular fuzzy number input prices: an application of DEA. Chaos Solitons Fractals 42:1631–1637CrossRefGoogle Scholar
  3. Banker RD, Charnes A, Cooper WW (1984) Some method for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci 30(9):1078–1092CrossRefGoogle Scholar
  4. Battese GE, Coelli TJ (1992) Frontier production function, technical efficiency and panel data with application to paddy farmers in India. J Prod Anal 3:153–169CrossRefGoogle Scholar
  5. Bjurek H, Hjalmarsson L, Førsund FR (1990) Deterministic parametric and nonparametric estimating of efficiency in service production: a comparison. J Econom 46:213–227CrossRefGoogle Scholar
  6. Bruni ME, Conforti D, Beraldi P, Tundis E (2009) Probabilistically constrained models for efficiency and dominance in DEA. Int J Prod Econ 117(1):219–228CrossRefGoogle Scholar
  7. Camanho AS, Dyson RG (2005) Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments. Eur J Oper Res 161:432–446CrossRefGoogle Scholar
  8. Camanho AS, Dyson RG (2008) A generalization of the Farrell cost efficiency measure applicable to non-fully competitive settings. Omega 36(2008):147–162CrossRefGoogle Scholar
  9. Charnes A, Cooper WW (1959) Chance constrained programming. Manag Sci 6:73–79CrossRefGoogle Scholar
  10. Charnes A, Cooper WW (1962) Programming with linear fractional functions. Nav Res Logist Q 9:181–186Google Scholar
  11. Charnes A, Cooper WW (1963) Deterministic equivalents for optimizing and satisfying under chance constraints. Oper Res 11(1):18–39CrossRefGoogle Scholar
  12. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444CrossRefGoogle Scholar
  13. Coelli TJ (1996) Simulators and hypothesis tests for a stochastic model: a Monte Carlo analysis. J Prod Anal 6:247–268CrossRefGoogle Scholar
  14. Cook WD, Seiford LM (2009) Data envelopment analysis (DEA)—thirty years on. Eur J Oper Res 192:1–17CrossRefGoogle Scholar
  15. Cooper WW, Tone K (1997) Measures of inefficiency in data envelopment analysis and stochastic frontier estimation. Eur J Oper Res 99:72–88CrossRefGoogle Scholar
  16. Cooper WW, Huang Z, Li SX (1996) Satisfy DEA models under chance constraints. Ann Oper Res 66:279–295CrossRefGoogle Scholar
  17. Cooper WW, Huang ZM, Lelas V, Li SX, Olesen OB (1998) Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J Prod Anal 9:530–579CrossRefGoogle Scholar
  18. Cooper WW, Deng H, Huang Z, Li SX (2002) Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis. J Oper Res Soc 53:1347–1356CrossRefGoogle Scholar
  19. Cooper WW, Deng H, Huang Z, Li SX (2004) Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Eur J Oper Res 155:487–501CrossRefGoogle Scholar
  20. Emrouznejad A, De Witte K (2010) COOPER-framework: a unified process for non-parametric projects. Eur J Oper Res 207(3):1573–1586CrossRefGoogle Scholar
  21. Emrouznejad A, Yang G (2018) A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Econ Plann Sci 61(1):1–5Google Scholar
  22. Fang L, Li H (2012) A comment on “cost efficiency in data envelopment analysis with data uncertainty”. Eur J Oper Res 220:588–590CrossRefGoogle Scholar
  23. Fang L, Li H (2013) Duality and efficiency computations in the cost efficiency model with price uncertainty. Comput Oper Res 40:594–602CrossRefGoogle Scholar
  24. Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer-Nijhoff Publishing, BostonCrossRefGoogle Scholar
  25. Huang Z, Li SX (1996) Dominance stochastic models in data envelopment analysis. Eur J Oper Res 95(2):390–403CrossRefGoogle Scholar
  26. Jahanshahloo GR, Soleimani-damaneh M, Mostafaee A (2008) A Simplified version of the DEA cost efficiency model. Eur J Oper Res 184:814–815CrossRefGoogle Scholar
  27. Kuosmanen T, Post T (2001) Measuring economic efficiency with incomplete price information: with an application to European commercial banks. Eur J Oper Res 134:43–58CrossRefGoogle Scholar
  28. Kuosmanen T, Post T (2002) Nonparametric efficiency analysis under price uncertainty: a first-order stochastic dominance approach. J Prod Anal 17(3):183–200CrossRefGoogle Scholar
  29. Kuosmanen T, Post T (2003) Measuring economic efficiency with incomplete price information. Eur J Oper Res 144:454–457CrossRefGoogle Scholar
  30. Lahdelma R, Salminen P (2001) SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Oper Res 49(3):444–454CrossRefGoogle Scholar
  31. Lahdelma R, Salminen P (2006) Stochastic multicriteria acceptability analysis using the data envelopment model. Eur J Oper Res 170:241–252CrossRefGoogle Scholar
  32. Lahdelma R, Hokkanen J, Salminen P (1998) SMAA—stochastic multiobjective acceptability analysis. Eur J Oper Res 106:137–143CrossRefGoogle Scholar
  33. Land KC, Lovell CAK, Thore S (1993) Chance constrained data envelopment analysis. Manag Decis Econ 14:541–554CrossRefGoogle Scholar
  34. Liu JS, Lu LYY, Lu WM, Lin BJY (2013) A survey of DEA applications. OMEGA 41(5):893–902CrossRefGoogle Scholar
  35. Luenberger DG (1995) Microeconomic theory. McGraw-Hill, BostonGoogle Scholar
  36. Morita H, Seiford LM (1999) Characteristics on stochastic DEA efficiency. J Oper Res Soc Jpn 42(4):389–404Google Scholar
  37. Mostafaee A, Saljooghi FH (2010) Cost efficiency measures in data envelopment analysis with data uncertainty. Eur J Oper Res 202:595–603CrossRefGoogle Scholar
  38. Olesen OB (2006) Comparing and combining two approaches for chance constrained DEA. J Prod Anal 26(2):103–119CrossRefGoogle Scholar
  39. Olesen OB, Petersen NC (1995) Chance constrained efficiency evaluation. Manag Sci 41:442–457CrossRefGoogle Scholar
  40. Olesen OB, Petersen NC (2015) Stochastic data envelopment analysis—a review. Eur J Oper Res 251(1):2–21Google Scholar
  41. Ray SC, Chen L, Mukherjee L (2008) Input price variation across locations and a generalized measure of cost efficiency. Int J Prod Econ 116(2):208–218CrossRefGoogle Scholar
  42. Schafinit C, Rosen D, Paradi JC (1997) Best practice analysis of bank branches: an application of DEA in a large Canadian bank. Eur J Oper Res 98:269–289CrossRefGoogle Scholar
  43. Simon HA (1957) Models of man. Wiley, New YorkGoogle Scholar
  44. Sueyoshi T (2000) Stochastic DEA for restructure strategy: an application to a Japanese petroleum company. Omega 28(4):385–398CrossRefGoogle Scholar
  45. Talluri S, Narasimhana R, Nairb A (2006) Vendor performance with supply risk: a chance-constrained DEA approach. Int J Prod Econ 100:212–222CrossRefGoogle Scholar
  46. Tavana M, Khanjani Shiraz R, Hatami-Marbini A, Agrell P, Paryab K (2012) Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC). Expert Syst Appl 39(15):12247–12259CrossRefGoogle Scholar
  47. Tavana M, Khanjani Shiraz R, Hatami-Marbini A, Agrell P, Paryab K (2013) Chance-constrained DEA models with random fuzzy inputs and outputs. Knowl-Based Syst 52:32–52CrossRefGoogle Scholar
  48. Tavana M, Khanjani Shiraz R, Hatami-Marbini A (2014) A new chance-constrained DEA model with birandom input and output data. J Oper Res Soc 65:1824–1839CrossRefGoogle Scholar
  49. Thompson RG, Dharmapala PS, Humphrey DB, Taylor WM, Thrall RM (1996) Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application. Ann Oper Res 68:303–327Google Scholar
  50. Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130(3):498–509Google Scholar
  51. Tsionas EG, Papadakis EN (2010) A Bayesian approach to statistical inference in stochastic DEA. Omega 38:309–314CrossRefGoogle Scholar
  52. Udhayakumar A, Charles V, Kumar M (2011) Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems. Omega 39:387–397CrossRefGoogle Scholar
  53. US Census Bureau (2002) Economic census, manufacturing, subject series. General SummaryGoogle Scholar
  54. Wu D, Lee CG (2010) Stochastic DEA with ordinal data applied to a multi-attribute pricing problem. Eur J Oper Res 207:1679–1688CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Rashed Khanjani Shiraz
    • 1
  • Adel Hatami-Marbini
    • 2
  • Ali Emrouznejad
    • 3
  • Hirofumi Fukuyama
    • 4
  1. 1.School of Mathematical ScienceUniversity of TabrizTabrizIran
  2. 2.Department of Strategic Management and Marketing, Leicester Business SchoolDe Montfort UniversityLeicesterUK
  3. 3.Operations and Information Management Group, Aston Business SchoolAston UniversityBirminghamUK
  4. 4.Faculty of CommerceFukuoka UniversityFukuoka CityJapan

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