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Optimal value bounds in interval fractional linear programming and revenue efficiency measuring

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Abstract

This paper deals with the fractional linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. A method is provided for the situation in which the feasible set is described by a linear interval system. Moreover, certain dependencies between the coefficients in the nominators and denominators can be involved. Also, we extend this approach for situations in which the same vector appears in different terms in nominators and denominators. The applicability of the approaches developed is illustrated in the context of the analysis of hospital performance.

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References

  • Borza M, Rambely AS, Saraj M (2012) Solving linear fractional programming problems with interval coefficients in the objective function. A new approach. Appl Math Sci 6(69–72):3443–3452

    Google Scholar 

  • Camanho AS, Dyson RG (2005) Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments. Eur J Oper Res 161(2):432–446

    Article  Google Scholar 

  • Černý M, Hladík M (2016) Inverse optimization: towards the optimal parameter set of inverse LP with interval coefficients. Cent Eur J Oper Res 24(3):747–762

    Article  Google Scholar 

  • Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Naval Res Logist Q 9(3–4):181–186

    Article  Google Scholar 

  • Chinnadurai V, Muthukumar S (2016) Solving the linear fractional programming problem in a fuzzy environment: numerical approach. Appl Math Model 40(11–12):6148–6164

    Article  Google Scholar 

  • Chinneck JW, Ramadan K (2000) Linear programming with interval coefficients. J Oper Res Soc 51(2):209–220

    Article  Google Scholar 

  • Effati S, Pakdaman M (2012) Solving the interval-valued linear fractional programming problem. Am J Comput Math 2(1):51–55

    Article  Google Scholar 

  • Entani T, Tanaka H (2006) Improvement of efficiency intervals based on DEA by adjusting inputs and outputs. Eur J Oper Res 172(3):1004–1017

    Article  Google Scholar 

  • Fang L, Li H (2013) Lower bound of cost efficiency measure in DEA with incomplete price information. J Product Anal 40(2):219–226

    Article  Google Scholar 

  • Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc Ser A 120(3):253–290

    Article  Google Scholar 

  • Fiedler M, Nedoma J, Ramík J, Rohn J, Zimmermann K (2006) Linear optimization problems with inexact data. Springer, New York

    Google Scholar 

  • Hatami-Marbini A, Emrouznejad A, Agrell PJ (2014) Interval data without sign restrictions in DEA. Appl Math Model 38(7–8):2028–2036

    Article  Google Scholar 

  • He F, Xu X, Chen R, Zhu L (2016) Interval efficiency improvement in DEA by using ideal points. Measurement 87:138–145

    Article  Google Scholar 

  • Hladík M (2010) Generalized linear fractional programming under interval uncertainty. Eur J Oper Res 205(1):42–46

    Article  Google Scholar 

  • Hladík M (2011) Optimal value bounds in nonlinear programming with interval data. Top 19(1):93–106

    Article  Google Scholar 

  • Hladík M (2012) Interval linear programming: a survey. In: Mann ZA (ed) Linear programming—new frontiers in theory and applications, chap 2. Nova Science Publishers, New York, pp 85–120

  • Hladík M (2013) Weak and strong solvability of interval linear systems of equations and inequalities. Linear Algebra Appl 438(11):4156–4165

    Article  Google Scholar 

  • Hladík M (2014) On approximation of the best case optimal value in interval linear programming. Optim Lett 8(7):1985–1997

    Article  Google Scholar 

  • Inuiguchi M, Mizoshita F (2012) Qualitative and quantitative data envelopment analysis with interval data. Ann Oper Res 195(1):189–220

    Article  Google Scholar 

  • Jablonsky J, Fiala P, Smirlis Y, Despotis DK (2004) DEA with interval data: an illustration using the evaluation of branches of a Czech bank. Cent Eur J Oper Res 12(4):323–337

    Google Scholar 

  • Jahanshahloo G, Soleimani-damaneh M, Mostafaee A (2007a) Cost efficiency analysis with ordinal data: a theoretical and computational view. Int J Comput Math 84(4):553–562

    Article  Google Scholar 

  • Jahanshahloo G, Soleimani-damaneh M, Mostafaee A (2007b) On the computational complexity of cost efficiency analysis models. Appl Math Comput 188(1):638–640

    Google Scholar 

  • Jahanshahloo G, Soleimani-damaneh M, Mostafaee A (2008) A simplified version of the DEA cost efficiency model. Eur J Oper Res 184(2):814–815

    Article  Google Scholar 

  • Jain S, Arya N (2013) Inverse optimization for linear fractional programming. Int J Phys Math Sci 4(1):444–450

    Google Scholar 

  • Jeyakumar V, Li G, Srisatkunarajah S (2013) Strong duality for robust minimax fractional programming problems. Eur J Oper Res 228(2):331–336

    Article  Google Scholar 

  • Khalili-Damghani K, Tavana M, Haji-Saami E (2015) A data envelopment analysis model with interval data and undesirable output for combined cycle power plant performance assessment. Expert Syst Appl 42(2):760–773

    Article  Google Scholar 

  • Kuosmanen T, Post T (2001) Measuring economic efficiency with incomplete price information: with an application to european commercial banks. Eur J Oper Res 134(1):43–58

    Article  Google Scholar 

  • Kuosmanen T, Post T (2003) Measuring economic efficiency with incomplete price information. Eur J Oper Res 144(2):454–457

    Article  Google Scholar 

  • Li W, Xia M, Li H (2015) New method for computing the upper bound of optimal value in interval quadratic program. J Comput Appl Math 288:70–80

    Article  Google Scholar 

  • Li W, Xia M, Li H (2016) Some results on the upper bound of optimal values in interval convex quadratic programming. J Comput Appl Math 302:38–49

    Article  Google Scholar 

  • Mostafaee A (2011) Non-convex technologies and economic efficiency measures with incomplete data. Int J Ind Math 3(4):259–275

    Google Scholar 

  • Mostafaee A, Saljooghi FH (2010) Cost efficiency measures in data envelopment analysis with data uncertainty. Eur J Oper Res 202(2):595–603

    Article  Google Scholar 

  • Mostafaee A, Hladík M, Černý M (2016) Inverse linear programming with interval coefficients. J Comput Appl Math 292:591–608

    Article  Google Scholar 

  • Rohn J (1981) Strong solvability of interval linear programming problems. Computing 26:79–82

    Article  Google Scholar 

  • Rohn J (1998) Linear programming with inexact data is NP-hard. ZAMM Z Angew Math Mech 78(Supplement 3):S1051–S1052

    Article  Google Scholar 

  • Sakawa M, Nishizaki I, Uemura Y (2001) Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study. Eur J Oper Res 135(1):142–157

    Article  Google Scholar 

  • Shwartz M, Burgess JF, Zhu J (2016) A DEA based composite measure of quality and its associated data uncertainty interval for health care provider profiling and pay-for-performance. Eur J Oper Res 253(2):489–502

    Article  Google Scholar 

Download references

Acknowledgements

M. Hladík was supported by the Czech Science Foundation under Grant P403-18-04735S.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Islamic Azad University, North Tehran Branch, Tehran, Iran

    Amin Mostafaee

  2. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    Milan Hladík

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  1. Amin Mostafaee
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  2. Milan Hladík
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Correspondence to Milan Hladík.

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Mostafaee, A., Hladík, M. Optimal value bounds in interval fractional linear programming and revenue efficiency measuring. Cent Eur J Oper Res 28, 963–981 (2020). https://doi.org/10.1007/s10100-019-00611-6

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  • DOI: https://doi.org/10.1007/s10100-019-00611-6

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