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Optimal value bounds in interval fractional linear programming and revenue efficiency measuring. (English) Zbl 07252394
Summary: 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.

MSC:
90B50 Management decision making, including multiple objectives
90C31 Sensitivity, stability, parametric optimization
65G40 General methods in interval analysis
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[1] Borza, M.; Rambely, AS; Saraj, M., Solving linear fractional programming problems with interval coefficients in the objective function. A new approach, Appl Math Sci, 6, 69-72, 3443-3452 (2012) · Zbl 1264.90167
[2] Camanho, AS; Dyson, RG, Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments, Eur J Oper Res, 161, 2, 432-446 (2005) · Zbl 1134.91350
[3] Černý, M.; Hladík, M., Inverse optimization: towards the optimal parameter set of inverse LP with interval coefficients, Cent Eur J Oper Res, 24, 3, 747-762 (2016) · Zbl 1364.90323
[4] Charnes, A.; Cooper, WW, Programming with linear fractional functionals, Naval Res Logist Q, 9, 3-4, 181-186 (1962) · Zbl 0127.36901
[5] Chinnadurai, V.; Muthukumar, S., Solving the linear fractional programming problem in a fuzzy environment: numerical approach, Appl Math Model, 40, 11-12, 6148-6164 (2016) · Zbl 07160238
[6] Chinneck, JW; Ramadan, K., Linear programming with interval coefficients, J Oper Res Soc, 51, 2, 209-220 (2000) · Zbl 1107.90420
[7] Effati, S.; Pakdaman, M., Solving the interval-valued linear fractional programming problem, Am J Comput Math, 2, 1, 51-55 (2012)
[8] Entani, T.; Tanaka, H., Improvement of efficiency intervals based on DEA by adjusting inputs and outputs, Eur J Oper Res, 172, 3, 1004-1017 (2006) · Zbl 1086.90526
[9] Fang, L.; Li, H., Lower bound of cost efficiency measure in DEA with incomplete price information, J Product Anal, 40, 2, 219-226 (2013)
[10] Farrell, MJ, The measurement of productive efficiency, J R Stat Soc Ser A, 120, 3, 253-290 (1957)
[11] Fiedler, M.; Nedoma, J.; Ramík, J.; Rohn, J.; Zimmermann, K., Linear optimization problems with inexact data (2006), New York: Springer, New York · Zbl 1106.90051
[12] Hatami-Marbini, A.; Emrouznejad, A.; Agrell, PJ, Interval data without sign restrictions in DEA, Appl Math Model, 38, 7-8, 2028-2036 (2014) · Zbl 1427.90176
[13] He, F.; Xu, X.; Chen, R.; Zhu, L., Interval efficiency improvement in DEA by using ideal points, Measurement, 87, 138-145 (2016)
[14] Hladík, M., Generalized linear fractional programming under interval uncertainty, Eur J Oper Res, 205, 1, 42-46 (2010) · Zbl 1187.90287
[15] Hladík, M., Optimal value bounds in nonlinear programming with interval data, Top, 19, 1, 93-106 (2011) · Zbl 1225.90127
[16] 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
[17] Hladík, M., Weak and strong solvability of interval linear systems of equations and inequalities, Linear Algebra Appl, 438, 11, 4156-4165 (2013) · Zbl 1305.65139
[18] Hladík, M., On approximation of the best case optimal value in interval linear programming, Optim Lett, 8, 7, 1985-1997 (2014) · Zbl 1309.90047
[19] Inuiguchi, M.; Mizoshita, F., Qualitative and quantitative data envelopment analysis with interval data, Ann Oper Res, 195, 1, 189-220 (2012) · Zbl 1259.90064
[20] Jablonsky, J.; Fiala, P.; Smirlis, Y.; Despotis, DK, DEA with interval data: an illustration using the evaluation of branches of a Czech bank, Cent Eur J Oper Res, 12, 4, 323-337 (2004) · Zbl 1160.90524
[21] Jahanshahloo, G.; Soleimani-damaneh, M.; Mostafaee, A., Cost efficiency analysis with ordinal data: a theoretical and computational view, Int J Comput Math, 84, 4, 553-562 (2007) · Zbl 1149.90075
[22] Jahanshahloo, G.; Soleimani-damaneh, M.; Mostafaee, A., On the computational complexity of cost efficiency analysis models, Appl Math Comput, 188, 1, 638-640 (2007) · Zbl 1137.90612
[23] Jahanshahloo, G.; Soleimani-damaneh, M.; Mostafaee, A., A simplified version of the DEA cost efficiency model, Eur J Oper Res, 184, 2, 814-815 (2008) · Zbl 1168.90511
[24] Jain, S.; Arya, N., Inverse optimization for linear fractional programming, Int J Phys Math Sci, 4, 1, 444-450 (2013)
[25] Jeyakumar, V.; Li, G.; Srisatkunarajah, S., Strong duality for robust minimax fractional programming problems, Eur J Oper Res, 228, 2, 331-336 (2013) · Zbl 1317.90291
[26] Khalili-Damghani, K.; Tavana, M.; Haji-Saami, E., 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 (2015)
[27] Kuosmanen, T.; Post, T., Measuring economic efficiency with incomplete price information: with an application to european commercial banks, Eur J Oper Res, 134, 1, 43-58 (2001) · Zbl 1017.91082
[28] Kuosmanen, T.; Post, T., Measuring economic efficiency with incomplete price information, Eur J Oper Res, 144, 2, 454-457 (2003) · Zbl 1042.91562
[29] Li, W.; Xia, M.; Li, H., New method for computing the upper bound of optimal value in interval quadratic program, J Comput Appl Math, 288, 70-80 (2015) · Zbl 1320.65095
[30] Li, W.; Xia, M.; Li, H., Some results on the upper bound of optimal values in interval convex quadratic programming, J Comput Appl Math, 302, 38-49 (2016) · Zbl 1334.65104
[31] Mostafaee, A., Non-convex technologies and economic efficiency measures with incomplete data, Int J Ind Math, 3, 4, 259-275 (2011)
[32] Mostafaee, A.; Saljooghi, FH, Cost efficiency measures in data envelopment analysis with data uncertainty, Eur J Oper Res, 202, 2, 595-603 (2010) · Zbl 1196.90054
[33] Mostafaee, A.; Hladík, M.; Černý, M., Inverse linear programming with interval coefficients, J Comput Appl Math, 292, 591-608 (2016) · Zbl 1325.90064
[34] Rohn, J., Strong solvability of interval linear programming problems, Computing, 26, 79-82 (1981) · Zbl 0449.90062
[35] Rohn, J., Linear programming with inexact data is NP-hard, ZAMM Z Angew Math Mech, 78, Supplement 3, S1051-S1052 (1998) · Zbl 0915.90204
[36] Sakawa, M.; Nishizaki, I.; Uemura, Y., 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 (2001) · Zbl 1077.90564
[37] Shwartz, M.; Burgess, JF; Zhu, J., 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 (2016)
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