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Interval linear fractional programming: optimal value range of the objective function. (English) Zbl 07291006
Summary: In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP) problems. In this research, we propose two new methods for solving ILFP problems. In each method, we use two sub-models to obtain the range of the objective function. In the first method, we introduce two sub-models in which the objective functions are non-linear and the two sub-models have the largest and smallest feasible regions; therefore, the optimal value range of the objective function has been obtained. In the second method, two sub-models have been proposed in which the objective functions are linear and the optimal value of the objective function lies in the range obtained from the first method. We use our approaches to maximize the ratio of the facilities optimal allocation to the non-return fund in a bank.
MSC:
90C32 Fractional programming
90C30 Nonlinear programming
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[1] Alefeld, G.; Herzberger, J., Introduction to interval computations (1983), New York: Academic Press, New York
[2] Allahdadi, M.; Mishmast Nehi, H., The optimal solution set of the interval linear programming problem, Optim Lett, 7, 1893-1911 (2013) · Zbl 1311.90069
[3] Allahdadi, M.; Mishmast Nehi, H., Solving the interval linear programming problems by a new approach, ICIC Express Lett, 11, 17-25 (2017)
[4] Allahdadi, M.; Mishmast Nehi, H.; Ashayerinasab, HA; Javanmard, M., Improving the modified interval linear programming method by new techniques, Inf Sci, 339, 224-236 (2016)
[5] Ashayerinasab, HA; Mishmast Nehi, H.; Allahdadi, M., Solving the interval linear programming problem: a new algorithm for a general case, Expert Syst Appl, 93, 39-49 (2018)
[6] Bhurjee, AK; Panda, G., Efficient solution of interval optimization problem, Math Methods Oper Res, 76, 273-288 (2012) · Zbl 1258.49018
[7] Bhurjee, AK; Panda, G., Multi-objective interval fractional programming problems: an approach for obtaining efficient solutions, Oper Res Soc India, 52, 156-167 (2015) · Zbl 1332.90291
[8] Borza, M.; As, Rambely; Saraj, M., Solving linear fractional programming problems with interval coefficients in the objective function, a new approach, Appl Math Sci, 6, 3443-3452 (2012) · Zbl 1264.90167
[9] Charnes, A.; Cooper, WW, Programming with linear fractional functionals, Nav Res Logist Q, 9, 181-186 (1962) · Zbl 0127.36901
[10] Chen, L.; Wu, R.; He, Y.; Yin, L., Robust stability and stabilization of fractional order linear systems with polytopic uncertainties, Appl Math Comput, 257, 274-284 (2015) · Zbl 1338.93293
[11] Fiedler, M.; Nedoma, J.; Ramik, J.; Rohn, J.; Zimmermann, K., Linear optimization problems with inexact data, 35-100 (2006), New York: Springer, New York · Zbl 1106.90051
[12] Ghadle, KP; Pawar, TS, An alternative method for solving linear fractional programming problems, Int J Recent Sci Res, 6, 4418-4420 (2015)
[13] Gilmore, PG; Gomory, RE, A linear programming approach to the cutting stock problem, part II, Oper Res, 11, 863-888 (1963) · Zbl 0124.36307
[14] Hladik, M., Generalized linear fractional programming under interval uncertainty, Eur J Oper Res, 205, 42-46 (2010) · Zbl 1187.90287
[15] Hoa, NV, Existence results for extremal solutions of interval fractional functional integro-differential equations, Fuzzy Sets Syst, 347, 29-53 (2018) · Zbl 1397.34136
[16] Isbell, JR; Marlow, WH, Attrition games, Nav Res Logist Q, 3, 71-94 (1956)
[17] Jeyakumar, V.; Li, G.; Srisatkunarajah, S., Strong duality for robust minimax fractional programming problems, Eur J Oper Res, 228, 331-336 (2013) · Zbl 1317.90291
[18] Jiao, H.; Liu, S., A new linearization technique for minimax linear fractional programming, Int J Comput Math, 91, 1730-1743 (2014) · Zbl 1302.90210
[19] Mesquine, F.; Hmamed, A.; Benhayoun, M.; Benzaoui, A.; Tadeo, F., Robust stabilization of constrained uncertain continuous-time fractional positive systems, J Frankl Inst, 352, 259-270 (2015) · Zbl 1307.93355
[20] Mostafaee, A.; Hladik, M., Optimal value bounds in interval fractional linear programming and revenue efficiency measuring, Cent Eur J Oper Res (2016) · Zbl 07252394
[21] Odior, AO, An approach for solving linear fractional programming problems, Int J Eng Technol, 1, 298-304 (2012)
[22] Radhakrishnan, B.; Anukokila, P., Fractional goal programming for fuzzy solid transportation problem with interval cost, Fuzzy Inf Eng, 6, 359-377 (2014)
[23] Soradi Zeid, S.; Effati, S.; Vahidian Kamyad, A., Approximation methods for solving fractional optimal control problems, Comp Appl Math (2017) · Zbl 1438.49045
[24] Sun, XK; Chai, Y., On robust duality for fractional programming with uncertainty data, Positivity, 18, 9-28 (2014) · Zbl 1297.49061
[25] Tong, SC, Interval number, fuzzy number linear programming, Fuzzy Sets Syst, 66, 301-306 (1994)
[26] Veeramani, C.; Sumathi, M., Solving linear fractional programming problem under fuzzy environment: numerical approach, Appl Math Model, 40, 6148-6164 (2016) · Zbl 07160238
[27] Wen, CF, An interval-type algorithm for continuous-time linear fractional programming problems, Taiwan J Math, 16, 1423-1452 (2012) · Zbl 1286.90147
[28] Wen, CF, Continuous-time generalized fractional programming problems, part II: an interval-type computational procedure, J Optim Theory Appl, 156, 819-843 (2013) · Zbl 1282.90189
[29] Zieniuk, E.; Kapturczak, M.; Kuzelewski, A., Solving interval systems of equations obtained during the numerical solution of boundary value problems, Comp Appl Math, 35, 629-638 (2016) · Zbl 1370.65016
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