Bi-Level Multi-Objective Stochastic Linear Fractional Programming with General form of Distribution

Haneefa Kausar, Ahmad Yusuf Adhami

Abstract


This paper deals with the stochastic approach of bi-level multi-objective linear fractional programming problem.In this type of bi-level programming problem stochastic nature the right hand side resource vector is considered to follow a general form of distribution F (bi) = 1 − Bi^exp(Aih(bi))[13], which in itself includes many well known distributions such as Pareto distribution, Weibull distribution etc. After converting the problem into an equivalent deterministic form, each level of the problem is transformed into a single objective by using K-T conditions. Finally the problem is solved by Taylors series approach. A numerical example is also presented to illustrate how the proposed approach is utilized.


Keywords


Bi-level multi-objective programming, Stochastic programming, Fractional programming, Taylor series, Kuhn-Tucker conditions.

References


Aiyoshi, E.,& Shimizu, K. (1981). Hierarchical decentralized systems and its new solution by a barrier method.IEEE Transactions on Systems, Man and Cybernetics, (6), 444-449.

Abo-Sinna, M. A.,& A bi-level non-linear multi-objective decision taking under fuzziness.Opsearch New Delhi, 38(5) (2001) 484-495.

Abdelaziz, F. B., Aouni, B.,& El Fayedh, R. (2007). Multi-objective stochastic programming for portfolio selection.European Journal of Operational Research, 177(3), 1811-1823.

Bialas, W., Karwan, M.,& Shaw, J. (1980). A parametric complementary pivot approach for two-level linear programming.State University of New York at Bualo, 57.

Bialas, W. F.,& Karwan, M. H. (1984). Two-level linear programming.

Management science, 30(8), 1004-1020.

Ben-Ayed, O. (1993). Bilevel linear programming.Computers & operations re-search, 20(5), 485-501.

Baky, I. A. (2009). Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy sets and systems, 160(18), 2701-2713.

Charnes, A.,& Cooper, W. W. (1959). Chance-constrained programming. Management science, 6(1), 73-79.

Charnes, A.,& Cooper, W. W. (1963). Deterministic equivalents for optimizing and satiscing under chance constraints.Operations research, 11(1), 18-39.

Candler, W.,& Townsley, R. (1982). A linear two-level programming problem. Computers & Operations Research, 9(1), 59-76.

Charles, V., & Dutta, D. (2003, December). Bi-weighted multi-objective stochastic fractional programming problem with mixed constraints.|it In Proceedings of the 2nd National Conference on Mathematical and Computational Methods (pp. 29-36). New Delhi, India: Allied.

Charles, V.,& Dutta, D. (2006). Extremization of multi-objective stochastic fractional programming problem. Annals of Operations Research, 143(1), 297-304.

Charles, V., Ansari, S. I.,& Khalid, M. M. (2011). Multi-objective stochastic linear programming with general form of distributions.Int J Oper Res Optim, 2(2), 261-278.

Dantzig, G. B.(1955), Linear programming under uncertainty. Management science, 1(3-4) 197-206.

Dempe, S.,& Richter, K. (2000). Bilevel programming with knapsack constraints. TU Bergakademie, Fakultat fur Mathematik und Informatik.

Fortuny-Amat, J.,& McCarl, B. (1981). A representation and economic interpretation of a two-level programming problem. Journal of the operational Research Society, 783-792.

. Helmy, Y. M., Emam, O. E., and Abdelwahab, A. M. (2015),On stochastic multi-level multi-objective fractional programming problems, Journal of Statistics Applications and Probability, 4(1), 93

. Kumar, P., Dagar, J., and Sharma, B. (2016),Characterization of Generalized Invexity in Multi-objective Fractional Variational Problem, Statistics, Optimization and Information Computing, 4(4), 342-349.

.Maiti, S. K., and Roy, S. K. (2016),Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach, Journal of Industrial Engineering International, 12(3), 287-298.

.Ozaltn, O. Y., Prokopyev, O. A., and Schaefer, A. J. (2010), The

bilevel knapsack problem with stochastic right-hand sides,Operations Research Letters, 38(4), 328-333.

. Osman, M. S., Emam, O. E., and El Sayed, M. A. (2017),Stochastic fuzzy multi-level multi-objective fractional programming problem, A FGP approach. OPSEARCH, 54(4), 816-840

. Sahoo,N.P.,andBiswal,M.P.(2005),Computation

of Probabilistic linea programming problems involving normal and log-normal random variables with a joint constraint, Computer Mathematics, 82(11), 1323-1338.

. Saraj, M.,& Safaei, N. (2012), Solving bi-level programming problems on using global criterion method with an interval approach,

Applied Mathematical Science, 6(23), 1135-1141.

. Verma, R. (2014),Multi-objective fractional programming problems and second order generalized hybrid invexity frameworks,Statistics, Optimization and Information Computing, 2(4), 280-304.

. White, D. J., and Anandalingam, G. (1993), A penalty function approach for solving bi-level linear programs, Journal of Global Optimization, 3(4), 397-419.


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DOI: 10.19139/soic.v7i2.373

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