Solving Fully Interval Linear Programming Problems Using Ranking Interval Numbers
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
A. Hosseinzadeh
1
(Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.)
M. Vaez-Ghasemi
2
(Department of Mathematics, Rasht Branch, Islamic Azad University, Guilan, Iran.)
کلید واژه: Linear Programming, Interval number vector, ranking interval., Interval linear system,
چکیده مقاله :
Here the general form of an fully Interval linear programming problems (FILP) is considered where all the parameters and variables are considered to be intervals. Moreover, in this study more general conditions for variables are considered, variables which are unrestricted in sign. Although this is the case in most of the real world problems. In this paper a new method is presented in order to obtain FILP.
در این مقاله فرم کلی مساله برنامه ریزی خطی تمام بازه ای(FILP) در نظر گرفته می شود که در آن تمام پارامترها و متغیرها به صورت اعداد بازه ای در نظر گرفته می شوند. علاوه بر این ، در این مطالعه شرایط عمومی تری برای متغیرها در نظر گرفته شده است، و متغیرهای تصمیم از نظر علامت آزاد در نظر گرفته شده اند. چرا که این نوع مسائل در دنیای واقعی وجود دارند ولی محققان به آن نپرداخته اند. در این مقاله روش جدیدی برای حل FILP ارائه شده است.
[1] H. Ali Ashayerinasab, Hasan Mishmast Nehi, Mehdi Allahdadi. Solving the interval linear programming problem: A new algorithm for a general case, Expert Systems With Applications 93 (2018) 39-49.
[2] T. Allahviranloo, A. A. Hosseinzadeh, M. Ghanbari, E. Haghi, R. Nuraei, On the new solutions for a fully fuzzy linear system, Soft Comput. (2014), http://dx.doi.org/ 10.1007/s00500-013-1037-3/.
[3] A. Ben-Israel, P. D. Robers, A decomposition method for interval linear programming, Manage. Scie. 16 (1970) 374-387.
[4] J. W. Chinneck, K. Ramadan, Linear programming with interval coefficients, J. of the Oper. Rese. Socie. 51 (2000) 209-220.
[5] E. Garajov, Milan Hladk, Miroslav Rada. Interval linear programming under transformations: optimal solutions and optimal value range, Central European Journal of Operations Research, (2018), http://dx.doi.org/10.1007/s10100-018-0580-5/.
[6] M. Hladk, Robust optimal solutions in interval linear programming with for allexists quantifiers, (2016), http://10.1016/j.ejor.2016.04.032/.
[7] M. Hladik, Complexity of necessary efficiency in interval linear programming and multiobjective linear programming, Optim Lett. 6 (2012) 893- 899.
[8] M. Hladik, On necessary efficient solutions in interval multiobjective linear programming, In: Antunes, C. H., Insua, D.R., Dias, L.C. (eds.) CD-ROM Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making URPDM 2010, April 15-17, Coimbra, Portugal, pp. 1-10 (2010).
[9] M. Hladik, Generalized linear fractional programming under interval uncertainty,EJOR 205 (2010) 42-46.
[10] M. Hladik, Optimal value range in interval linear programming, Fuzzy Optim. Decis. Making 8 (2009) 283-294
[11] G. H. Huang, R.D. Moore, Grey linear programming, its solving approach, and its application, Int. J. of Sys. Scie. 24 (1993) 159-172.
[12] M. Ida, Necessary efficient test in interval multiobjective linear programming, Proceedings of the Eighth International Fuzzy Systems Association World Congress (1999) 500-504.
[13] M. Inuiguchi, M. Sakawa, Minimax regret solution to linear programming problems with an interval objective function,EJOR 86 (1995) 526-536.
[14] W. Li, J.Luo, Q. Wang, Y.Li. 2013. Checking weak optimality of the solution to linear programming with interval right-hand side, Optim. Lett. 8 (2014) 1287-1299.
[15] W. A. Lodwick, K. D. Jamison, Special issue, interfaces between fuzzy set theory and interval analysis, Fuzzy Sets and Sys. 135 (2003) 1-3.
[16] J. Novotn, Milan Hladk, Tom Masak, Duality Gap in Interval Linear Programming, Journal of Optimization Theory and Applications, (2019), http://dx.doi.org/10.1007/s10957-019-01610-y/.
[17] C. Oliveira, C. H. Antunes, An interactive method of tackling uncertainty in intervalmultiple objective linear programming, J. Math. Sci. 161 (2009) 854-866
[18] C. Oliveira, C. H. Antunes, Multiple objective linear programming models with interval coefficients- an illustrated overview, Eur. J. Oper. Res. 181 (2007) 1434-1463.
[19] H. Rommelfanger, R. Hanuscheck, J. Wolf, Linear programming with fuzzy objectives, Fuzzy Sets and Sys. 29 (1989) 31-48.
[20] A. Sengupta, T. K. Pal, D. Chakraborty, Interpretation of inequality constraints involving interval coefficients: a solution to interval linear programming, Fuzzy Sets and Sys. 19 (2001) 129-138.
[21] A. Sengupta, T. K. Pal, On comparing interval numbers,EUOR. 127 (2000) 28-43.
[22] A.L. Soyster, Inexact linear programming with generalized resource sets, Eur. J. Oper. Res. 3 (1979) 316- 321.
[23] A. L. Soyster, A duality theory for convex programming with set-inclusive constraints, Oper. Res. 22 (1974) 892-898.
[24] D. J. Thuente, Duality theory for generalized linear programs with computational methods, Oper. Res. 28 (1980) 1005-1011.
[25] S. C. Tong, Interval number, fuzzy number linear programming, Fuzzy Sets and Syst. 66 (1994) 301-306.
[26] H. C. Wu, Duality Theory in Interval-Valued Linear Programming Problems, J. Optim Theory Appl. 150 (2011) 298-316.
[27] F. Zhou, G. H. Huang, G. Chen, H. C. Guo, Enhanced-interval linear programming, EJOR. 199 (2009) 323-333.
