نوع مقاله: مقاله پژوهشی
نویسندگان
1 گروه ریاضی، دانشکده ریاضی، دانشگاه سیستان و بلوچستان، زاهدان،ایران
2 ریاضی، دانشکده ریاضی، دانشگاه سیستان و بلوچستان، زاهدان، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
In this paper, solution space of interval linear programming (ILP) models that is a NP-hard problem, has been considered. In all of the solving methods of the ILP, feasibility condition has been only considered. Best-worst case (BWC) is one of the methods for solving the ILP models. Some of the solutions obtained by the BWC may result in an infeasible space. To guarantee that solution is completely feasible, improved two-step method (ITSM) is proposed. By using a new approach, we introduce a space for solving ILP models in which by two tests, feasibility and optimality of the obtained space has been guaranteed.
کلیدواژهها [English]
Alefeld, G., & Herzberger, J. (2012). Introduction to interval computation. Academic press.
Allahdadi, M., Nehi, H. M., Ashayerinasab, H. A., & Javanmard, M. (2016). Improving the modified interval linear programming method by new techniques. Information sciences, 339, 224-236.
Allahdadi, M., & Nehi, H. M. (2013). The optimal solution set of the interval linear programming problems. Optimization letters, 7(8), 1893-1911.
Fiedler, M., Nedoma, J., Ramik, J., Rohn, J., & Zimmermann, K. (2006). Linear optimization problems with inexact data. Springer Science & Business Media.
Chinneck, J. W., & Ramadan, K. (2000). Linear programming with interval coefficients. Journal of the operational research society, 209-220.
Hladík, M. (2014). How to determine basis stability in interval linear programming. Optimization letters, 8(1), 375-389.
Huang, G., & Dan Moore, R. (1993). Grey linear programming, its solving approach, and its application. International journal of systems science, 24(1), 159-172.
Koníckocá, J. (2001). Sufficient condition of basis stability of an interval linear programming problem. ZAMM‐Journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik, 81(S3), 677-678.
Rohn, J. (1993). Cheap and tight bounds: The recent result by E. Hansen can be made more efficient. Interval computations, 4(13-21), 2.
Rohn, J. (2009). Forty necessary and sufficient conditions for regularity of interval matrices: A survey. Electronic journal of linear algebra, 18(500-512), 86.
Rohn, J. (1993). Stability of the optimal basis of a linear program under uncertainty. Operations research letters, 13(1), 9-12. Shaocheng, T. (1994). Interval number and fuzzy number linear programmings. Fuzzy sets and systems, 66(3), 301-306.
Wang, X., & Huang, G. (2014). Violation analysis on two-step method for interval linear programming. Information sciences, 281, 85-96.
Zhou, F., Huang, G. H., Chen, G. X., & Guo, H. C. (2009). Enhanced-interval linear programming. European journal of operational research, 199(2), 323-333.
)