An Interval Model in Interdiction Network Flow
الموضوعات : مجله بین المللی ریاضیات صنعتیR. Keshavarzi 1 , H. Salehi ‎Fathabadi‎ 2
1 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
الکلمات المفتاحية: Simplex method, Interdiction problem, bi-level programming, duality, Decomposition, Interval data, network flow,
ملخص المقالة :
One of the key issues raised in networks flow is its interdiction. Keshavarzi et al. scrutinized the issue with the multi-sources and multi-sinks conditions in mind while considering the specific conditions of flow being sent from sources to sinks [R. Keshavarzi et al., Multi-source-sinks network flow interdiction problem, International Journal of Academic Research, 2015]. Moreover, the matter was also examined in the state of multi-interdictors and a practical solution was presented [Keshavarzi and, Salehi, Multi commodity multi source-sinks network flow interdiction problem with several interdictors, Journal of Engineering and Applied Sciences, 2015]. In this paper, the networks flow interdiction in multi-source and multi-sink conditions was addressed; meanwhile, bearing in mind the uncertain data (from a specified beginning to an ending interval), an optimal interval was presented. Finally, a numerical example for this issue was provided and then solved by the program "Lingo".
[1] K. J. Cormican, D. P. Morton, R. K. Wood, Stochastic network interdiction, Operations Research 46 (1998) 184-197.
[2] S. Dempe, Foundations of Bilevel Programming, Kluwer Academic Publishers, Dordrecht (2002).
[3] D. R. Fulkerson, G. C. Harding, Maximizing the minimum source-sink path subject to a budget constraint, Mathematical Programming 13 (1977) 116-118.
[4] E. Israeli, System interdiction and defense, Doctoral dissertation, Naval Postgraduate School, Monterey, California (March 1999).
[5] R. Keshavarzi, F. H. Salehi, Multi commodity multi source-sinks network flow interdiction problem with several interdictors, Journal of Engineering and Applied Sciences 10 (2015) 118-122.
[6] R. Keshavarzi, F. H. Salehi, Multi-sourcesinks network flow interdiction problem, International Journal of Academic Research 7 (2015) 108-115.
[7] N. Nam, F. Bobick, Sequential Interval Network for parsing complex structured activity, Computer Vision and Image Understanding 143 (2016) 147-158.
[8] R. D. Wollmer, Algorithm for targeting strikes in a lines-of-communication network, Operations Research 18 (1970a) 497-515.
[9] R. K. Wood, Deterministic network interdiction, Mathematical and Computer Modeling 17 (1993) 1-18.