An Interval Model in Interdiction Network Flow
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
R. Keshavarzi
1
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
H. Salehi ‎Fathabadi‎
2
(
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
)
کلید واژه: Simplex method, Interdiction problem, bi-level programming, duality, Decomposition, Interval data, network flow,
چکیده مقاله :
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".
یکی از موضوعات کلیدی در شبکه های جریان، تحریم آنهاست. کشاورزی و صالحی این مساله را با در نظر گرفتن چند مبداء و چند مقصد برای شبکه و داشتن شرایط خاص برای جریان ارسالی از مبداءها به مقصدها بیان کردند. علاوه بر این مساله، در حالت چند تحریم کننده معرفی و یک روش معادل برای حل مساله بیان شده است. در این مقاله جریان شبکه تحریم شده با چند مبداء و چند مقصد به گونه ای بیان شده است که داده های مساله غیر قطعی هستند (در یک بازه با ابتدا و انتهای مشخص قرار گرفته اند). در انتها یک فاصله بهینه برای جواب مساله ارائه شده است و به حل یک مثال عددی با استفاده از نرم افزار لینگو پرداخته شده است.
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