Modeling and visualizing maximum multi-product flows in the networks

• Дата: 2018
• Автори: Dodonov, E. О., Dodonov, О. G., Kuzmychev, A. I.
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Інститут проблем реєстрації інформації НАН України 2018
• Теми: flows in the networks; uni- and multi-product flows; maximum multi-product flows; network optimization; потоки в сетях; одно- и многопродуктовые потоки; сетевая оптимизация; maximum multicommodity flows; потоки у мережах; одно- та багатопродуктові потоки; мережева оптимізація
• Онлайн доступ: http://drsp.ipri.kiev.ua/article/view/142911
• Назва журналу: Data Recording, Storage & Processing

Multiproduct flows are the usual natural situation when continuous or discrete flows of anything, passengers, vehicles, water, electricity, raw materials, products or information, shortly, commodities, are moving in the network from one node to another. Here, the node can simultaneously be the source, intermediate point or terminal of one or different commodities (goods or services) flows of products, and each arc is a channel of simultaneous flow of different products in a definite direction with limited capacity. The multi-product flow problem is an important component of the network optimization, which can be used to deal with problems arising, for example, in emergency logistics management, in computer science and technique, in communication and transportation systems performance, in product distribution planning, in network design etc. This is both an ancient and new line of research. The amount of flow one can push through a network from a source to a sink clearly cannot exceed the capacity of a cut separating them, and max-flow min-cut theorem of Ford and Fulkerson showed that the capacity upper bound is always tight. The value of the maximum flow is equal to the capacity of the minimum cut. A technique for solving the maximum multi-product flow problem with using standard linear optimization tools built-in in Excel is proposed.The developed technique for modeling the problem of the maximum K-commodity flow allows investigating practical network situations reduced to a linear model, having the ability, unlike the heuristic (approximate) algorithms, to automatically determine precisely the separating set as the critical zone, to the definition which often focuses as the subject. This technique does not require additional tools or programming skills, therefore it is a perfect software product for research and development in any field of information and analytical activity.