Capacity networks in modeling logistics processes

The main reason for the great interest in network analysis methods is the simplicity of interpreting network models, which in graphical form are easily understood by people not directly involved in operations research. Examples of effects achieved in practice after applying network analysis methods are simple and convincing.

Network models allow for the description of many existing systems, even very complex ones. They also enable the decomposition of such systems, point to relationships between subsystems, and are helpful in selecting characteristics relevant from the point of view of the research objective, etc. Many network analysis methods are characterized by high computational efficiency, significantly higher than methods for solving corresponding mathematical programming tasks. This is all the more important as many problems studied in the field of network analysis are discrete in nature, and general methods for solving combinatorial tasks are characterized by high computational complexity. The advantages of network analysis create a constant demand for new network models designed to solve relevant practical problems. Exemplary achievements in this process include so-called generalized networks with flow increase or decrease on arcs [8], small-world networks [10], fractal networks [9], random graph networks [4], multi-commodity flows [5], evolving networks [1], networks with hidden variables [2], and others presented more broadly, e.g., in [7]. The research presented in this article is also part of this trend. It was inspired by the analysis of certain logistics processes, including transport using the railway network. (…)

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