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1
Content available Properties of an α-clique approach to obtaining the hub and spoke structure in optimization of transportation systems
Mazbic-Kulma B., Owsinski J. W., Barski A., Sęp K., Stańczak J.
Control and Cybernetics
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2018
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Vol. 47, no. 2
173--189
EN
The paper is devoted to the analysis of a graph transformation, pertinent for the transport and logistic systems and their planning and management. Namely, we consider, for a given graph, representing some existing transport or logistic system, its transformation to a (non-equivalent) so-called ”hub-and-spoke” structure, known from both literature and practice of transportation and logistics. This structure is supposed to bring benefits in terms of functioning and economic performance of the respective systems. The transformation into the ”hub-and-spoke” is not only non-equivalent (regarding the original graph of the system), but is also, in general, non unique. The structure sought is composed of two kinds of elements - nodes of the graph (stations, airports, havens, etc.), namely: the subgraph of hubs, which, in principle, ought to constitute a complete sub-graph (a clique), and the ”spokes”, i.e. the subsets of nodes, each of which is connected in the ultimate structure only with one of the hubs. The paper proposes a relaxation of the hub-and-spoke structure by allowing the hub subgraph not to be complete, but at least connected, with a definite ”degree of completeness” (alpha), from where the name of ”alpha-clique”. It is shown how such structures can be obtained and what are the resulting benefits for various assumptions, regarding such structures. The benefits are measured here with travel times. The desired structures are sought with an evolutionary algorithm. It is shown on an academic example how the results vary and how the conclusions, relevant for practical purposes, can be drawn from such analyses, done with the methods here presented.
2
Content available Hub- and- spoke : Centralny Port Lotniczy
Kowalska-Napora E.
Autobusy : technika, eksploatacja, systemy transportowe
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2018
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R. 19, nr 12
1094--1098
PL
Artykuł przedstawia problematykę właściwej interpretacji hub- and- spoke na przykładzie Centralnego Portu Lotniczego. Paradygmat hub- and- spoke jest formą optymalizacji topologii transportu, gdzie trasy przepływu zorganizowane są poprzez serię „szprych łączących odległe punkty z centralnym koncentratorem”.
EN
This paper presents the consideration of proper interpretation of hub-and- spoke structure for the example: Central Airport Project. The hub- and- spoke paradigm is a form of transport topology optimization in which traffic routes are organized as a series of „spokes” that connect outlying points to a central „hub”.
3
Content available The kernel and shell structure as a tool for improving the graph of transportation connections
Mażbic-Kulma B., Owsiński J. W., Sęp K., Stańczak J.
Operations Research and Decisions
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2013
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Vol. 23, No. 2
91--105
EN
A model of a transportation system is expected to be useful in simulations of a real system to solve given transportation tasks. A connection graph is routinely used to describe a transportation system. Vertices can be train stations, bus stops, airports etc. The edges show direct connections between vertices. A direct approach can be difficult and computational problems can arise in attempts to organize or optimize such a transportation system. Therefore, a method for aggregating such graphs was introduced, using a general kernel and shell structure and its particular instances: α-clique structured graphs of connections and a hub and spoke transformation of the source graph. These structures enable the concentration and ordering of transport between vertices and reduction of the analyzed graph. To obtain the desired structures, several versions of a specialized evolutionary algorithm were developed and applied.
4
Content available Evolutionary approach for obtaining the hub and spoke structure in the logistic network
Mażbic-Kulma B., Stańczak J., Owsiński J. W., Sęp K.
Total Logistic Management
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2011
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no. 4
89-105
EN
In order to describe transportation system, as a routine a connection graph would be used. Vertices of the graph can be train stations, bus stop, airports etc. The edges show direct connections between vertices. A direct application of such graph can be difficult and computational problems can occur while one would try to organize or optimize such a transportation system. Therefore, a method of aggregation of such graph was introduced, using the general kernel and shell structure and a hub and spoke transformation method of the source graph. These structures allow to concentrate and order the transport of goods/persons among vertices and enable to reduce the number of analyzed vertices as well as edges of the graph. In the presented paper we continue our work on kernel and shell and its instance hub and spoke methods of connection graph transformation. In this paper we develop model of the transportation system using the hub and spoke method with predetermined, minimum and indirectly described numbers of hub nodes. To obtain the desired structures, several versions of specialized evolutionary algorithm (EA) were developed and applied.
5
Content available remote Application of selected methods of graph theory and combinatorial heuristics to minimising the number of transits nodes in an air network
Mażbic-Kulma B., Owsiński J. W., Sęp K.
Total Logistic Management
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2008
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no. 1
111-123
EN
In the paper we present the notion of alpha-clique and some of its properties. Covering with alpha-cliques is a preprocessing method for an air network, described as a graph, in which vertices correspond to airports and edges correspond to air connections. Using the alpha-clique cover we obtain a hypergraph, in which we find the minimum transversal. The set of vertices thus obtained is the sought-for set of transits nodes, called hubs. Using the alpha-clique concept instead of proper cliques we can obtain the solution to the graph covering problem easier.
PL
W niniejszej pracy prezentujemy pojęcie alfa-kliki i pewne jej własności. Znalezienie pokrycia alfa-klikami traktujemy jako metodę preprocessingu dla sieci lotniczych opisanych jako graf, w którym węzły odpowiadają lotniskom, a krawędzie odpowiadają połączeniom lotniczym. Znajdując pokrycie alfa-klikami, uzyskujemy hipergraf, dla którego otrzymujemy minimalną transwersalę. W ten sposób uzyskujemy zbiór wierzchołków będących węzłami tranzytowymi czyli hubami. Stosując alfa-kliki zamiast odpowiednich klik, możemy uzyskać lepsze pokrycie grafu.
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