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The bi-partial version of the p-median / p-center facility location problem and some algorithmic considerations

100%

Owsinski J. W.

tom Vol. 8, No. 3

59--63

The paper introduces the bi-partial version of the well known p-median or p-center facility location problem. The bi-partial approach, developed by the author, primarily to deal with the clustering problems, is shown here to work for a problem that does not possess some of the essential properties, inherent to the bi-partial formulations. It is demonstrated that the classical objective function of the problem can be correctly interpreted in terms of the bi-partial approach, that it possesses the essential properties that are at the core of the bi-partial approach, and, finally, that the general algorithmic precepts of the bi-partial approach can also be applied to this problem. It is proposed that the use of bi-partial approach for similar problems can be beneficial from the point of view of flexibility and interpretation.

Properties of an α-clique approach to obtaining the hub and spoke structure in optimization of transportation systems

45%

Mazbic-Kulma B. , Owsinski J. W. , Barski A. , Sęp K. , Stańczak J.

2018

tom Vol. 47, no. 2

173--189

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.