MATHEMATICAL MODELS OF MULTIPLEX PARTITIONING AND MULTIPLE COVERAGE OF SETS FOR THE LOCATION-ALLOCATION PROBLEMS
DOI:
https://doi.org/10.32782/IT/2023-4-3Keywords:
logistics, area zoning, multiple coverage of set, mathematical modeling, multiplex partitioning of sets, center capacity.Abstract
We developed the mathematical models for the problems of optimal service centers’ placement and traffic flow distribution, as well as area zoning to estimate the capacity of the located centers and the necessary number of vehicles in logistics systems. Presented are models and methods of optimal division of the region into service center zones based on the criteria of the minimum distance or the fastest service providing the service by any of several service centers closest to consumers. The mathematical formulation of the continuous problem of optimal multiple coverage of sets is improved by considering the peculiarity of the set on which the centers can be placed, which ensures the avoidance of the location of centers too close to each other. Methods and approximate algorithms for solving these problems are described. An analysis of the results of computational experiments is presented.
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