Locational optimization problems solved through Voronoi diagrams

Article Abstract:

The use of the Voronoi diagram in solving local optimization problems is discussed. The Voronoi diagram is a common geometrical diagram that is used for developing a computational method and for formulating valid behavioral implications. The Voronoi diagram involves a set of two or more distinct points in the Euclidean plane where all locations are associated with the closest member or members of the point set with respect to the Euclidean distance. Application of the diagram to optimization problems of line-like and area-like facilities need further investigation.

Methods, Geometrical models, Mathematical optimization, Optimization theory

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Analysis of centroid aggregation for the Euclidean distance p-median problem

Article Abstract:

A study was conducted to carry out a theoretical evaluation of the centroid aggregation effect on the Euclidean distance p-median locating problem. Case errors and the multi-facility location framework Source C error were also analyzed. Euclidean distances were used in the cost function while the centroid aggregation scheme was utilized in the aggregation process. Results indicated that centroid aggregation supported the generation of positive cost errors, and that the optimality error is significantly much less than the cost error.

Facility management, Facilities management, Euclidean geometry

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Stability in P5- and banner-free graphs

Article Abstract:

Polynomial solvability of the maximum stable set problem in P5-free banner-free graphs is proved.

Polynomials, Graph theory

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