Approximation algorithms for three-dimensional assignment problems with triangle inequalities

Article Abstract:

Computation models for resolving three-dimensional assignment problems (3DA) with triangle inequalities are presented. The 3DA problem focuses on finding a minimum-weight collection of triangles covering each point exactly once. Experiments indicate that these approaches are excellent in finding 3DA in randomly generated cases where the cost of a triangle is either the sum of the lengths of its sides or the sum of the lengths of its shortest sides.

Models, Integer programming, Numerical analysis, Heuristic programming

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Geometric three-dimensional assignment problems

Article Abstract:

Two geometric special cases of the three-dimensional assignment problem are examined. Three sets called B (blue), R (red) and G (green) are given with each set having n grid points in the Euclidean plane. The goal is to look for a partition of B union R union G into n three-colored triangles so that the total circumference of all triangles or the total area of all triangles is minimized. Both versions of the problem are found to be NP-hard.

Computational complexity, Computational complexity (Machine theory), Combinatorial optimization, Production planning

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Modeling and solving the periodic maintenance problem

Article Abstract:

A method for tackling the periodic maintenance problem, by using discrete and optimization functions, are presented.

Europe, Management dynamics, Plant Maintenance, Management, Company business management, Mathematical optimization, Optimization theory, Factory maintenance, Discrete mathematics

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