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arXiv · 1303.5457

Explicit solution of a tropical optimization problem with application to project scheduling

Nikolai Krivulin
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Abstract

A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition operator. A special case of the problem, which arises in just-in-time scheduling, serves as a motivation for the study. To solve the general problem, we derive a sharp lower bound for the objective function and then find vectors that yield the bound. Under general conditions, an explicit solution is obtained in a compact vector form. This result is applied to provide new solutions for scheduling problems under consideration. To illustrate, numerical examples are also presented.

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Nikolai Krivulin. 2013-03-21. Explicit solution of a tropical optimization problem with application to project scheduling. https://arxiv.org/abs/1303.5457

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