On some mathematical models of facility location problems of mining and concentration industry

Us, S. A.; Станіна, Ольга

doi:10.1201/b19901-73

Cited by 4 publications

(2 citation statements)

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“…Note that Task 1 is a continuous placement task [23]. The dependencies necessary for its full description are usually not analytically defined.…”

Section: Research Results and Their Discussion Experimental Studies O...mentioning

confidence: 99%

Selection and justification of drilling and blasting parameters using genetic algorithms

Us,

Ishchenko,

Koba

et al. 2023

Nauk. visn. nat. hirn. univ.

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Purpose. Using experimental and theoretical studies to justify the rational location of charges of various types and their technological parameters in the fan, taking into account the physical and mechanical properties and structural features of the rocks in the mountain massif. Methodology. In the experiments, an improved method of geostructural analysis of rocks was used to obtain detailed data on their properties, the block structure of the massif, and the type and direction of development of crack systems. Identification of crack systems, their density, intensity, and direction of development of crack systems is carried out on petrographic sections using microscopic analysis, these are used to calculate the average indicator of the cracking coefficient, while the funneling method – the anisotropy coefficient. The justification of the rational location and the number of charges in each fan was performed using the methods of genetic algorithms and the developed software product. Findings. The coefficient of cracking and anisotropy of physical and mechanical properties of uranium ores was calculated, which was 78 cr/sm2 and 1.4, respectively. According to the developed mathematical models and the software product, the optimization problem was solved using genetic algorithms, which determined the main priorities: the location of the charge in the fan according to the structure of the massif and the rational diameter of the well, which helps to limit the number of oversized blocks of reflected ore. Originality. The regularities are established of the change in the anisotropy coefficient from the cracking coefficient, the nature of the distribution and the number of microcracks (cr/sm2) in the quartz grains, which is present in uranium ore according to a linear law, and the output (in %) of oversized blocks during the destruction of uranium ore from the cracking coefficient – according to the polynomial law. For the first time, the optimal location and the number of charges in each fan, the diameter of the wells, taking into account the type of rock, its strength and fissure, and the geometric parameters of the ore deposit, were determined based on the constructed mathematical models and the developed software product. Practical value. The indicated results of the experimental and theoretical studies will form the basis for the development and substantiation of rational parameters of resource-saving and seismically safe methods for breaking strong rocks of complex structure during the extraction of uranium and iron ores by the energy of the explosion in mines.

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“…Note that Task 1 is a continuous placement task [23]. The dependencies necessary for its full description are usually not analytically defined.…”

Section: Research Results and Their Discussion Experimental Studies O...mentioning

confidence: 99%

Selection and justification of drilling and blasting parameters using genetic algorithms

Us,

Ishchenko,

Koba

et al. 2023

Nauk. visn. nat. hirn. univ.

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show abstract

“…For the first time, those problems were analysed in [2]. Their continuity was stipulated not only by the possibility to locate fist-stage centres at any point of the specified continual set but also by the necessity to partition the set itself (or its share) into several zones.…”

Section: Introductionmentioning

confidence: 99%

Solution of the problem to optimize two-stage allocation of the material flows

Bulat¹,

Dziuba²,

Minieiev³

et al. 2020

Min. miner. depos.

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Purpose is to elaborate innovative and computationally efficient algorithm to solve a problem of two-stage allocation of the resource occupying continuously the specified area as well as to demonstrate the behaviour of the corresponding software developed with the application of advanced geoinformation resources. Methods. The paper involves mathematical models of continuous problems of optimal set partitioning with additional connections to describe two-stage problems of the material resource location-allocation. Methodological approach to the solution of such problems is based on the idea of their reducing to the problem of infinite-dimensional mathematical programming for which it is possible to obtain optimal solution in the analytical form with the help of the duality theory apparatus. Findings. Mathematical and algorithmic apparatus to solve continuous problems applied for the fuel and energy complex enterprises has been developed making it possible to obtain partitioning of the deposit area into the zones, which are allocated to the first-stage enterprises exclusively. The algorithm operation is demonstrated in terms of the model problem solution. It has been defined that the benefit of such an approach is in the reducing of the infinite-dimensional programming problem to the problem of finite-dimensional nonsmoth optimization since the obtained computational formulas contain the parameters which determination requires solving the auxiliary problem of the nondifferentiable function optimization. Originality. Contrary to the previously developed one, the proposed algorithm does not stipulate solution of the linear programming problem of transport type at each step of the iteration process. Such a problem is solved only once to find the volumes of product transportation between the first-stage and second-stage enterprises after defining all the optimal solution components. Practical implications. Software implementation of the algorithm on the basis of the advanced geoinformation technologies and resources, in terms of the solution of raw material flow allocation, makes it possible to reduce total costs for the management of material flows and their accompanying service flows throughout the whole logistic chain beginning from the flow origin up to its arrival to the end user.

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Generalized Models of Logistics Problems and Approaches to Their Solution Based on the Synthesis of the Theory of Optimal Partitioning and Neuro-Fuzzy Technologies

Bulat,

Kiseleva,

Hart

et al. 2023

Studies in Computational Intelligence

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On some mathematical models of facility location problems of mining and concentration industry

Cited by 4 publications

References 0 publications

Selection and justification of drilling and blasting parameters using genetic algorithms

Selection and justification of drilling and blasting parameters using genetic algorithms

Solution of the problem to optimize two-stage allocation of the material flows

Generalized Models of Logistics Problems and Approaches to Their Solution Based on the Synthesis of the Theory of Optimal Partitioning and Neuro-Fuzzy Technologies

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