Optimized design of mining production processes under resource constraints using the knapsack problem
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Author |
Oleksandr Krukovskyi, Andrii Khorolskyi, Volodymyr Medyanyk, Volodymyr Lapko and Oleksandr Mamaikin
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e-ISSN |
1819-6608 |
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On Pages
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690-703
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Volume No. |
21
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Issue No. |
10
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Issue Date |
July 20, 2026
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DOI |
https://doi.org/10.59018/052674
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Keywords |
parameter optimization, objective function, technological scheme, resources, rational area.
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Abstract
Develop a new approach to designing mining processes under limited resources. Combinatorial optimization methods were applied to develop the new approach. The problem of designing technological processes can be solved by interpreting it as the "knapsack problem" with a private solution, "knapsack 0-1". Dynamic programming algorithms were used to search for the optimal solution. A new approach to designing mining management processes under limited resources has been developed. If the goal is to achieve maximum efficiency with minimal costs, the forward pass method is applied. If there are constraints on throughput capacity, energy characteristics, or specific costs, then the backward pass method is applied. In the final part of the research, verification of the proposed approach was carried out. The task involved developing recommendations for choosing the structure of the technological chain of longwall under given technological and mining-geological development parameters. The specific extraction cost was imposed as a constraint. As a result of solving the design problem using the backward pass method, recommendations were developed for replacing mechanical equipment. This allowed achieving the specified level of productivity and reducing specific costs by 10.6%. As a result of solving the problem of organizing the transport chain using the method described in the paper, an 8% reduction in electricity costs was achieved. This was achieved by reducing the total power of the motors that drive the conveyors. By imposing constraints on the size of the operating productivity, the optimal number of vehicles is chosen. The application of combinatorial optimization methods allowed obtaining an optimal solution within the specified parameters. The originality of the work lies in establishing the regularities of efficient formation in the processes of mineral deposits development. For the first time, combinatorial optimization methods have been applied to the design of processes accompanying the development of mineral deposits, determining their scope of application, and formalizing a series of dynamic programming problems and algorithms: reverse pass, spanning tree. Verification of the developed approach to designing mining production processes under limited resources has been carried out. The approach obtained allows finding optimal solutions with specified constraints at the design stage. Constraints may include: throughput capacity of the transport chain, energy characteristics of technological processes accompanying extraction, specific cost of extraction, etc. The design task can be solved in a direct manner - if the objective function is to maximize a parameter- or in reverse - if there are constraints.
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