Solution of the problem to optimize two-stage allocation of the material flows
Anatolii Bulat1, Serhii Dziuba1, Serhii Minieiev1, Larysa Koriashkina2, Svitlana Us2
1Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, Dnipro, 49005, Ukraine
2Dnipro University of Technology, Dnipro, 49005, Ukraine
Min. miner. depos. 2020, 14(1):27-35
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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 alloca-ted 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.
Keywords: multistage problems, set partitioning, geoinformation technologies, location-allocation, nonsmooth optimization
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