An optimal two-stage distribution of material flow at the fuel and energy complex enterprises

¹ Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, 49005, Dnipro, Simferopolska Str., 2a, Ukraine
² National Technical University «Dnipro Polytechnic», 49005, Dnipro, Dmytra Yavornytskoho Ave., 19, Ukraine

^* Correspondent author: sergejdzuba@gmail.com

Abstract

The two-stage distributing of material flows in the transport-logistics system of fuel and energy complex is considered. The structural elements of such system are mines (centers of the first stage), extracting coal from various mineral deposits in a certain area, and enterprises that consume or process coal (centers of the second stage). A presented method for solving this problem is based on elements of the theory of continuous linear problems of optimal set partitioning, duality theory, and methods for solving linear programming problems of transport type. The optimal solution of the two-stage location-allocation problem is obtained in an analytical form, which contains parameters that are the optimal solution of the auxiliary finite-dimensional optimization problem with a non-differentiable objective function. Therefore, the part of numerical algorithm is non-differentiable optimization method – modification of Shor’s r-algorithm. The results of computational experiments solving model problems confirm the correctness of the presented method and algorithm. It is demonstrated the synergistic effect obtained from formulation of continuous problems of optimal partitioning sets with additional constraints. It is showed, how important to take into account the multi-stage distributing of raw materials when it is necessary to locate new transport-logistics system objects in a given territory.