Systems analysis and mathematical modeling of partially two-stage processes of material flow distribution

Abstract

The partially two-stage process of material flow distribution in a logistics system is considered, which consists of enterprises that produce certain products and sell them directly to consumers or through distribution centers. It is assumed that the demand for products is continuously distributed throughout the territory of a certain region. The purpose of the work is to reduce transportation and organizational costs associated with the sale and storage of finished products for a network of production enterprises by developing models and methods of optimization tasks that allow determining the quantity, capacity, and coordinates of distri-bution centers and organizing logistics processes, rationally distributing transportation and material flows among all participants in the logistics process. The relevance of the work is due to the creation of territorially distributed multilevel companies that carry out the entire production cycle from raw material procurement with its comprehensive use, production of products to transportation to end consumers through distribution centers. The mathematical support of the formulated placement-distribution tasks is developed using the basic provisions of the theory of continuous problems of optimal subset division with the placement of subset centers, duality theory, linear programming methods of the transport type, modern algorithms of non-differentiable optimization. The presented models and algorithms allow solving a whole range of strategic planning problems that arise in the production, social, and economic spheres of activity.