Mathematical modeling of the supply chain for freight transportation within the logistics system

Abstract

In the article, mathematical modeling of the supply chain for freight transportation within the logistics system is carried out. It is emphasized that mathematical modeling of freight flows in real time requires a large amount of computing resources, improvement of mathematical models and numerical methods. A method of modeling the problem of operational formation of the supply chain for freight transportation within the logistics system taking into account the possibility of transit was proposed, a review of the limitations of the operational problem of freight transportation with the possibility of transit from client a to client b was carried out, which made it possible to reduce the multi-product distribution problem to a single-product task of constructing a minimum cost flow. A method of modeling the problem of operational distribution of goods by logistics centers is proposed, including a decision support system in case of incompatibility of the constraints of the problem that arises. It is emphasized the need to approximate the operational problem of distribution of cargo transportation with the possibility of transit and the problem of distribution of orders by logistics centers. It is noted that it is mandatory to organize a decision support system for the problem of operational distribution of goods across logistics centers in case of incompatibility of its limitations. A typical problem is considered, when a logistics center delivers goods to customers through intermediate centers, and each of the intermediate centers serves its group of customers. The formal statement of the problem is given and the features of the constructed problem are noted, which allowed to build an effective mathematical model of its solution within the framework of the general logistics system, which contributed to minimizing the delivery time and increasing the productivity of the supply company. The features of this task are the interval nature of the restrictions and the clearly expressed presence of modules, each of which is responsible for a specific block of the overall task. The purpose of further research is to build an effective algorithm for solving the problem based on the given mathematical model and its optimization analysis