Model of Distributed Cargo Delivery Under the Conditions of a State of War

Abstract

The article is devoted to the problem of cargo delivery in conditions of unreliable transport connections. The problem considered in the work belongs to the field of transport logistics. In particular, this problem often arises when planning the rear support of troops in the context of military operations. The peculiarity of cargo delivery under such conditions is that some transport routes may become impossible, and therefore it is necessary to distribute cargo flows in such a way as to minimize losses during delivery. Similar tasks arise in the civil sphere, when the reliability of transport communications is not guaranteed and can change quite quickly. Mathematical formulations of problems of this type are quite complex, the mathematical model is multi-criteria with a large number of limitations. But even after simplification and transition to one integrated criterion, the tasks remain difficult. The article considers the simplest mathematical model for this type of problem with the criterion of minimizing the risk of losses during cargo delivery with minimal information. As a rule, when solving transport problems by linear programming methods are limited to finding a basic acceptable plan with the minimum possible number of transportation routes. However, when implementing such plans, the reliability of cargo delivery is sharply reduced, and the risks of losses during transportation increase. In the presence of possible losses during cargo transportation, it is much more reasonable to diversify delivery routes. In addition, even in peacetime, diversification allows more efficient use of existing ways of delivering goods. For example, the load on the road surface is reduced, the intensity of traffic on individual routes is reduced, and the risks of traffic accidents are reduced. All of the above shows the relevance of the study of mathematical models of transport problems, in which in addition to the known criteria (transportation costs) there are also criteria related to the minimization of possible losses. One of these mathematical models is the subject of research in this work.