The tutorial outlines some approaches to using modern mathematical tools in managing modern logistics systems. In addition to the theoretical base, it sets out the basics and examples of using the system approach and mathematical apparatus in various applications, each topic is illustrated by examples. The solutions to the considered examples and problems are presented in detail using one of the modern computer mathematics systems - the Mathcad application package, which makes the analysis of various control approaches more efficient and allows the student to focus on the logic of methods and algorithms, freeing him from the need to master cumbersome computational procedures.