The development of modern, innovative, and effective management and planning
is currently impossible without the use of statistical and mathematical methods supported
by modern computer science.
Classical methods of managing logistics services, based solely on intuition
and the decision-maker's experience, are becoming less and less effective, and increasingly inaccurate
and unjustified. Therefore, there is a growing interest in methods that improve
the management process. These opportunities are seen in the increasingly widespread use
of quantitative methods, also known as mathematical, and computer science.
The increasing mathematization and computerization of science necessitates the construction and application
of quantitative (mathematical) models in logistics as well. Therefore, there is a growing understanding among researchers of the need and inevitability of mathematizing the operation of logistics systems.
In the process of managing a studied facility, appropriate
forecasts are usually used to make rational decisions. It is then concluded that these forecasts
support the process of effective facility management. The aim of my work is to present a new, innovative method for building forecasts supporting the service management process of logistics enterprises based on the laws of operation of a probabilistic logistics system, i.e., analytical models of these processes in the form of certain systems of equations.
The work consists of two parts.
Part I includes two chapters, the first of which is devoted to a review of selected mathematical models used in logistics, while the second presents the basic research directions used in forecasting.
Part II presents my original contribution to this work and consists of eight chapters.
The first describes the logistics system I studied. In Chapters 2 and 6, I presented a mathematical analysis of the functioning of the logistics system I studied in the two variants considered. Chapters 3, 4, and 7 contain a probabilistic model of the functioning of the system studied in both variants, based on this analysis. This model enabled me to determine forecasts of the values ​​characterizing the system's operation, which are presented in Chapters 5 and 8 of Part II of this work.

Analysis of the operation of the logistics system I studied allowed me to obtain two variants of my own probabilistic model of this system's operation in the form of mathematical equations (see Chapters 2, 3, and 4, and 6 and 7 of Part II of this work).

Based on the obtained model, I also presented my own innovative method for determining forecasts (see Chapters 5 and 8 of Part II). These forecasts depend on the parameters of the logistics system being studied.

If these forecasts prove unfavorable for the operation of the logistics system,
they can be corrected by adjusting the values ​​of the system's operating parameters, in order to obtain forecasts that will guide decision-makers towards effectively pursuing their customers' interests. Forecasts obtained from time series data do not offer such a possibility. This is my innovative method for supporting the service management process. It is based on the analysis of the logistics system's operation, which led to the development of two variants of my own probabilistic model of this system's operation (see Chapters 3, 4, and 7 of Part II).
These characteristics and the corresponding forecasts, depending on the operating parameters of the system under study, along with the possibility of using them to support the management process and improve the economic competitiveness of logistics enterprises, are presented in Chapters 4, 5, and 8 of Part II.