Applications of Finite Markov Chain Models to Management

TL;DR

This paper reviews how finite Markov Chain models, particularly ergodic and absorbing types, are applied to solve management problems across various fields, highlighting their historical development and practical relevance.

Contribution

It provides a comprehensive overview of finite Markov Chain applications in management, emphasizing the distinction between ergodic and absorbing chains and their problem-solving capabilities.

Findings

Markov Chains are effective for modeling management scenarios.

Ergodic and absorbing chains address different problem types.

Applications span natural, social, and applied sciences.

Abstract

Markov Chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary texts. Since then, the Markov Chain theory was developerd by a number of leading mathematicians, such as Kolmogorov, Feller etc. However, only from the 1960's the importance of this theory to the Natural, Social and most of the other Applied Sciences has been recognized. In this review paper we present applications of finite Markov Chains to management problems, which can be solved, as most of the problems concerning applications of Markov chains in general do, by distinguishing between two types of Chains, the Ergodic and the Absorbing ones.