Markov Models Related to Inventory Systems, Control Charts, and Forecasting Methods

Abstract

A Markov model describes a randomly varying system that satisfies the Markov property. This means that future and past states at any time are independent of the current state. The two most commonly used types of Markov models are Markov chains and higher-order Markov chains. Therefore, three types of Markov models are proposed in this chapter of the book: (i) supply chain management, (ii) Markov queue waiting time monitoring, and (iii) Markov fuzzy time series forecasting. The introduction introduces Markov chain (MC) and summarizes the most important aspects of Markov chain analysis. The first model explores a Markov queue model coupled to a storage system using the classical (0, Q) policy. The second model focuses on the M/M/1/N service mode and develops a control chart for an Ms/Ms/1/N type simulated queue to monitor customer waiting times. The third is a higher-order Markov model (HOMM), which uses fuzzy sets to predict future states based on given hypothetical time series data. Numerical calculations are designed to find optimal order quantities, monitor customer wait times, and predict future HOMM conditions.