Application of Markov Chains to the Problem of Migration in Inventory Systems

摘要

The objective of this thesis was to model the migration of items between categories in a large inventory system as a Markov chain. The Markovian states were defined as the various inventory categories. Transition matrices were constructed from five years of quarterly data. A maximum likelihood estimate of the actual transition matrix was developed and the system was tested for stationarity and prediction capability. The transition probabilities were found to be time dependent and this led to a division of the population into two subgroups. These subgroups were then modeled as separate Markov chains. While none of the Markov models accurately described the actual system, the information gathered on the time dependent nature of the system was used to develop an alternative inventory policy. The proposed policy takes advantage of this improved understanding of the migration process and will help control inventory costs and reduce backorders in a system where forecasting demand accurately is difficult.