Multi-level hierarchic Markov processes as a framework for herd management support

A general problem in relation to application of Markov decision processes to real world problems is the curse of dimensionality, since the size of the state space grows to prohibitive levels when information on all relevant traits of the system being modeled are included. In herd management, we face a hierarchy of decisions made at different levels with different time horizons, and the decisions made at different levels are mutually dependent. Furthermore, decisions have to be made without certainty about the future state of the system. These aspects contribute even further to the dimensionality problem. A new notion of a multi-level hierarchic Markov process specially designed to solve dynamic decision problems involving decisions with varying time horizon has been presented. The method contributes significantly to circumvent the curse of dimensionality, and it provides a framework for general herd management support instead of very specialized models only concerned with a single decision such as, for instance, replacement. The applicational perspectives of the technique are illustrated by potential examples relating to the management of a sow herd and a dairy herd.