Simultaneous optimization of management decisions at the operational and tactical level in animal production

In herd management, we face a hierarchy of decisions made at different levels with different time horizon, 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. If, for instance, a decision has to be made at the tactical level, it is necessary to assume some policy to be followed concerning decisions at the operational level. This policy has to be optimal given the tactical decision and the present state of the system, which may very well deviate from the state observed at the time of the tactical decision. On the other hand, it is not possible to choose an optimal decision at the tactical level, unless a policy has been determined at the operational level. A new notion of a multi-level hierarchic Markov process has been developed in order to become able to perform a simultaneous optimization of management decisions at the operational and tactical level in animal production. The applicational perspectives of the method are illustrated through an example referring to a sow herd decision problem involving decisions at several levels with different time horizons. The method also contributes significantly to circumventing the well known curse of dimensionality in Markov decision processes.