Markov decision processes in minimization of expected costs

Abstract

Basics of Markov decision processes will be introduced in order to obtain the optimization goal function for minimizing the long-run expected cost. We focus on minimization of such cost of the farmer's policy consisting of different decisions in specic states regarding both milk quality and quantity (lactation states) produced by a dairy cow. The transition probability matrix of the Markov process, used here for modeling of transitions of a dairy cow from one state to another, will be estimated from the data simulated from the lactation model that is often used in practice. We want to choose optimal actions in
the states of this Markov process regarding the farmer's costs. This problem can be solved by exhaustive enumeration of all possible cases in order to obtain the optimal policy. How-
ever, this is feasible only for a small number of states. Generally, this problem can be approached in the linear programming setting which yields an efficient solution. In order to demonstrate and compare these two approaches, we present an example based on the simulated data regarding milk quality and quantity.