Optimal replacement in the dairy herd: A multi-component system

The dairy herd is described as a multicomponent system, where the components are the cows and heifers. The problem of finding an optimal replacement policy to the multi-component system is considered. The complication of the multi-component model is that, if the supply of heifers is limited (i.e. the dairy farmer uses only home-grown heifers), the replacement decision concerning a cow does not only depend on the state of that particular cow but also on the states of the other cows and heifers in the herd. Initially, it is demonstrated that the multi-component replacement problem may be formulated as an ordinary Markov decision process. Unfortunately, the model is far too large to be solved by any known methods. Therefore, an approximate method combining dynamic programming and stochastic simulation in the determination of a set of descriptive parameters is suggested. The parameters are used in the calculation of the multi-component replacement criterion for cows as well as for heifers. The method has been tested by extensive simulations under 100 different conditions concerning prices and average milk yield of the herd. It was concluded that, when the replacement costs (the price of a heifer minus the price of a calf and the carcass value of a cow) are small, the method improves the economic results considerably compared to the usual models, assuming an unlimited supply of heifers. The information concerning heifers, which is provided by the method, makes it relevant even in cases where the replacement costs are large. The basic idea of the study may be relevant in a more general range of problems involving replacement under some constraint.