Effects of limits in milking capacity, housing capacity, or fat quota on economic optimization of dry period lengths.

The economically optimal dry period length (DPL) of dairy cows remains a topic of interest. Increasing daily milk production and improved management of the transition period require frequent evaluation of the optimal DPL. The economically optimal DPL also depends on the most limiting farm resource such as milking capacity, housing capacity, or fat quota. Therefore, the objective of this study was to determine economically optimal DPL under farm constraints on milking capacity, housing capacity, and fat quota given variations in 12 input factor levels. We developed a deterministic whole herd simulation model, including a nonlinear optimizer of the DPL in the first 3 parities. The model included estimates of milk, fat, and protein yield deviations in the subsequent parity and hazard ratios of culling risk and pregnancy rates as functions of the DPL in the current parity. The DPL could vary between 20 and 90 d with step size of 1 d. In addition to a one-factor-at-a-time analysis, we used a definitive screening design and a space-filling design with Latin hypercube sampling to determine important linear and curvature effects of input factors and their interactions. Results indicated that the economically optimal DPL were typically between 35 and 50 d under a large variation in input factor levels. The opportunity costs of equal DPL in all parities were small compared with optimal policies where the DPL were allowed to vary between parities. The DPL under the parlor constraint were generally less than 5 d longer than the optimal DPL under the housing constraint. The optimal DPL under the quota constraint were between those under the parlor and housing constraints. Opportunity costs compared with 50 d dry were often small, but in some cases large. A formal global sensitivity analysis revealed important interactions of input factors that were not discovered with one-factor-at-a-time analyses. In conclusion, economically optimal DPL were often shorter than typically are recommended. Adding uncertainty about the date of calving at the date of dry-off might extend these optimal DPL by some days depending on the risk attitude of the decision maker.