When a large oil or gas field is produced, several reservoirs often share the same processing facility. This facility is typically capable of processing only a limited amount of oil, gas and water per unit of time. In the present paper only single phase production, e.g., oil production, is considered. In order to satisfy the processing limitations, the production needs to be choked. That is, for each reservoir the production is scaled down by suitable choke factors between zero and one, chosen so that the total production does not exceed the processing capacity. Huseby & Haavardsson (2008) introduced the concept of a production strategy, a vector valued function defined for all points of time t ≥ 0 representing the choke factors applied to the reservoirs at time t. As long as the total potential production rate is greater than the processing capacity, the choke factors should be chosen so that the processing capacity is fully utilized. When the production reaches a state where this is not possible, the production should be left unchoked. A production strategy satisfying these constraints is said to be admissible. Huseby & Haavardsson (2008) developed a general framework for optimizing production strategies with respect to various types of objective functions. In the present paper we present a parametric class of admissible production strategies. Using the framework of Huseby & Haavardsson (2008) it can be shown that under mild restrictions on the objective function an optimal strategy can be found within this class. The number of parameters needed to span the class is bounded by the number of reservoirs. Thus, an optimal strategy within this class can be found using a standard numerical optimization algorithm. This makes it possible to handle complex, high-dimensional cases. Furthermore, uncertainty may be included, enabling robustness and sensitivity analysis.