In emergency response volunteer programs, volunteers in the vicinity of an emergency are alerted via their mobile phones to the scene of the event to perform a specific task. Tasks are usually assigned based on predetermined rules disregarding real-world uncertainties. In this paper, we consider some of these uncertainties and propose an optimization model for the dispatch of volunteers to emergencies, where all task assignments must be done before dispatch. This means that each volunteer must be given a task before knowing whether (s)he is available. The model becomes computationally demanding for large problem instances; therefore, we develop a simple greedy heuristic for the problem and ensure that it can produce high quality solutions by comparing it to the exact model. While the model is for a general emergency, we test it for the case of volunteers responding to out-of-hospital cardiac arrest (OHCA) incidents. We compare the results of the model to the dispatch strategies used in two ongoing volunteer programs in Sweden and in the Netherlands and use simulation to validate the results. The results show that the model most often outperforms the currently used strategies; however, the computational run times, even for the heuristic, are too high to be operationally useful for large problem instances. Thus, it should be possible to improve the outcome using optimization-based task assignments strategies, but a fast solution method is needed for such strategies to be practically useable.