The ground delay program is a mechanism used to decrease the rate of incoming flights into an airport when it is projected that arrival demand into the airport will exceed capacity. In this paper, we present an integer programming model for plannning ground delay programs. The model considers a stochastic capacity profile which is represented by a set of airport capacity scenarios and their probabilities. Both the demand on the airport and the output of the model are represented at an aggregate level in terms of number of flights per unit time. This allows the model to be used in conjunction with arbitrarily complex preprocesses for allocating individual flights to slots. It was specifically designed to be used in the Collaborative Decision Making setting where individual flight assignments result from an iterative process involving both the airlines and traffic flow managers. We show that the linear programming dual of the model can be transformed into a network flow problem. This implies that the integer program can be solved efficiently using linear programming or network flow models.