Equitable models for the stochastic ground-holding problem under collaborative decision making

The adoption of collaborative decision making within the ground-delay program rendered obsolete much of the published research on the ground-holding problem as the emphasis was on control of individual flights. We focus on two pertinent static-stochastic models that exercise control on groups of flights instead of individual flights. We show that the first model, developed previous to the collaborative decision-making initiative, is capable of providing the information needed for the assignment of ground holds under the current system; however, the integrality and equity of solutions is not guaranteed. We then prove that by focusing on marginally nondecreasing ground-hold cost functions, solutions to the linear programming relaxation of the first model are guaranteed to be integer and equitable. We also show that the second model, a model with linear costs developed after collaborative decision-making procedures were in place, is a simplified version of the first that offers the advantage of a smaller number of variables at the expense of modeling flexibility. Our computational results show that the size advantage does not translate into significantly faster running times and demonstrate the relevance of the modeling flexibility associated with the first model. These results suggest that implementation of the earlier model is still an attractive option.