Major airports are suffering from congestion problems. Air traffic demand has been increasing rapidly while airport and sector capacities have been stagnating, causing delays. These delays result in significant losses, depending on fuel cost, maintenance, and the service-hour costs for fleet and crew. To optimally control the flow of air traffic, we develop a model that considers different management policies: rerouting, air and ground holding, and cancellation. We use a nonlinear cost function that depends on the delay duration and the aircraft’s type. This model also tries to assign delays between flights fairly. Our numerical experiments reveal that modeling delay costs as a function of the delay duration and aircraft model type help exploring a more extensive set of strategies and avoid possible flight rerouting. It also reduces the total delay cost in most cases compared to the fixed delay cost case. Our results revealed that with the consideration of aircraft model type, more delays are assigned to small aircraft, and fewer delays are assigned to heavy aircraft delay.