Given today s limited capacity at airports, and the continuous increase in air transportation, the need for new ways to handle airport logistics will soon be needed. The task of managing arriving and departing flights is complex, and is today solved by several air traffic managers at each airport. While these managers operate well within their zone, the overall performance with respect to capacity and punctuality would benefit from viewing the airport as a whole. In addition, this may increase accuracy in predicting take-off times, allowing more reliable information for the arrival of flights, and reduce the environmental impact of air traffic. This thesis provides insight into how the network simplex algorithm can be used to find a conflict free solution between flights. The focus lies on mitigating the overall delay at airports and on reducing the taxi time of each individual flight while at the same time complying with safety regulations on the runway. This research also provides a basis for future integration with other airport operations such as runway sequencing and gate allocation. A data set from Stockholm Arlanda Airport was used in order to test the algorithms.