This paper is aimed to develop the optimization model of time slot utilization for both runway and apron gate of airport system. The model considers the objectives of airline company to minimize flight-taxiing-time and waiting-time for both landing and take-off. The optimization makes use of Network Representation (NR) in the form of two bipartite networks in order to transform the problem of runway and apron gate assignment into the network flow problem. Maximum Matching and Minimum Cost Flow on NR are the core of the model. An illustrative example is presented. The result shows that the model could increase both runway and apron gate capacities to as close as their theoretical capacities. Compared to the common practice which concerns only; the nearest available runway slot time, behind the scheduled time, and the nearest location of available gates to serve the flight, the model could reduce the total taxiing and waiting time.