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In this work, the first target is to model and effectively resolve the Arrival Sequencing and Scheduling problem (ASS). The problem is NP-hard and exists in the Air Traffic Control (ATC) for a long time. It has been the hottest topic in transportation research due to the constantly increasing aviation traffic volume around the world. This paper attempts to design a mathematical integer linear model, with the constraints of limited time windows. We begin by modeling the (ASS) problem by a quadratic integer program and propose a change of variables to linearize the problem, i.e. transforming the quadratic constraints to linear constraints. The second target is to resolve the model by an exact method based on the algorithm of branch and bound. Numerical simulations are applied to real data to show the effectiveness of our new formulation and our approach. They are presented at the end of this article.