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In this study we present a deterministic model based on a linear programming approach for optimizing the route assignment in a trajectory-based Air Traffic Management (ATM) environment. This study is essentially intended to reduce the airspace congestion through an appropriate route assignment. The latter one can be easily seen as a multi-period (dynamic) problem. Indeed, the time dimension is an essential ingredient to consider when constructing flight plans for a large number of flights and evaluating the number of potential en-route conflicts. This dynamic problem can be transformed into a static one by using standard technique of time-expanding the underlying network. We propose here a model to consider the airspace congestion in a finer way: we consider the number of aircraft involved in potential en-route conflicts rather than the number of aircraft in a sector, sometimes implicitly understood as en-route capacities in ATM. In other words, the routing computing which is the choice of the most appropriate routes with respect to congestion avoidance (in terms of the number of potential en-route conflicts) and economical considerations are our main concern.