This paper investigates a service network design problem, which is motivated by the case of freight transportation in a port city. We describe the novel features of this problem, which are based on the possible (but still unexploited) knowledge on the composition of the disaggregated loads in containers and semitrailers entering the port. In this problem, the transportation requests of these loads are highly customized and have different delivery costs. We must determine the paths of vehicles and loads, which result in costs paid by carriers and customers, as well as external costs for the city itself. The resulting network design problem is faced from the holistic viewpoint of a possible mobility manager, which must minimize the overall system costs. We present a mixed integer linear programming model (MILP) for this problem. Since it is very difficult to solve by standard MILP solvers, we present a Tabu Search algorithm exploiting the specific problem features. The computational experiments show to what extent this problem can be tackled by a general purpose mixed-integer programming solver and the Tabu Search algorithm.