This paper deals with the solution of multimode-multiproduct assignment models which are used to analyse freight transportation networks at regional and national levels. We evaluate the efficiency of some variants of the linear approximation algorithm, where at each iteration and for each product, a few extremal solutions are generated by the linear approximation approach, and then, an approximate search is performed on the convex hull of the extremal solutions and the current solution. The variant where two extremal solutions are generated, and the approximate search consists of two Partan iterations, appears to be the most efficient. Finally, this paper points out some costly computations that may be avoided, in order to reduce the total execution times.
