On combining maximum entropy trip matrix estimation with user optimal assignment

This note shows how the maximum entropy trip matrix estimation procedure incorporated in ME2 as proposed by Willumsen (Van Zuylen and Willumsen, 1980) can be combined with a user optimal assignment model such as SATURN (Van Vliet, 1982) into a single mathematical problem. The resulting problem has the form of a bilevel programming problem similar to matrix estimation methods proposed by Nguyen (1981). The mathematical framework for the user optimal assignment problem is summarized, followed by a description of the maximum entropy trip matrix estimation procedure proposed by Willumsen. The two models are then combined into a single problem and a discussion follows on solution procedures.