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Transportation problems, in terms of both passenger and freight applications, are increasingly being addressed with inter-modal solutions. This chapter discusses the problem of computing optimum paths on a network with many modes of transport and time-varying link costs and travel times, accounting for the fixed schedule modes and mode-switching delays. An efficient algorithm is introduced that computes optimum path trees from all nodes and possible discrete departure times, while accounting for travel and transfer delays, as well as differences in perceived costs associated with specific modes and transfers. The algorithm, called the time-dependent inter-modal minimum cost path (TDIMCP) algorithm, is extended to set the necessary framework for solving the problem of inter-modal routing of hazardous materials, taking into consideration both risk and cost at the transfer points and travel links. Travel and transfer risk associated with hazmat routing are incorporated into the cost calculation of the TDIMCP problem, considering both the likelihood of an incident and the consequences of that incident. The inter-modal hazmat routing algorithm is then applied to a series of scenarios on a test network to illustrate the behavior of the algorithm

This paper introduces a Variational Inequality (VI) formulation for the time-dependent combined mode split and traffic assignment problem. Travel costs are represented by generalized cost functions and mode choices are deterministically obtained based on assignment to intermodal least cost paths without accounting for possible randomness in travelers’ choices. The intermodal user equilibrium (IUE) is estimated using an inner approximation (IA) algorithm that results in a nonlinear program with linear constraints. The algorithm converges assuming continuous and monotonic path travel cost functions. The paths on multimodal networks are computed with an intermodal optimum path algorithm; a cell transmission-based simulator, enhanced to account for both automobile and transit vehicles, is used to estimate the path travel costs. A heuristic search approach is proposed and implemented in the VISTA simulation-based framework. Computational results are presented on example networks to test convergence and equilibrium.