In intermodal transport multiple types of vehicles are used to transport containers. If the routes of the vehicles are known, then the container allocation can be optimized. This problem can be modelled as an integral multi-commodity min cost flow problem on a time-space graph. This model has an arc-based and path-based form. In this thesis, the path-based form is derived from the arc-based form. Some of the methods that can be used to solve this model are column generation, Lagrangian relaxation and the repeated cheapest path heuristic.
If the routes of the vehicles are not known, then we also need to create routes for the vehicles. The problem of routing vehicles and scheduling containers can be modelled as a multi-commodity network design problem on a time-space graph. Variable reductions, cutting planes and other additional constraints are looked into to make the problem easier to solve. Additions to the model are researched that can make the model more suitable for use in practice. Additionally, ILP based solution methods are developed. Finally, some of these
reductions, extensions and solution methods are implemented and reviewed.

This thesis addresses synchromodal planning at operational level from the perspective of a logistics service provider. The existing infrastructure and the transportation activities are studied and modeled as an optimization problem with simultaneous vehicle routing and container-to-mode assignment. A special characteristic of this problem is the uncertain data. In other words, it is assumed that the release times of the containers belong to an uncertainty interval, and no further statistical information is available. The problem is then classified according to an extensive framework previously developed within the project. An extensive body of literature is reviewed to identify current modeling approaches and their theoretical and practical limitations. This literature study shows that, although discrete time models have been intensively investigated, there are few studies which propose continuous modeling of time. The container routing problem is modeled as a mixed integer program with explicit time variables and lateness penalties. A robust formulation is then proposed to eliminate the uncertain parameters from the objective function and constraints. By solving the new model exactly, with the aid of an optimization solver, robust solutions are obtained corresponding to transportation plans which remain feasible for any realization of the release times within the pre-specified uncertainty interval. In order to introduce some flexibility in the transportation plan, the continuous time variables are modeled as affine functions of the uncertain parameters. The resulting two-stage decision model is tested for a small-sized instance in both situations, with high and low lateness penalties. The computational results show that the adjustable robust model yields on the one hand, route-dependent adjusted solutions for the case of penalized lateness, and on the other hand, a direct improvement of the objective function for the case of tolerated lateness. The results suggest that the adjustable robust optimization framework has sufficient potential to model the synchromodal container routing problem. This thesis concludes with addressing some of the limitations of the proposed model and indicating concrete approaches for countering them.

The goal of this thesis is to provide a method to obtain a User Equilibrium (UE) in a synchromodal transportation network in which we transport containers for multiple customers.
We use the Space Time Network (STN), in which the travel time of modalities is fixed and independent of the occupancy of the network.
We define the User Equilibrium solution as the solution wherein each customer can travel via their cheapest paths possible, and no customer is harmed by the route choice of other customers. We define the System Optimal (SO) solution as the solution in which the total costs of the network are minimized.
We expand the goal of finding a UE on the STN to finding a solution where the solution is both SO as well as UE.
The solving method we developed in this thesis, consists of finding SO solutions by solving the Minimum Cost Multi-Commodity Flow (MCMCF) problem on the STN to find an SO solution, and create tolls schemes to create a UE solution, while maintaining the SO solution.
We investigate several types of tolls in order to obtain sufficient both SO and UE solutions.

Synchromodal freight transport is introduced as intermodal transport, so container transport that uses several transportation vehicles, with an increased focus on a-modal booking, cooperation and real-time flexibility.

It is confirmed that general synchromodal network planning methods are rare or non-existent at the operational level. An extensive framework is developed that describes characteristics of different mathematical synchromodal optimisation problems on the tactical-operational levels.

Three different problems are defined using this framework. Solution methods for these three problems are developed in this thesis, with a focus on low computation times so as to facilitate decision-support and real-time flexibility, and a focus on generality so as to make the methods applicable throughout different organisation structures.

In the first problem, it is assumed that the transportation vehicles have fixed time tables and one only has to decide on a container-to-mode assignment, so by what modality-paths all containers reach their destination against minimal total cost. The containers have release times and deadlines. A model that also allows soft due dates is developed. Moreover, the option of using trucks or other ‘infinite resources’ to help fulfil requests is added. With appropriate graph reductions, this problem can be solved to optimality in little time by solving
the minimum cost multi-commodity flow problem on an appropriate space-time network.

In the second problem, the goal is the same but almost any element can be stochastic: for instance, travel times and container release times could be given a discrete probability distribution rather than a fixed value. Rigorous definitions are formulated to capture the generalities in this stochasticity. Multistage stochastic optimisation and Markov Decision Processes are illustrated, but advised against for their computing time: instead, Expected Future Iteration
and 70%-Pessimistic Future Iteration are developed and shown to yield near-optimal results in a small amount of time in the simulated environment.

In the final problem, there are no stochastic elements, but the decision-maker is given control over the vehicle time tables in addition to the control over container-to-mode assignments. This problem is argued to be a departure from classical optimisation problems, but shown to still be strongly NP-hard. An integer linear program is developed to solve the problem, but
the results show that it scales too poorly to solve problems of ‘real life size’ in an appropriate amount of time for decision support. The Greedy Gain heuristic and Compatibility Clustering heuristic are developed: they solve much more limited sub-problems with the ILP, but unfortunately, even these sub-problems require too much computational effort at the wished instance size.

A number of topics for future research are formulated, giving concrete advice on how to solve the second problem more robustly and how to solve the third problem more quickly.

In this report we present an interactive multi-objective optimization tool that was developed as part of this graduation project. This appliance is meant to be used as a decision support tool for transportation planners working on a synchromodal transportation network on the container-to-mode assignment, where different attributes are considered important. The tool offers the planner a range of solutions according to her/his preferences, and offers the opportunity to seek for new ones if the planner is not satisfied with the solutions found so far. Before presenting the tool, a framework for synchromodal transportation problems is introduced (which was developed as part of a collaborative work with two other students and two supervisors). Then an analysis is done on mathematical modeling approaches of container-to-mode assignment, with special emphasis on computational time, given the time-sensitivity of this problem on synchromodal transport networks. From this analysis a model is chosen on which to built upon the multi-objective optimization tool, for which a thorough analysis on the attributes to be considered is carried out.