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. ... Read more

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. ... Read more

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. ... Read more