Optimizing Liner Shipping Fleet Repositioning Plans

With the incredible growth of containerization over the past half century, shipping lines and ports are facing increasing challenges in ensuring that containers arrive at their destinations on time and on budget. This dissertation addresses several critical problems to the operations of shipping lines and ports, and provides algorithms and mathematical models for use by shipping lines and port authorities for decision support. One of these problems is the repositioning of container ships in a liner shipping network in order to adjust the network to seasonal shifts in demand or changes in the world economy. We provide the first problem description and mathematical model of repositioning and define the liner shipping fleet repositioning problem (LSFRP). The LSFRP is characterized by chains of interacting activities with a multi-commodity flow over paths defined by the activities chosen. We first model the problem without cargo flows with a variety of well-known optimization techniques, as well as using a novel method called linear temporal optimization planning that combines linear programming with partial-order planning in a branch-and-bound framework. We then model the LSFRP with cargo flows, using several different mathematical models as well as two heuristic approaches. We evaluate our techniques on a real-world dataset that includes a scenario from our industrial collaborator. We show that our approaches scale to the size of problems faced by industry, and are also able to improve the profit on the reference scenario by over US$14 million. This dissertation also addresses the topic of inter-terminal transportation (ITT), which involves minimizing the delay experienced by containers being transported between terminals in a port under varying infrastructure configurations and material handling equipment properties. Minimizing the delay of ITT is an important problem in the strategic planning of new ports and port expansions, and one that has not yet been addressed in an optimization based approach. We provide the first mathematical model of ITT and show how the model can be used to provide critical information to port authorities on two real ports, the port of Hamburg, Germany, and the Maasvlakte area of the port of Rotterdam, Netherlands. Finally, this thesis gives a polynomial time algorithm for an open problem from the container stowage literature, the capacitated k-shift problem with a fixed number of stacks and stack heights, providing an answer to a 13 year old theoretical question in the container stowage domain.