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In tramp shipping, ships operate much like taxies, following the available demand. This contrasts liner shipping where vessels operate more like busses on a fixed route network according to a published timetable. Tramp operators can enter into long term contracts and thereby determine some of their demand in advance. However, the detailed requirements of these contract cargoes can be subject to ongoing changes, eg the destination port can be altered. For tramp operators, a main concern is therefore the efficient and continuous planning of routes and schedules for the individual ships. Due to mergers, pooling, and collaboration efforts between shipping companies, the fleet sizes have grown to a point where manual planning is no longer adequate in a market with tough competition and low freight rates. This thesis therefore aims at developing new mathematical models and solution methods for tramp ship routing and scheduling problems. This is done in the context of Operations Research, a research field that has achieved great success within optimisation-based planning for vehicle routing problems and in many other areas. The first part of this thesis contains a comprehensive introduction to tramp ship routing and scheduling. This includes modelling approaches, solution methods as well as an analysis of the current status and future direction of research within tramp ship routing and scheduling. We argue that rather than developing new solution methods for the basic routing and scheduling problem, focus should now be on extending this basic problem to include additional complexities and develop suitable solution methods for those …