This project is concerned with making the most of available resources given limited availability and uncertainty about consumption. The project considers planning problems with 'preferences': soft constraints that are desirable in a solution, but not essential. These preferences are each weighted according to their importance; the task is then to find the best quality plan according to the relative importance of preferences, whilst also achieving any hard constraints. Later work in the project considers solving these problems in the presence of uncertainty about how much resource each activity will consume. This introduces a challenging trade-off between adherence to safety constraints giving certainty in plan completion, and making the maximum use of resources in order to achieve the best possible combination of preferences.