In this Master thesis we study decision analysis, in which time on a quantitative level is an aspect. This study has, in addition to the studies of our Dat5 work, resulted in a series of requirements for frameworks modelling decision problems involving time, DPITs. We present a framework for modelling and solving DPITs, which fulfills all of these requirements.
The framework, influence diagrams involving time, IDITs, was originally proposed in ~\cite{broe03}. In this thesis it is extended to handle additional aspects of time, amongst these are local utility functions realized later than the end-time of the last decision. Furthermore, we devise a method for solving IDITs with respect to finding an optimal strategy. We solve an IDIT by resolving all asymmetries introduced by time. This leads to a number of symmetric sub-problems, which we solve using a method based on strong junction trees with lazy propagation.
We illustrate the solution method using two examples in order to demonstrate how the framework is used. Furthermore, we discuss the benefits and drawbacks of having one framework handling all issues of time as opposed to multiple smaller frameworks.