Multi-resolution modelling and Pseudo-Boolean encoding of the SNAP scheduling problem

We describe a Pseudo-Boolean encoding of a time-discretized model of the large and complex scheduling problem coming from the SNAP system. This problem involves the precise scheduling (with 1-minute resolution) of flight missions with multiple requirements of variable duration over large (several weeks at least) planning horizons. The problem is actually a combination of scheduling and planning, where the scheduling of some tasks in the right order might enable resources to perform additional tasks, thus improving the overall quality of the schedule. In order to maintain the scalability of our approach to large planning horizons, we introduce a time discretization of the planning horizon that enable us to solve the problem at variable resolutions. The encoding is fully integrated into the SNAP system and uses the OPARIS (CIRL) Pseudo-Boolean search engine to solve the resulting Pseudo-Boolean formula.