Explaining Time-Table-Edge-Finding Propagation for the Cumulative
  Resource Constraint
  Cumulative resource constraints can model scarce resources in scheduling
problems or a dimension in packing and cutting problems. In order to
efficiently solve such problems with a constraint programming solver, it is
important to have strong and fast propagators for cumulative resource
constraints. One such propagator is the recently developed
time-table-edge-finding propagator, which considers the current resource
profile during the edge-finding propagation. Recently, lazy clause generation
solvers, i.e. constraint programming solvers incorporating nogood learning,
have proved to be excellent at solving scheduling and cutting problems. For
such solvers, concise and accurate explanations of the reasons for propagation
are essential for strong nogood learning. In this paper, we develop the first
explaining version of time-table-edge-finding propagation and show preliminary
results on resource-constrained project scheduling problems from various
standard benchmark suites. On the standard benchmark suite PSPLib, we were able
to close one open instance and to improve the lower bound of about 60% of the
remaining open instances. Moreover, 6 of those instances were closed.
