Propagation Of Idle Times Costs For Fixed Job Scheduling

We present a new global constraint to propagate idle times costs for the Fixed Job Scheduling (FJS) problem, in particular to minimize their variance so as to optimize the robustness of solutions w.r.t. schedule deviations. The propagation of this constraint is based on the computation of the shortest path in the compatibility directed acyclic graph of each resource to obtain an exact lower bound. It ensures Bound Consistency on the resource cost in polynomial time, as well as the filtering of the resource variables associated with compatible tasks.We show on tailored FJS problems and real instances of the airport Gate Allocation Problem (a variant of the FJS problem) that this new constraint provides significant improvements in terms of number of backtracks and computation time, up to orders of magnitude in some cases.