Petri Net Induced Heuristic Search for Resource Constrained Scheduling
For operations research practitioners, it provides a new exact method for RCPSP that is complementary to MIP, performing better on resource-tight instances.
The paper formulates the Resource-Constrained Project Scheduling Problem as optimal search over a Petri net reachability graph and solves it with A* using a consistent heuristic. On PSPLIB benchmarks, it outperforms strong MIP solvers (SCIP, CBC) in both success rate and solve time.
We formulate the Resource-Constrained Project Scheduling Problem (RCPSP) as optimal search over the reachability graph of a Timed Transition Petri Net with Resources, using relative-delay tokens so that scheduling decisions correspond to transition firings in the induced state space. We solve the resulting problem with $A^*$ guided by a heuristic that combines Critical Path and resource-based lower bounds, and prove that it is consistent under our token-based time semantics. Experiments on the PSPLIB benchmarks show that the approach outperforms strong exact Mixed-Integer Linear Programming (MIP) baselines (SCIP, CBC) in both success rate and solve time. Per-instance analysis shows that heuristic search and MIP degrade along independent axes, resource tightness for $A^*$ and formulation size for MIP, with resource strength mediating which solver benefits from scale.