Petri Net Induced Heuristic Search for Resource Constrained Scheduling

Abstract

We formulate the Resource-Constrained Project Scheduling Problem (RCPSP) as optimal search over the reachability graph of a Timed Transition Petri Net with Resources, us- ing relative-delay tokens so that scheduling decisions cor- respond 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 se- mantics. 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 heuris- tic 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.