Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with SMT

The Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP) is a generalization of the well known Resource-Constrained Project Scheduling Problem (RCPSP). The most common exact approaches for solving this problem are based on branch-and-bound algorithms, mixed integer linear programming and Boolean satisfiability (SAT). In this paper, we present a new exact approach for solving this problem, using Satisfiability Modulo Theories (SMT). We provide two encodings into SMT and several reformulation and preprocessing techniques. The optimization algorithm that we propose uses an SMT solver as an oracle, and depending on its answer is able to update the encoding for the next optimization step. We report extensive performance experiments showing the utility of the proposed techniques and the good performance of our approach that allows us to close several open instances.