On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations

For variants of the single-mode resource-constrained project scheduling problem, state-of-the-art exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming and Boolean Satisfiability Solving. In our paper, we propose new exact approaches extending the above principles to the multi-mode RCPSP (MRCPSP) with generalized precedence relations (GPRs). More precisely, we implemented two constraint handlers cumulativemm and gprecedencemm for the optimization framework SCIP. With the latter, one can model renewable resource constraints and GPRs in the context of multi-mode activities, respectively. Moreover, they integrate domain propagation and explanation generation techniques for the above problem characteristics. We formulate three SCIP-models for the MRCPSP with GPRs, two without and one with our constraint handler gprecedencemm. Our computational results on instances from the literature with 30, 50 and 100 activities show that the addition of this constraint handler significantly strengthens the SCIP-model. Moreover, we outperform the state-of-the-art exact approach on instances with 50 activities when imposing time limits of 27 s. In addition, we close (find the optimal solution and prove its optimality for) 289 open instances and improve the best known makespan for 271 instances from the literature.