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Strong bounds for resource constrained project scheduling: preprocessing and cutting planes. (English) Zbl 1458.90247
Summary: Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known \(\mathcal{NP}\)-hard combinatorial optimization problems. A feasible RCPSP solution consists of a time-ordered schedule of jobs with corresponding execution modes, respecting precedence and resources constraints. In this paper, we propose a cutting plane algorithm to separate five different cut families, as well as a new preprocessing routine to strengthen resource-related constraints. New lifted versions of the well-known precedence and cover inequalities are employed. At each iteration, a dense conflict graph is built considering feasibility and optimality conditions to separate cliques, odd-holes and strengthened Chvátal-Gomory cuts. The proposed strategies considerably improve the linear relaxation bounds, allowing a state-of-the-art mixed-integer linear programming solver to find provably optimal solutions for 754 previously open instances of different variants of the RCPSPs, which was not possible using the original linear programming formulations.

90B35 Deterministic scheduling theory in operations research
90C11 Mixed integer programming
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