Strong Bounds for Resource Constrained Project Scheduling: Preprocessing and Cutting Planes

Janniele A. S. Araujo; Haroldo Gambini Santos; Bernard Gendron; Sanjay Dominik Jena; Samuel S. Brito; Danilo S. Souzaa

doi:10.1016/j.cor.2019.104782

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arXiv · 1909.02737

Strong Bounds for Resource Constrained Project Scheduling: Preprocessing and Cutting Planes

Janniele A. S. Araujo·Haroldo Gambini Santos·Bernard Gendron·Sanjay Dominik Jena·Samuel S. Brito·Danilo S. Souzaa

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Abstract

Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known 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.

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Janniele A. S. Araujo, Haroldo Gambini Santos, Bernard Gendron, Sanjay Dominik Jena, Samuel S. Brito, Danilo S. Souzaa. 2019-09-06. Strong Bounds for Resource Constrained Project Scheduling: Preprocessing and Cutting Planes. https://doi.org/10.1016/j.cor.2019.104782

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