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Parallel computation is fundamental to satisfy the performance requirements of advanced safety-critical systems. OpenMP is a good candidate to exploit the performance opportunities of parallel platforms. However, safety-critical systems are often based on static allocation strategies, whereas current OpenMP implementations are based on dynamic schedulers. This paper proposes two OpenMP-compliant static allocation approaches: an optimal but costly approach based on an ILP formulation, and a sub-optimal but tractable approach that computes a worst-case makespan bound close to the optimal one.This work is funded by the EU projects P-SOCRATES (FP7-ICT-2013-10) and HERCULES (H2020/ICT/2015/688860), and the Spanish Ministry of Science and Innovation under contract TIN2015-65316-P.Peer ReviewedPostprint (author's final draft