Eukaryotic genomes are duplicated from multiple replication origins exactly once per cell cycle. In Saccharomyces cerevisiae, a complex molecular network has been identified that governs the assembly of the replication machinery. Here we develop a mathematical model that links the dynamics of this network to its performance in terms of rate and coherence of origin activation events, number of activated origins, the resulting distribution of replicon sizes and robustness against DNA rereplication. To parameterize the model, we use measured protein expression data and systematically generate kinetic parameter sets by optimizing the coherence of origin firing. While randomly parameterized networks yield unrealistically slow kinetics of replication initiation, networks with optimized parameters account for the experimentally observed distribution of origin firing times. Efficient inhibition of DNA rereplication emerges as a constraint that limits the rate at which replication can be initiated. In addition to the separation between origin licensing and firing, a time delay between the activation of S phase cyclin-dependent kinase (S-Cdk) and the initiation of DNA replication is required for preventing rereplication. Our analysis suggests that distributive multisite phosphorylation of the S-Cdk targets Sld2 and Sld3 can generate both a robust time delay and contribute to switch-like, coherent activation of replication origins. The proposed catalytic function of the complex formed by Dpb11, Sld3 and Sld2 strongly enhances coherence and robustness of origin firing. The model rationalizes how experimentally observed inefficient replication from fewer origins is caused by premature activation of S-Cdk, while premature activity of the S-Cdk targets Sld2 and Sld3 results in DNA rereplication. Thus the model demonstrates how kinetic deregulation of the molecular network governing DNA replication may result in genomic instability.