DNA replication is a complex and remarkably robust process: despite its inherent uncertainty, manifested through stochastic replication timing at a single-cell level, multiple control mechanisms ensure its accurate and timely completion across a population. Disruptions in these mechanisms lead to DNA re-replication, closely connected to genomic instability and oncogenesis. Here, we present a stochastic hybrid model of DNA re-replication that accurately portrays the interplay between discrete dynamics, continuous dynamics and uncertainty. Using experimental data on the fission yeast genome, model simulations show how different regions respond to re-replication and permit insight into the key mechanisms affecting re-replication dynamics. Simulated and experimental population-level profiles exhibit a good correlation along the genome, robust to model parameters, validating our approach. At a single-cell level, copy numbers of individual loci are affected by intrinsic properties of each locus,  in cis  effects from adjoining loci and  in trans  effects from distant loci.  In silico  analysis and single-cell imaging reveal that cell-to-cell heterogeneity is inherent in re-replication and can lead to genome plasticity and a plethora of genotypic variations.