This paper focuses on the last two stages of genome assembly, namely, scaffolding and gap-filling, and shows that they can be solved as part of a single optimization problem. Our approach is based on modeling genome assembly as a problem of finding a simple path in a specific graph that satisfies as many distance constraints as possible encoding the insert-size information. We formulate it as a mixed-integer linear programming (MILP) problem and apply an optimization solver to find the exact solutions on a benchmark of chloroplasts. We show that the presence of repetitions in the set of unitigs is the main reason for the existence of multiple equivalent solutions that are associated to alternative subpaths. We also describe two sufficient conditions and we design efficient algorithms for identifying these subpaths. Comparisons of the results achieved by our tool with the ones obtained with recent assemblers are presented.