It is well known that the magnitude and the impact on schedule quality of uncertainty in problem data both increase when the integration of scheduling decisions takes place. This paper aims at comparing the standard robust optimization and the recoverable robust optimization frameworks to tackle scenario-based uncertainty in integrated production and distribution scheduling. While the standard robust optimization aims at providing an integrated baseline schedule that optimizes a performance criterion for the worst scenario, the recoverable robustness framework adds a repairing/recovering component, which is able to react to the realized scenario by modifying in a limited way the issued baseline schedule. Hence, the recoverable robustness framework has two merits: it is more realistic, as such repairing elements are often present in practice, and it is able in theory to reach better worst-case performances on the scenario set. However, the question remains whether under limited CPU time, recoverable robustness algorithms are able to actually reach better performance than robust algorithms for reasonable problem instance size. This paper proposes new MILP models and heuristics for a recoverable robust optimization framework based on the concept of groups of permutable jobs and carries out such a comparison on a one-machine production facility coupled with a single vehicle distribution system. For this problem, the experimental results exhibit conditions under which a recoverable robust approach is likely to yield better results than the standard robust approach.