• Exact branch-and-cut algorithm using fragments. • Algorithm is easily configured to solve flexible or fix return problems. • First use of fragments in a problem where requests must be served multiple time. • Significantly outperforms existing exact algorithms for the problem. We present a new fragment-based model for two versions of the Skip Pickup and Delivery Problem (SPDP). Our new algorithm outperforms the state-of-the-art for these problems by at least two orders of magnitude. In these pa