The escalating disasters and increasingly complex external environment are forcing humanitarian organizations to continually improve their operations to provide better humanitarian relief. Transformation towards hyperconnected humanitarian supply chains is one of the most promising paths and the Physical Internet could provide a paradigm for this evolution. However, the impact of this shift on the humanitarian supply chain's performance, particularly readiness, has been understudied. To address this issue, a simulation-based assessment of hyperconnected humanitarian supply chains' response readiness is conducted. Different combinations of multiple potentials of the Physical Internet are simulated, and the corresponding effects on relief operations are analyzed. The findings of this work provide greater insight into the transformation towards hyperconnectivity and thus are helpful for decision-makers to design appropriate evolutionary avenues for today's humanitarian supply chains