  This study focuses on relay transport carriers (RTCs) that contract with hub
providers to lease hub capacity and employ relay transportation via hubs. It
enables long-haul freight shipments to be transported by multiple short-haul
drivers commuting between fixed-base hubs, promoting a driver-friendly
approach. Inspired by Physical Internet, our paper addresses the multi-period
capacity planning of logistic hubs within relay networks, accounting for
uncertainty in demand and travel times. We model the problem as a two-stage
stochastic optimization to determine the dynamic logistic hub throughput
capacities for each planning period, ensuring the fulfillment of logistic
demand while simultaneously minimizing both hub and transportation costs. This
optimization problem falls within the NP-hard complexity class. To alleviate
the inherent challenges in solving this problem, we employ a scenario reduction
algorithm based on the fast forward selection (FFS) method to reduce
computational effort while preserving approximation quality. Experiments with
an automotive-delivery RTC in the Southeastern US demonstrate that our capacity
planning model enables RTCs to proactively respond to dynamic circumstances,
curtail avoidable expenditures, and enhance overall logistical efficiency.
