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.
