A multi-stage stochastic programming model for relief distribution networks considering road collapse

To address the challenges of uncertain road capacity caused by collapses, reliance on single-mode transportation, inefficient relief allocation, and low algorithmic efficiency in existing earthquake relief scheduling, this study develops a multi-stage stochastic programming model for emergency relief distribution. The model incorporates multiple phases of earthquake emergency response, ten scenarios of road-capacity variations induced by collapses, and a cooperative transportation scheme involving four vehicle types. To solve the model efficiently, the Progressive Hedging Algorithm (PHA) is employed, enhanced with adaptive rules that dynamically adjust penalty parameters to improve convergence performance. The comprehensive disaster index is used to predict relief demand at affected areas, and the total expected cost—minimizing the sum of rental cost, transportation cost, handling cost and penalty cost—is calculated while satisfying demand. Finally, based on actual disaster data from the 2008 Wenchuan Earthquake in China, the study computes the quantities of each vehicle type used and the amounts of each relief type allocated under each scenario at minimal cost. Sensitivity analyses are conducted on initial inventories at regional distribution center, road capacities, and the number of helicopters to validate the model’s effectiveness. This research provides a typical multi-stage stochastic programming network model and methodology for emergency relief scheduling in complex earthquake disaster scenarios.