Dynamic Relief Provision Planning for En Route Refugees: Modeling Probabilistic Movements Using Migration Pull Drivers

Forced displacement crises have become a pressing humanitarian concern. Refugee movements expose individuals to dire living conditions with severe inaccessibility to essential resources. Humanitarian organizations play a vital role in alleviating these hardships through relief aid interventions. This study aims to optimize the fulfillment of recurring needs for geographically dispersed refugee groups en route to safe destinations. Here, capacitated mobile facilities are tasked with delivering relief aid to refugee groups periodically to ensure equitable service frequency. We formulate the problem as a Markov decision process with multinomial state-transition distributions, shaped by external migration pull factors such as safety conditions, road accessibility, and spatial proximity. The objective is to minimize the relocation and replenishment costs of mobile facilities, along with the deprivation costs faced by underserved refugees. We develop an approximate dynamic programming algorithm featuring a novel policy replication routine. To complement this offline method, we introduce a state-dependent variable threshold policy that enables high-quality, real-time relief provision. Using instances inspired by the Syrian refugee crisis, our results demonstrate the substantial value of stochastic modeling, yielding a 25% reduction in expected total costs compared to deterministic baselines and up to 12% savings through coordinated planning among humanitarian actors. The proposed methods remain effective under dispersed and cohesive refugee group dynamics and multi-destination migration scenarios. Furthermore, we uncover high-frequency traversal and service hotspots along migration paths to provide tactical insights for parameter calibration and resource prepositioning. Collectively, our findings offer practical insights for managing ongoing and future refugee migration crises.