CPU-GPU solution for bus-based freight scheduling under uncertainty

Freight service based on urban–rural bus systems is an emerging logistics model, advocated for its ability to simultaneously improve the profitability of the passenger system and reduce freight costs in rural areas. However, a key challenge for this model is the long-term, strategic decision on bus schedules for transporting freight, given the high degree of uncertainty in short-term freight demand. To tackle this challenge, we propose a two-stage stochastic programming model that minimizes the total expected operational cost by balancing the strategic, first-stage schedule selection against the operational, second-stage order assignments across a large set of stochastic scenarios. The model is solved by a novel two-layer CPU-GPU based algorithm. The outer-layer employs a tabu search to explore strategic-level schedule selections, while the inner-layer utilizes a GPU-accelerated adaptive large neighborhood search to resolve the freight order assignments at the operational-level. This CPU-GPU heterogeneous architecture overcomes the prohibitive computational burden inherent in large-scale scenario-based optimization. The framework demonstrates exceptional scalability, achieving speedups of 26.5, 50.7, 166.5, and 246.1 times over the CPU version on four increasingly large instance groups, reducing computational times from hours to minutes or even seconds. Further sensitivity analysis is conducted to examine the impacts of freight demand volatility, the fixed operational cost structure, and policies for improving the order fulfillment rate. These analyses provide actionable managerial insights for designing robust and cost-effective freight scheduling plans under uncertainty.