Service pricing in resilient multimodal transportation networks

We study a fourth-party logistics platform that aims to build a resilient multimodal transportation network. The platform does not operate its own physical assets but constructs the network by renting transportation resources from third-party logistics carriers and making pricing and capacity planning decisions. To address this problem, we develop a scenario-based stochastic programming model embedded with robust optimization, which seeks to maximize the platform’s total profit under both demand and supply uncertainties. The model captures two key sources of uncertainty: (i) demand is modeled as a price-dependent function, where uncertainty is introduced via a demand scaled factor that is bounded by an uncertainty set; (ii) the remaining capacity on each transportation arc varies across a set of disruption scenarios, reflecting supply-side risks. To solve this model, we propose a customized column-and-constraint generation algorithm that addresses the violation of the relatively complete recourse assumption by integrating feasibility and optimality subproblems. To further enhance scalability for large instances, we develop a CPU-GPU hybrid heuristic that accelerates second-stage evaluations through parallelization. We conduct a series of computational experiments based on real data from southeastern China to evaluate model performance and derive managerial insights. Results show that the platform should pay attention to the impact of OD-level demand heterogeneity on profit. Ignoring capacity disruptions may lead to overly optimistic and fragile solutions, highlighting the importance of explicitly modeling disruption scenarios. Moreover, results provides guidelines for identifying key nodes that are critical to mitigating the impact of disruptions.