Revenue Maximization for Seaport Terminal Operations Considering Multimodal Cargo Flows

We study the optimal pricing problem for operations at a seaport terminal within a multimodal transport network, where the terminal operator sets differentiated prices for processing cargoes arriving via and transferred to various modes of transport. The problem incorporates two critical features: (i) the influence of port congestion on cargo suppliers’ terminal selection and (ii) the hierarchical choice structure that predicts how cargo suppliers select transport modes and routes for their cargoes. To capture these features, we formulate the problem as a nonconvex, nonlinear program involving a nested logit choice model and an equilibrium constraint reflecting the congestion effect, which is challenging to solve or analyze. To address this difficulty, we apply a change of variables to reformulate the price-based model as a flow-based model, where cargo flows, rather than prices, are the decision variables, thereby making the model more amenable to analysis. By exploiting the structure of the flow-based model, we derive an optimality equation whose dimension scales only with the number of origin-destination (O/D) pairs, which effectively reduces the computational complexity by avoiding directly handling the numerous variables associated with transport routes. This approach not only applies to seaport revenue management problems that often involve multiple transport modes and a substantial number of routes, but also contributes a structure-exploiting method for addressing a broader class of nonlinear programs involving equilibrium constraints and customer choice models. We show that, for each O/D pair, the optimal mode-dependent prices decompose into a component common across modes plus a mode-specific adjustment. We also establish analytical bounds on the revenue loss induced by misspecifying cargo suppliers’ choice structure. We evaluate the performance of the algorithm by comparing it with several widely used benchmark methods through numerical analysis. Our findings indicate that our algorithm outperforms the benchmark methods in both revenue maximization and runtime. Moreover, we find that accurately modeling the choice structure has a larger impact on revenue than explicitly modeling congestion.

History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis.

Funding: X. Wang received financial support from the National Science Foundation [Award CMMI-2127779].

Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1238) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2025.1238). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.