Intermodal Cargo-Container Joint Flow Equilibrium and Pricing

The coastal intermodal cargo-container joint supply chain is a complicated system with several stakeholders and a few challenging decision-making concerns, such as the laden container acceptance and routing problem, the empty container relocation problem, and the water transportation services pricing problem. Motivated by the abovementioned background, this paper investigates a combined cargo-container joint flow equilibrium and pricing problem. We demonstrate the existence of a special flow equilibrium in which empty container flows that are derived from the non-empty container flows exist and each waterway link has a capacity constraint. Meanwhile, a mathematical analysis is presented to define a liner company’s price setting behavior. The abovementioned behavior ensures that the liner company maximizes its own profit while reasonably allocating empty container relocation costs to different service orders. Finally, we use a modified active set algorithm to offer a local optimal pricing decision of the liner company while ensuring that the cargo-container joint flow satisfies the equilibrium state we defined. Overall, the proposed model and algorithm provide effective support to liner companies in their daily operations in coastal areas