Coordinating the port-carrier supply chain: Optimal design of volume-commitment discount contracts [Link]

Ports operate as capacity-constrained service platforms that face substantial demand volatility and congestion risk from multiple heterogeneous carriers. In this context, effective contracts between ports and carriers can help mitigate the inefficiency. This study develops a contract-based coordination framework that enables risk sharing and efficiency improvement in port-carrier cargo transfer. Specifically, we focus on volume-commitment discount contracts, under which the port offers a price incentive in exchange for the carriers’ binding commitment to a specific cargo volume, enhancing resource planning and operational efficiency. We first demonstrate that simple volume-commitment discount contracts, while Pareto-improving compared to no contract, fail to achieve full coordination due to double marginalization. In a multi-carrier context, shared and congestible port resources further make the contract design problem nonseparable across carriers. To achieve coordination, we develop a coupled volume-commitment discount and shortage-subsidy contract that induces system-optimal commitments, mitigates congestion externalities, and flexibly allocates surplus among participants. Comparative statics show that carrier heterogeneity shapes differentiated contract design. In particular, a substitution effect is revealed: the port tends to offer deeper discounts to carriers with lower shortfall-settlement costs when commitments from other carriers are harder to secure. The port also offers stronger incentives to carriers with higher demand uncertainty to manage congestion-related risks. Moreover, our findings further suggest that differentiated incentive contracts are more valuable for congestion-vulnerable ports with high planning benefits.