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

Ports operate as capacity-constrained service platforms that face substantial demand volatility and congestion risk from multiple heterogeneous carriers. In such case, a delicate design of contracts between the ports and carriers can foster their ability to cope with 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 volumecommitment discount contracts, which refer to the port offering 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. To address this inefficiency, we propose a coupled volume-commitment discount and shortage-subsidy contract that simultaneously induces system-optimal commitment, mitigates congestion externalities, and flexibly allocates surplus among participants. Analytically, we establish that the coupled contract can fully coordinate the decentralized system and recover the system-optimal outcome under both single-carrier and multi-carrier settings with correlated stochastic demand. Comparative statics analyses further reveal that the port strategically designs differentiated contract terms considering carrier heterogeneity, offering more favorable discounts to carriers with less shortage-replenishment cost. Moreover, the port offers deeper discounts as a risk premium to carriers with higher demand uncertainty to manage systemic risks. This research contributes to the literature on supply chain coordination and maritime logistics by formalizing a risk-sharing contract that internalizes congestion externalities and enhances the operational resilience of port-carrier supply chain under uncertainty.