Optimal price decisions for joint ventures between port operators and shipping lines under the congestion effect

The congestion effect refers to the phenomenon that more customers choosing to use the same facility reduces the facility’s utility. This work addresses the optimal pricing problem for a firm operating a joint-venture terminal under the congestion effect. The firm is formed between a port terminal operator and a shipping line, thus being able to provide a bundle of ocean transportation and port terminal solutions to cargo suppliers. The objective is to determine the optimal prices charged to cargo suppliers to maximize the total profit of the firm. First, we develop a tractable flow-based optimization model that uses a fixed-point equation to capture the interaction between the congestion effect and cargo suppliers’ choice. Second, we characterize the optimal solution for a variety of cases, including the single origin-destination case, partially homogeneous case that includes the fully homogeneous case as a special case, and heterogeneous case. Third, we evaluate the profit loss incurred by ignoring the congestion effect with numerical studies. Moreover, we propose one-variable and two-variable search methods for the partially homogeneous and heterogeneous cases, respectively. We learn that the firm should quote the same price to all cargo suppliers under the fully homogeneous case. However, this is not necessarily optimal under the partially homogeneous or heterogeneous cases. The profit loss incurred by neglecting the congestion effect can be significant and increases as cargo suppliers become less tolerant of congestion.