Dynamic pricing and competition of container liner shipping services in a duopoly spot market

With the application of online booking technology in the spot market of container liner shipping, dynamic pricing is considered an important tool and development trend to balance container shipping supply and demand from the spot market. This study examines the dynamic pricing and competition of container liner shipping services in a duopoly spot market where two shipping companies compete on liner routes with multiple overlapping origin-destination (O-D) pairs. The demand within the spot market for one shipping company is sensitive to both the freight rate set by the shipping company and its competitor. To tackle this complex challange, a nonlinear mixed-integer generalized Nash equilibrium optimization model was formulated for the dynamic pricing and competition problem to maximize the profits of both shipping companies. To effectively reach the optimal solution for the dynamic pricing and competition problem, the proposed model is reformulated as a linear complementary problem with a Karush-Kuhn-Tucker (KKT) conditional system. An optimal response decomposition algorithm is developed to obtain the global optimal solution of the model. Numerical experiments with the Trans-Pacifc shipping network of two oligarchic shipping companies were conducted to demonstrate the efficiency of the solution algorithm and the applicability of the proposed model in improving the two companies' profits from the spot market.