Ship Scheduling and Refueling for Container Liner Cold Chain Shipping

Liner shipping companies commonly pursue strategies such as forming strategic alliances and attracting new customers to strengthen competitiveness and improve operational performance. However, in the shipping of perishable goods, inadequate ship scheduling and bunker management can result in substantial customer loss and increased operational costs. This paper examines a scenario in which a large volume of perishable goods is shipped by liner ships. The specific demand characteristics of perishable goods—requiring rapid port handling and expedited shipping—are analyzed. To address these challenges, we propose a mixed-integer nonlinear programming (MINLP) model to optimize ship scheduling and refueling decisions for liner cold chain services under cooperative agreements. The model minimizes total liner shipping service costs while explicitly accounting for the decay of perishable goods. Nonlinear elements are linearized using a piecewise linear secant approximation, enabling efficient solution of the model with commercial solvers. Numerical experiments based on the AEU6 route operated by China COSCO Shipping Group validate the model and provide practical managerial insights. The results indicate that: (1) incorporating collaborative agreements can reduce total route service costs by 4.5% and total port handling costs by 7.5%, while also lowering late arrival penalties and losses from perishable goods decay; (2) joint consideration of refueling strategies and collaborative agreements improves both decision flexibility and solution accuracy; (3) the shipping of perishable goods has differentiated effects across voyage legs, highlighting the need for liner shipping companies to enhance cooperation with ports and refine bunker fuel procurement planning; and (4) it is essential to improve ship performance and appropriately design bunker fuel tank capacity to respond to dynamic changes in the shipping market.