Due to the COVID-19/Omicron pandemic and the trade war and tariffs between China and America, the supply chain between Asia and America, or Asia and Europe, faced unprecedented challenges. With the outbreak of the Russian-Ukrainian war, the global supply chain has become increasingly unbalanced. In particular, the shortage of container ships and the continuous fluctuation of the BDI and CCFI make shipping scheduling increasingly important for ocean carriers. To solve this problem, in this study, we propose an analytic approach considering the fluctuation of BDI and CCFI based on interval evidence reasoning and the Hungarian algorithm. The proposed approach uses two pairs of nonlinear optimisation models to construct a Nash equilibrium assignment model to compute the shipping company’s scheduling and maximum utility in the CCFI and BDI cycles. Compared to the simulation algorithm, the analytical algorithm can take advantage of stability and efficiency. Finally, a COSCO company’s container shipping scheduling problem was examined to demonstrate the efficiency and effectiveness of the proposed approach.