Abstract: Under the Carbon Intensity Indicator (CII) rules of the International Maritime Organization (IMO), most theoretical studies manage ship carbon intensity primarily by reducing carbon emissions. However, reducing carbon emissions at the expense of ship transport work no longer aligns with the goal of carbon peaking intensity. Therefore, considering sulfur emission limits, a model was developed to determine whether fuel switching or scrubber retrofitting should be adopted. Combining with carbon intensity management, a decision model for the ship deployment and scheduling problem is proposed, subject to the constraints on sailing speed, fleet deployment, and carbon intensity compliance. To solve the proposed mixed-integer nonlinear programming model, a hybrid algorithm combining linearization and CPLEX is designed. The model is validated using five routes operated by COSCO Shipping. The results show that, compared with the genetic algorithm, the proposed hybrid algorithm increases the solution time slightly by 7.6%, while reducing the operating cost significantly by 33.4%, and all solutions satisfy the engineering constraints. Without carbon intensity management, the carbon intensity of some routes deteriorates to a non-compliant level, which confirms that carbon intensity management can effectively reduce the risk of ship downgrade and service suspension. Based on the above results, two managerial insights are obtained. First, to reduce fleet fuel consumption, liner companies should reduce ship deadweight while still meeting cargo demand, and lower sailing speed within the allowable range. To reduce fleet carbon intensity, besides lowering speed within the allowable range, liner companies should also increase cargo demand to increase ship deadweight. Second, a higher reduction factor imposes stricter carbon intensity requirement. Limited by the minimum and maximum sailing speeds, carbon intensity management requires the deployment of ships with larger deadweight. To avoid carbon intensity non-compliance and excessively low ship loading rate, liner companies should focus on improving transport work by increasing cargo demand.