Joint Optimization of Voyage and Speed for Semi-Submersible Ships Considering Loading Safety of Heavy Cargo

To address the joint optimization problem of heavy-lift cargo stowage and speed decisions during transportation by semi-submersible ships, a joint optimization model of voyage and speed is established for semi-submersible ships. In this model, the initial metacentric height (GM) after free-surface correction is taken as the core safety constraint. Factors such as cargo mass, loading and unloading time windows, ship deadweight, and speed range are comprehensively considered. The objective function is set to minimize total transportation cost. A two-stage method is used to solve the model. Case study results show that the optimized total cost is 20.7% lower than that of the cargo allocation and speed scheme formulated based on manual experience. Fuel cost is reduced by 29.5%. Charter cost and port cost are reduced by 3.1% and 14.3%, respectively. The sensitivity analysis results for the minimum limit of GM and the fuel oil price show that improving the safety standard reduces the compliance of small vessels for heavy-lift cargo. This causes the tight capacity of large vessels. It may even make some cargo transportation demand difficult to satisfy. A rise in the fuel oil price significantly increases the fuel cost and reduces the enterprise profitability. Appropriately reducing speed is an effective strategy to mitigate the effect of the fuel oil price.