Sample Distribution Approximation for the Ship Fleet Deployment Problem Under Random Demand

The ship fleet deployment problem plays a critical role in maritime logistics management, requiring shipping companies to determine optimal vessel configurations for cargo transportation. This problem inherently contains stochastic elements due to the random nature of cargo demand fluctuations. While the Sample Average Approximation (SAA) method has been widely adopted to address this uncertainty through empirical distributions derived from historical observations, its effectiveness is constrained by data scarcity in practical scenarios. To overcome this limitation, we propose a novel Sample Distribution Approximation (SDA) framework that employs estimated probability distributions, rather than relying solely on empirical data. We implement a leave-one-out cross-validation mechanism to optimize distribution estimation accuracy. Through comprehensive computational experiments, using decision cost as the primary evaluation metric, our results demonstrate that SDA achieves superior performance compared to the conventional SAA method. This advantage is particularly pronounced in realistic operational conditions, where historical demand observations range from 15 to 25 data points, or fleet configurations involve two to six candidate vessel types. The proposed methodology provides shipping operators with enhanced decision-making capabilities under uncertainty, especially valuable in data-constrained environments.