Strategic Fleet Planning Under Carbon Tax and Fuel Price Uncertainty: An Integrated Stochastic Model for Fleet Deployment and Speed Optimization

This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the first stage, while the second stage optimizes operational decisions, including vessel assignment to routes and sailing speeds on individual voyage legs, after observing stochastic parameter realizations. The model incorporates nonlinear fuel consumption functions that are approximated using piecewise linearization techniques, with the resulting formulation being solved using the Sample Average Approximation (SAA) method. To enhance computational tractability, we employ big-M methods to linearize mixed-integer terms and introduce auxiliary variables to handle nonlinear relationships in both the objective function and constraints. The proposed model provides shipping companies with a comprehensive decision-support tool that effectively captures the complex interdependencies between long-term strategic fleet planning and short-term operational speed optimization. Numerical experiments demonstrate the model’s effectiveness in generating optimal solutions that balance economic objectives with environmental considerations under uncertain market conditions, highlighting its practical value for resilient shipping operations in volatile fuel and carbon pricing environments.