Dynamic Carbon Intensity Indicator (CII) management in stochastic tramp shipping market

In the maritime sector, tramp shipping companies manage fleets to maximize profit while navigating market uncertainties. The International Maritime Organization (IMO) recently introduced the Carbon Intensity Indicator (CII) to reduce greenhouse gas emissions, further complicating deployment decisions. This paper introduces a novel two-stage stochastic programming model for long-term fleet deployment under market uncertainty and CII regulation. It is the first to integrate key operational uncertainties—fuel prices, freight rates, and cargo demand—into a unified tactical planning framework under CII regulation, simultaneously optimizing routing, cargo allocation, and speed. Furthermore, we develop a novel efficient heuristic algorithm that reliably converges to solutions within a 5% normalized deviation from exact solutions, enabling practical decision-support under uncertainty. Numerical analysis highlights two key findings based on our model: (1) It uncovers the “CII paradox,” a critical counterintuitive phenomenon where the present Supply-based CII regulation may increase total emissions significantly and drastically reduce profits. This challenges the conventional wisdom that stricter carbon-intensity rules invariably reduce emissions. (2) It demonstrates the advantage of stochastic modeling, showing that accounting for future uncertainties significantly narrows the revenue gap with perfect-foresight solutions, thereby offering superior economic performance over deterministic approaches. Collectively, these results deepen the understanding of environmental regulation’s operational impacts and pave the way for more effective and sustainable fleet management strategies.