Mitigating the financial risk behind emission cap compliance: A case in maritime transportation

The enforcement of ever-stringent regulatory requirements capping emission limits is challenging the traditional operations of various transportation sectors. In maritime transportation, the recent regulation tightening fuel sulfur limits to 0.50%, known as the "IMO 2020," has been enforced. There is a flurry of activities by ocean carriers to equip their vessels to comply with this regulation. Although the technical conditions are clear, investment decisions are hard to make due to inevitable uncertainties in the current transition period, especially on the impact of fuel prices in the long run. In this study, we consider an ocean carrier's technology investment decisions. Each compliance solution is subject to uncertain operating costs with a partially characterized probability distribution that may deviate from current expected norms. The carrier chooses a portfolio of compliance solutions for its entire fleet that would best adhere to two decision criteria characterized by a net present value (NPV) target in investment and a capacity utilization rate target in fleet deployment. To find optimal decisions that will perform well in the uncertain transition period, we introduce a tractable mathematical model, termed the ambiguous robustness optimization model, to minimize the financial riskiness index associated with the risk of expected NPV not meeting a specified target. We further propose a solution scheme through mixed-integer second-order cone programming approximation that can be efficiently solved by off-the-shelf solvers. We show that this decision support system performs well in numerical experiments constructed using real data on the Asia-North America West Coast shipping network.