<p>In this paper, under some environment policies, we take the stochastic volatility of fuel prices caused by public emergency events into account to study liner speed optimization and fuel oil replenishment problems. By minimizing the total expected costs including fuel replenishment and stockpiling, time penalty, carbon tax, and so on, we propose a chance-constrained stochastic programming model with adjustable confidence level to balance cost efficiency and risk management. Methodologically, we model fuel prices with stochastic perturbations, embed risk tolerance through a tunable chance constraint, and exploit structural properties to transform and simplify the original model for practical computation. This provides a general way to convert a high-dimensional stochastic planning problem into an implementable decision tool. Then, we take an Asia-Europe route of China Shipping Group during a public health emergency as an example to carry out simulation experiments and analyze the numerical results related to optimal speed and refueling strategies of each segment before and during epidemic. Furthermore, we give a sensitivity analysis on random disturbance of fuel price and confidence level to verify their impact on the total costs and optimal speed. Our numerical results show that, during the epidemic, the liner company could make decisions based on the fluctuation of fuel prices to adapt to the changes in the market, however, the greater the fluctuation of fuel price, the more pollutant emissions increase. Therefore, flexible fuel replenishment strategies and speed adjustment plans may play an important role in emission reduction.</p>