Hybrid power systems are increasingly adopted onboard. Lithium-ion batteries now serve as a viable energy storage solution that enhances fuel efficiency and reduces the operating hours of main power units, thereby reducing operational expenses. However, integrating batteries onboard requires decision-making that accounts for diverse scenarios, including battery chemistry, variations in vessel operational profiles, and fluctuating fuel prices. To address these challenges, this study investigates whether battery sizing and scheduling of the power and energy management system require a scenario-based stochastic decision framework. Specifically, it examines how energy storage requirements are influenced by varying load profiles, whether the optimal battery size and power management strategy are affected by fuel price fluctuations, and how robust the overall strategy remains under operational uncertainties. A deterministic equivalent of a two-stage stochastic decision framework is introduced to incorporate these uncertainties, offering insights into the required battery technology, capacity, and correlated behavior of onboard energy management. Multiple scenarios are applied to a trailing suction hopper dredger, analyzing three load profiles with distinct variations in power demand. With reserve power constraints enforced, the optimal battery capacity remains fixed. However, when these constraints are relaxed, the optimal battery size becomes more sensitive to fuel price changes. In addition, the results showcase reduction in diesel engine operating hours—thereby lowering both fuel consumption and maintenance costs, demonstrating that these operational benefits depend not only on the battery's size but also on its available throughput, which allows for deeper cycling.