Regulations set by governmental and non-governmental maritime regulatory bodies are set to highly impact the cruise ship industry and put pressure on ship owners to invest in energy-efficient ships as well as improve the overall ship operation. To this end, various studies have been performed to analyze the economic and environmental impact of energy efficient technologies and ship operation strategies. These studies typically involve modelling the cruise ship energy consumers and producers as a non-linear model and analyzing the impact of the technology being studied. In this paper, we propose a formulation of the cruise ship energy system design optimization as a generic mixed integer linear program (MILP). The generic formulation of the model allows for a variety of technologies to be tested without much modification to the underlying formulation. The model is instantiated using internal combustion engines (ICEs) and solid oxide fuel cell (SOFC) technologies and an analysis of the optimization results is carried out for three objective functions: greenhouse gas (GHG) emissions, lifecycle cost, and lifecycle cost including carbon tax. The model's design and operation results were validated by experts. Results from the case studies indicated significant reductions in GHG emissions using SOFCs, consistent with the literature. However, the carbon tax analysis over a period of 15 years showed a surprisingly lower impact of carbon tax measures than expected, which could have potential consequences on the adoption of cleaner, yet cost intensive technologies in the cruise ship industry.