In a world with increased pressure on reducing fuel consumption and carbon dioxide emissions, thecruise industry is growing in size and impact. In this context, further effort is required for improvingthe energy efficiency of cruise ship energy systems.In this paper, we propose a generic method for modelling the power plant of an isolated system withmechanical, electric and thermal power demands and for the optimal load allocation of the different componentsthat are able to fulfil the demand.The optimisation problem is presented in the form of a mixed integer linear programming (MINLP)problem, where the number of engines and/or boilers running is represented by the integer variables,while their respective load is represented by the non-integer variables. The individual components aremodelled using a combination of first-principle models and polynomial regressions, thus making thesystem nonlinear.The proposed method is applied to the load-allocation problem of a cruise ship sailing in the Baltic Sea,and used to compare the existing power plant with a hybrid propulsion plant. The results show thebenefits brought by using the proposing method, which allow estimating the performance of the hybridsystem (for which the load allocation is a non-trivial problem) while also including the contribution ofthe heat demand. This allows showing that, based on a reference round voyage, up to 3% savings couldbe achieved by installing the proposed system, compared to the existing one, and that a NPV of11 kUSD could be achieved already 5 years after the installation of the system.