This paper deals with the optimization of a multi-generation system (integrating a dual-purpose desalination plant and a low-scale absorption refrigeration system). A nonlinear mathematical programming (NLP) optimization model that integrates a natural gas combined-cycle (NGCC) plant, a multi-effect distillation (MED) desalination plant, a series flow double-effect water-lithium bromide absorption refrigeration system (H2O-LiBr ARS), and a water heater, is developed based on first-principle models of the system components. The model is implemented in the General Algebraic Modelling System (GAMS) platform. Given design target specifications for electricity generation, freshwater production, refrigeration capacity, and thermal load for heating, the integrated system is optimized by minimizing the total heat transfer area of the integrated system. The influence of the total number of effects in the MED subsystem on the total heat transfer area are analyzed in terms of the variations in the heat transfer areas, heat loads, driving forces, as well as the operating conditions of all components of the system. As a result, a minimum value of 43184 m2 is required to generate 36971 kW, 100 kg/s of freshwater, 2000 kW refrigeration effect, and 761.9 kW hot water when four MED evaporation effects are considered. For the same specified outputs of the multi-generation system, if an additional effect is considered in the MED system (5 effects in total), the total heat transfer area is reduced by around 9.5%. While adding a sixth effect, the total heat transfer area decreases by 3.2% with respect to a 5-effect MED system and 12.4% with respect to a 4-effect system. This paper provides optimal solutions for the proposed multi-generation system allowing for better energy utilization at minimum total heat transfer area requirements.