This article presents an innovative combined heat and power system comprising a solid oxide fuel cell (SOFC), a heat recovery unit, and a lithium bromide absorption power cycle (APC). The energy, exergy, economic, and environmental perspectives of the proposed system are compared against the same configuration using an organic Rankine cycle (ORC), recovering the waste heat of the SOFC. A multi-criteria optimization based on the Grey Wolf approach is applied to each system to specify the best operation conditions having the exergy efficiency and total cost rate as the objectives. Furthermore, a parametric investigation is conducted to assess the effects of changing the decision variables on the systems proficiencies. The results indicate that although the ORC-based cycle is economically very slightly superior, the integration of the SOFC with the APC offers a much higher exergy efficiency due to the better temperature matching between the working fluid and heat source. Optimization can increase the exergy efficiencies of the SOFC-ORC and the SOFC-APC systems by about 13.8% and 14.7% while reducing the total cost rate by 11.2 $/h and 11.0 $/h, respectively, compared to the base system. Environmental analysis results reveal that APC use leads to a lower emission of 2.8 kg/MWh.