Parallel flow double and triple-effect vapor absorption cooling systems (VACS) are trying to meet the challenges of vapor compression cooling systems due to their better performance. Therefore, the present study deals with the review, thermodynamic analysis, and optimization of operating parameters for both double and triple-effect VACS. Lithium bromide water was selected as the working fluid, while liquified petroleum gas (LPG) and compressed natural gas (CNG) were taken as the source of energy to drive both the VACS. Detailed First Law analysis, i.e., coefficient of performance (COP), was examined along with the optimization of operating parameters (such as salt concentration and operating generators temperature at different pressure levels) and the volume flow rate of the gases. Optimization was carried out for maximum COP of the VACS using an iterative technique. Our results show that the COP of the triple-effect system was approximately 32% higher than the double effect, while 15−20% less consumption of the gases (LPG and CNG) was observed. The most optimum stage for the operation of triple-effect VACS was reached at Te = 4 °C and Tc = Ta = 30 °C, Tg = 180 °C, Tc4 = 104 °C, Tc3 = 66 °C, Z1 = 0.5, and Z2 = 0.45.