In this study, transient modelling for a solar-powered adsorption-based multi-generation system working under the climatic conditions of the Gulf Cooperation Council (GCC) countries is conducted. Three cities are selected for this study: Sharjah in the United Arab Emirates, Riyadh in Saudi Arabia, and Kuwait City in Kuwait. The system comprises (i) evacuated tube solar collectors (ETCs), (ii) photovoltaic-thermal (PVT) solar collectors, and (iii) a single-stage double-bed silica gel/water-based adsorption chiller for cooling purposes. A MATLAB code is developed and implemented to theoretically investigate the performance of the proposed system. The main findings of this study indicate that among the selected cities, based on the proposed systems and the operating conditions, Riyadh has the highest cooling capacity of 10.4 kW, followed by Kuwait City, then Sharjah. As for the coefficient of performance (COP), Kuwait City demonstrates the highest value of 0.47. The electricity generated by the proposed system in Riyadh, Kuwait City, and Sharjah is 31.65, 31.3, and 30.24 kWh/day, respectively. Furthermore, the theoretical results show that at 18:00, the overall efficiency of the proposed system reaches about 0.64 because of the inclusion of a storage tank and its feeding for the adsorption chiller. This study analyzes the feasibility of using a combination of ETCs and PVT collectors to drive the adsorption chiller system and produce electricity in challenging weather conditions.