This study presents the numerical development of a generator–rectifier combined component (called a “combined-generator”) composed of plate heat exchangers, designed and meant to be integrated in a single-stage ammonia–water absorption cooling system. Investigations are made to find the most compact and efficient design. Numerical simulations are presented describing parameters such as the ammonia fraction in the vapor produced and the combined generator efficiency as a function of the inlet temperatures or mass flow rate of the heat transfer fluid. The combined generator produces vapor with a high ammonia mass fraction and high mass efficiency for a solution inlet temperature range of [315–320 K] and a mass flow rate of the heat transfer fluid between [0.4 and 0.6 kg.s−1]. The impacts of the length and number of plates as well as the adiabatic/heated ratio of the plates are also examined. The ammonia fraction increases with the increase in the adiabatic/heated ratio, and the combined generator efficiency increases with the increase in the plate aspect ratio of length/width. The proposed system is developed to be operated in compact and medium-capacity absorption chillers (approximately 5 kW cold) for air-conditioning.