© 2018 by the authors. Licensee MDPI, Basel, Switzerland. An analytical model is proposed to evaluate the performance of a Direct Expansion Solar-Assisted Heat Pump under a given environmental condition. These thermal machines commonly employ uncovered flat plate solar collectors, and given this, the convection phenomenon is taken into account as well as the effect of the diffuse and reflected solar radiation in addition to the normal beam radiation absorbed by the tilted surface of the collectors. The heat pump cycle is modelled through a first law of thermodynamics approach in order to compute the heat yielded through condensation and the minimum heat required by the volume of water in the thermal storage unit. Consequently, the thermal capacity of the heat pump, the ratio at which the system yields heat to a given load of water, is calculated and discussed. The results of the model proposed are compared with the experimental data provided by three research papers with experiments conducted in different geographic coordinates and test rigs operating during diverse atmospheric conditions. A maximum relative error of 20% was obtained and furthermore, a statistical analysis of the data was conducted having found that there is no significant statistical difference between the analytical and experimental data samples within the 95% confidence interval. Finally, based on the thermal capacity, the performance of the heat pump is evaluated and a multi-objective optimization technique is implemented to obtain the best possible combination of factors to further enhance the performance of the heat pump.