Desalinators are traditionally driven by fossil-fuels but in order to avoid greenhouse emissions, renewable energy must be used. In this paper, a coupling between multi-stage flash distillation apparatus and a parabolic trough solar collector is analyzed. The purpose of this study is to determine the economic feasibility of the system, considering four cities of Saudi Arabia and three different potable water productions. To avoid solar energy intermittency and unavailability at night, thermal storage is implemented. Whereas other researchers made parametric analyses, in this paper, the authors developed a mathematical program which was optimized with the help of GAMS software, where the capital cost of the plant was the objective function. After that, a life cycle cost analysis was carried out for each scenario. Depending on the region and water production, the costs of drinking water vary from 2.26 to 3.93 US$/m³, and from 7440 to 23825 tons of carbon dioxide emissions are avoided. As a consequence of the approach used, low costs are obtained; even though no auxiliary heater is implemented and the lowest irradiance conditions are considered. The results of this study reflect that the proposed process is competitive with respect to the traditional one.