Multi-Effect Desalination system with thermal vapor compression (MED-TVC) is a promising large-scale thermal water production technique. In MED, multiple evaporators are used where vapor is formed in each one using the heat generated from condensing steam/vapor in the previous effect, resulting in high Performance Ratio (PR). A thermal Vapor compressor is used with the MED system to extract a portion of the formed vapor formed in an effect and mix it with motive steam to reduce the rate of steam from a power plant and decrease the pressure in the effects. The top brine temperature of MED system is limited to a value around 65 degrees C to avoid scale formation on the outer surface of tubes in the evaporator. In this study, a mathematical model is developed to identify the optimum location of the thermal-vapor compressor (TVC or ejector) attached to the Multi Effect Evaporation system. Both forward and parallel feed configurations are investigated. The performance of the system is evaluated using the main performance indicators such as performance ratio (PR), surface area of the evaporators and condenser, and the specific cooling water flow rate needed for condensing the vapor that reaches the down condenser. Locating the TVC at the middle effect resulted in the best unit performance regardless of the number of effects. That is, the highest PR, lowest specific cooling water flow rate are resulting from placing the ejector (TVC) at N/2 where N is the number of effects. Changing the TVC location did not affect the specific heat transfer area, which means that the plant capital cost is not affected by placing the TVC in its optimum location within the practical range of TBT.