Thermo-vapor compressor (TVC) is used for compressing the low-pressure vapor with the help of the high-pressure motive steam, to produce the medium pressure vapor. A substantial portion of energy may be conserved by integrating TVC with the multiple-effect evaporator (MEE). The common practice in desalination industry is to compress the vapor produced in the last effect of a MEE using TVC to reduce the overall motive steam requirement. Such integration does not necessarily guarantee energy optimality. The objective of the present work is to optimally integrate TVC with a MEE system to maximize the gain output ratio (GOR). GOR is defined as the ratio of the mass flow rate of vapor produced in MEE to the mass flow rate of the motive steam supplied to TVC. GOR is the measure of the energy efficiency of MEE system. Using the principles of Pinch Analysis and techniques of mathematical optimization, a new methodology for integration of TVC with MEE is proposed in this paper. This is the first analytical methodology to optimally integrate TVC with MEE, avoiding multiple simulations of the overall system. A Theorem is proposed to directly calculate the optimal location of TVC suction position. The proposed methodology gives the designer the freedom to design an MEE-TVC with minimum energy consumption and without carrying out the detailed simulation of the entire system. The methodology is demonstrated through the illustrative case studies for concentrating corn glucose, and freshwater production through thermal desalination. In the case of corn glucose, the optimal integration of TVC with 2-effect MEE resulted in the increase in GOR by 10.1% with a decrease in the specific area requirement by 4.1%. For a desalination system with 11-effect MEE, the optimal integration of TVC improves the GOR by 1.5% and reduces the specific area by 4.3%. Furthermore, sensitivity analysis is carried out to determine the optimal operating parameters for both case studies. (C) 2016 Elsevier Ltd. All rights reserved.