There is an robust algorithm for solving Multi-Objective Optimization (MOO) in GAMS and the authors have published one of their finest research outcomes which is
"Mavrotas, G, Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems. Applied Mathematics and Computation 213, 2 (2009), 455-465"
For Pdf: http://www.gams.com/modlib/adddocs/epscmmip.pdf
In GAMS library there is file named "epscmmip.gms" which is improved version of eps-Constraint Method for Multiobjective Optimization. The authors have given clear illustration considering an Mixed Integer Programming example. Moreover, the algorithm will generate Pareto sets as trade-off between objective functions. Using MATLAB, PYTHON or Excel one can plot the gridpoints from the pay-off table.
I have used the same algorithm for one of my researchers and found it way more robust and finest thing in GAMS. I recommend you to study the algorithm from PDF document and try working on some of literature case studies to replicate the results. Later, you can apply this approach to various variety of optimization problems.