I was wondering if it were possible to solve a model using gams, and then to add a single constraint to the model with out rebuilding the entire model.
There are two ways to interpret your question: Can one add a constraint without regenerating the rest of the model? Here the answer is no; the entire model is regenerated, even if only one parameter (say, an objective coefficient) changes, or indeed if none change. “Smart” regeneration has been on our “wish-list” for some time, but we have not implemented it yet.
However, if you solve a model and add a constraint, the model is regenerated and the solver starts from the optimum value of the previous model, so from the solver standpoint, there is likely to be very little work required in the second solve. For an LP problem, one can choose to use dual simplex on the second solve so that a feasible start is guaranteed and the algorithm will take probably very few pivots before reaching optimality.