I am a new user to CPLEX and currently trying to implement a Column Generation Method using C++ as the API.
For example, the formulation is :
We can see that y1,y2 are non-decision variable, that is it is not in the objective. Commonly, if we formulate the problem by column, we use like:
Problem1: for c1 and c2, the lower bound is 0 but upper bound is y1 and y2, respectively. The cplex does not allow me to put variables or expressions in A1 and A2 place in (1).
Problem2: if we cannot add the y with (1), we need to add the column for y in (2). However, y is not in the objective, if we use (2) and set obj(0) for y, I feel like we will change the formulation and y is in the objective with coefficient 0. Am I right? It seems that this problem does not matter. However, if we want to get the dual, then it does matter. At first, when only x is the objective variable, dual is only related with c1 and c2. However, when y is add with (2), I feel that the c3 also has to be counted into the dual issue, since y now is in the objective variable although coefficient is 0. This is my worry.
Can any one help me figure this point out? Thank you very much.