I am doing Lagrangian Relaxation with Gurobi for a minimization problem. The relaxed constraint has two integer variables in both right-hand side and left-hand side, meaning that both Xijskm and Y'ijsm are integer variables and Vm is a parameter to the model. This constraint explains the capacity limitation of different vehicles.
When I add the relaxed constraint as a penalty to the objective function, it gives a very huge value to the variable Y'ijsm, which has a Lagrangian multiplier with negative sign in the objective function, so the model is unbounded in iteration 2.
In order to better explain, this term is added to the objective function due to relaxing the above-mentioned constraint:
When I ran the model, the process of running the algorithm is stopped at the second iteration with this error “The model is unbounded or infeasible”. I checked it by adding a couple of lines of commands to the code. It is unbounded, not infeasible.
It seems that because of negative sign of this term in the objective function, it assigns a very huge value to Y'ijsm, so the objective function will be a big negative value.
Is there a way to handle this issue? I do appreciate you.
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