Problem with the dual variables fixing the value of a variable

[giuseppes...@gmail.com]

Hi,
I am pretty new to Pyomo. I am sorry if the question is trivial, but I do not understand.
I have the following LP:

S = pyo.ConcreteModel()
S.dual = pyo.Suffix(direction=Suffix.IMPORT_EXPORT)
S.x = pyo.Var(within=NonNegativeReals)
S.y = pyo.Var(within=Integers)
S.obj = pyo.Objective(expr= S.x, sense=minimize)
S.cc = pyo.ConstraintList()
S.cc.add(2*S.x >= 3-S.y)

Now we fix the variable S.y = -5:

S.y.fix(-5.0)

We solve the model and we got x = 4, y=-5 and the dual variable u = -0.5.

Now we solve the equivalent model where we do the sum (3-(-5)):

S = pyo.ConcreteModel()
S.dual = pyo.Suffix(direction=Suffix.IMPORT_EXPORT)
S.x = pyo.Var(within=NonNegativeReals)
S.y = pyo.Var(within=Integers)
S.obj = pyo.Objective(expr= S.x, sense=minimize)
S.cc = pyo.ConstraintList()
S.cc.add(2*S.x >= 8)

We got x = 4, y=-5 and the dual variable u = 0.5.

Why? I expect to see the same value for u. I need to fix the value for the Bender Decomposition.