Hi @kin006. Your understanding of the range of a variable is correct. The range will enforce that the solution value of a(t) must be between -400,000 and 2,000,000.

What do you mean by “if the variable a(t) has a value larger than 2,000,000, it should be set to 2,000,000”? Do you mean that if a(t) is large than 2,000,000 then the objective value should be the same as for a(t) = 2,000,000?

Thank you for the response, @Marcel Hunting!

Yes, I think that is what I am looking for!

This is going to be ugly. I am going to ignore the index t (you have to add them to all variables and constraints below). Let lb = -400,000 and ub = 2,000,000. We need 5 more variables:

y with range: glb,ub]

z1: nonnegative

z2: nonnegative

bz1: binary

bz2: binary

And then the following constraints:

y = a - z1 + z2

y >= lb + (ub - lb) * bz1

y <= ub + (lb - ub) * bz2

z1 <= BigM * bz1

z2 <= BigM * bz2

bz1 + bz2 <= 1

Here BigM is a large value. As you already use large values in your model (2,000,000) it might become tricky to select an appropriate value for BigM.

Finally, the variable a(t) should be changed into a free variable, and a(t) should be replaced by y(t) in the objective.

Note the binary variables change the model into a mixed-integer nonlinear problem (MINLP).

A better reformulation might exist.

Thank you, @Marcel Hunting! I will try it :)