I am working on mathematical modeling using Gurobi as a solver and python as an interface. In my model, I would like to create a binary variable but the variable is allowed to take a value of 1 if a>=1 else 0 where a is another decision variable in the model.
the binary variable should look like this as follows in the picture:-
To summarize, you want to model the implications:
x>=1 => y=1
x=0 => y=0
x >= 0 (non-negative variable)
y ∈ {0,1} (binary variable)
There are different ways to do this.
Note that we can invert the implications:
y=0 => x=0
y=1 => x>=1
indicator constraints
y=0 => x=0
y=1 => x>=1
can be directly implemented as indicator constraints. See https://www.gurobi.com/documentation/9.1/refman/py_model_agc_indicator.html.
Big-M approach
x <= M*y (this will do y=0 => x=0)
x >= y (this will do y=1 => x>=1)
Here the constant M is an upper bound on x. If M is very large, it is better to use indicator constraints.
