# Linearize if-then constraints

For continuous variables $$x$$ and $$y$$, the constraints are:

if x >= 0 and x < 1 then y <= 10 and
if x >= 1 and x < 2 then y <= 5 and

(up to the ten lines of inequalities)

if x >= 2 then y <= 2


The problem is on modeling nonlinear behaviour of gas storage pumping efficiency, which decreases for high load in case of very large gas storages (decrease is seen for storages with capacity above 5 million cubic meters). I have to write these constrains using MIP (or LP) formulation. I can use SOS1/SOS2 variables in GAMS with cplex/gurobi solvers.