Mathematically, the Mixed Integer Linear Programming (MIP) Problem looks like:
where the
t variables are continuous real numbers
u variables can only take on integer values bounded above by L2
v variables can only take on binary values
w variables fall into SOS1 sets exhibiting one nonzero
x variables fall into SOS2 sets exhibiting no more than two, adjacent nonzeros
y variables are semi-continuous being zero or in excess of L6
z variables are semi-integer being zero or in excess of L7 and integer
c1t + c2u + c3v + c4w + c5x + c6y + c7z is the objective function,
A1t + A2u + A3v + A4w + A5x + A6y + A7z α b represents the set of constraints of various equality and inequality forms.
For information on the names of the solvers that can be used on models in the MIP class see the section on Solver Model type Capabilities. Note not all solvers cover all the cases associated with the SOS and semi variables. Thus, if you have such a problem, you should refer to the MIP capable solver manuals to discover capability. GAMS will also reject the problem if the solver cannot handle the types of variables contained.