guys! :)
So, I'm solving the following problem:
Imagine you have some MxN rectangle - a big field made up of parcels
\begin{matrix} x_{11} & ... & x_{1N} \\ \vdots & \ddots & \vdots \\ x_{M1} & ... & x_{MN} \end{matrix}
We have decision (binary) variables $x_{ij}^k$ that represent whether $x_{ij}$ belongs to one of k groups, i.e. for a fixed $(i,j)$, $x_{ij}$ can belong to only one of k groups or to no group at all. Our program will try and find these variables, however one of the constraints of the problem is that the groups need to form a reactangle w.r.t. the $x_{ij}$. For example group 1 might look like $x_{11}, x_{12}, x_{21}, x_{22}$, i.e. the $x_{ij}$ need to form a rectangle.
I have worked on this and managed to find an expression of this constraint in terms of the max and min of the coordinates of the $x_{ij}$, however am wondering whether a linear version of this constraint exists. Does it?