Relating indexes for parameters and variables I am trying to solve a referee assignment problem, but I simply can't think of a way to relate my variable to one of the parameters, and I hope that someone in here can help.

I have the following binary variable


x(r,m) = 1 if referee r is assigned match m


and the following parameters:


time(m,t) = 1 if match m takes place at time t
avail(r,t) = 1 if referee cannot officiate a game at time t


I want to define my x variable to 0, when avail(r,t)=1, but is this even possible?
Yes.

This appears to be an instance of the assignment problem.  In the assignment problem, you construct a bipartite graph.  The vertices on the left represent referees.  The vertices on the right represent matches.  You draw an edge from a referee $r$ to a match $m$ if the referee $r$ is potentially available to officiate in that match.  You can use the time() and avail() parameters to work out which edges to draw.  Then, a solution to the assignment problem (a maximum matching in this bipartite graph) will represent a way to assign referees to matches.  Thus, this captures the restrictions you want to enforce in a simple and natural way.