I am not able to find a valid inequality with chvatal gomory for my problem that increases the value of the relaxed problem.
My problem:
Determine the optimal allocation of n workers to m machines in two instants (t ∈ {1, 2}) in such a way that: (1) each worker is assigned to a single machine, (2) each machine has at least one worker assigned, (3) one worker cannot be assigned to the same machine in the two instants, (4) the sum of the costs of assignment of workers to machines does not exceed a fixed value Uc and (5) the objective function is to minimized the highest allocation cost between a worker and a machine. enter image description here
Please use MathJax rather than linking to an image. Your formulation is almost correct, but $z > c_{i,j}$ should instead be $z \ge c_{i,j} x_{i,j,t}$, which you can strengthen to $z \ge \sum_t c_{i,j} x_{i,j,t}$ because of $(3)$.