Unboundedness can be viewed as an under-constrained condition; such an outcome can be from a modeler forgetting to include one or more constraints in the model. Therefore carefully checking that your problem formulation is complete is a good first step in diagnosing unboundedness.

The default variable type in CPLEX has a lower bound of 0 (zero) and an upper bound of infinity. If you declare a variable to be of type Free, its lower bound is negative infinity instead of 0 (zero). A model can not be unbounded unless one or more of the variables has either of these infinite bounds. Therefore, one straightforward tactic in avoiding unboundedness is to assign finite bounds to every variable in your model; if no variable can go on an unbounded ray to infinity, then your model can not be unbounded.

Other forms of avoiding under-constrained conditions, such as adding a constraint that limits the sum of all variables, are also possible.

If an unbounded solution is not possible in the physical system you are modeling, then adding finite lower and upper bounds or adding other constraints may represent something realistic about the system that is worth expressing in the model anyway. However, great care should be taken to assign meaningful bounds, in cases where it is not possible to be certain what the actual bounds should be. If you happen to select bounds that are tighter than an optimal solution would obtain, then you can get a solution of worse objective function value than you want. On the other hand, picking extremely large numbers for bounds (just to be safe) carries some risk, too: on a finite-precision computer, even a bound of one billion may introduce numeric instability and cause the optimizer to solve less rapidly or not to converge to a solution at all, or may result in solutions that satisfy tolerances but contain small infeasibilities.