ILOG CPLEX uses numerical methods of finite-precision arithmetic. Consequently, the feasibility of a solution depends on the value given to tolerances. Two parameters define the tolerances that assess the feasibility of a MIP solution:

A solution may be considered feasible for one pair of values for these two parameters, and infeasible for a different pair. This phenomenon is especially noticeable in models with numeric difficulties, for example, in models with Big M coefficients.

Since the definition of a feasible MIP solution is subject to tolerances, the total number of solutions to a MIP model may vary, depending on the approach used to enumerate solutions, and on precisely which tolerances are used. In most models, this tolerance issue is not problematic for ILOG CPLEX. But, in the presence of numeric difficulties, ILOG CPLEX may create solutions that are slightly infeasible or integer infeasible, and therefore create more solutions than expected.