Limitations due to numeric difficulties

Describes limitations due to numeric difficulties.

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 CPLEX. But, in the presence of numeric difficulties, CPLEX may create solutions that are slightly infeasible or integer infeasible, and therefore create more solutions than expected.

You can find more details about the topic of numeric difficulties in the CPLEX User’s Manual in Numeric difficulties and Slightly infeasible integer variables.