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When you solve a problem with integer constraints (a
mixed-integer programming or MIP problem, which can take a great
deal of time), the solution process is governed by the Tolerance
option in the Solver Options dialog. Since the default
setting of the Tolerance option is 0.05, the Solver stops when
it has found a solution satisfying the integer constraints whose
objective is within 5% of the true integer optimal value. Therefore,
you may know of or be able to discover an integer solution which is
"better" than the one found by the Solver.
The reason that the default setting of the
Tolerance option is 0.05 is that the solution process for integer
problems -- which can take a great deal of time in any case -- often
finds a near-optimal solution (sometimes the optimal solution)
relatively quickly, and then spends far more time exhaustively
checking other possibilities to find (or verify that it has
found) the very best integer solution. The Tolerance option default
setting is a compromise value that often saves a great deal of time,
and still ensures that a solution returned by the Solver will be
within 5% of the true integer optimal solution.
To ensure that the Solver finds the true integer
optimal solution -- possibly at the expense of far more solution
time -- set the Tolerance option to a value of zero. For more
information on how the Tolerance option is used, consult Precision
and Tolerance.
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Diagnosing Solver Results
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