We formulated an integer programming problem P, this integer programming problem P can be solved with CPLEX solver within about 2 seconds.

we added an equality constraint to the programming problem P, then we get an new integer programming problem P'.

When we solved the new integer programming problem P' with CPLEX solver, it can not be solved with about 20000 seconds. I want to kown why the solving time becomes so long?

Generally speaking, it is possible to make a model much harder by adding one constraint.

If the difficulty is in finding a feasible solution, you can try to add some slack variable to relax the equality constraint.

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