I have an optimization problem for which I have the optimal solution obtained by the ILP. However, when I introduced the McCormick Envelope to replace the product of a bi-lnear term in its LP relaxation, after rounding the cost function value is much higher than that of the ILP.

Are there alternatives to the McCormick Enevelopes to get a better cost function value after rounding or even a better approach for the bi-linear term ?