let ILP be an integer linear program with constraints-matrix $\boldsymbol{\mathrm{M}}\in\mathbb{Z}^{m\times n}$ and cost vector $\boldsymbol{\mathrm{c}}\in\mathbb{Z}^n$,
${\boldsymbol{\mathrm{x}}^*}\in\mathbb{Z}^n,\,{\boldsymbol{\mathrm{x}}^*}^T\boldsymbol{\mathrm{c}}\in\mathbb{Z}\le\boldsymbol{\mathrm{x}}^T\boldsymbol{\mathrm{c}}\quad \forall\boldsymbol{\mathrm{x}}\in\mathbb{Z}^n$ the optimal integral solution of ILP.
${\boldsymbol{\mathrm{y}}^*}\in\mathbb{R}^n,\,{\boldsymbol{\mathrm{y}}^*}^T\boldsymbol{\mathrm{c}}\notin\mathbb{Z}\le\boldsymbol{\mathrm{y}}^T\boldsymbol{\mathrm{c}}\quad \forall\boldsymbol{\mathrm{y}}\in\mathbb{R}^n$ the optimal solution of the relaxed ILP, then we have: ${\boldsymbol{\mathrm{y}}^*}^T\boldsymbol{\mathrm{c}}\lt{\boldsymbol{\mathrm{x}}^*}^T\boldsymbol{\mathrm{c}}$
Question:
would adding the constraint $\boldsymbol{\mathrm{x}}^T\boldsymbol{\mathrm{c}}\ge\lceil{\boldsymbol{\mathrm{y}}^*}^T\boldsymbol{\mathrm{c}}\rceil$ to the ILP constraints be beneficial for finding the optimal integral solution e.g. via cut and branch?
