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When we analyzed the transhipment problem, we found that the simplex algorithm would always generate an integer solution because the problem had some property. All the vertices of the constraint polyhedron were integer. Unfortunately, it is not always the case. But maybe, if we take a general mixed integer linear problem, we could actually shrink the constraint polyhedron, and try to make sure that all its vertices are actually integer. In that case, the simplex algorithm would solve the problem as well. This would mean to add more constraints that would exclude only fractional solutions. These constraints are called amp;quot;valid inequalitiesamp;quot; if they are actually included by the modeler. Or they are called amp;quot;cutsamp;quot; if it is included by an algorithm. And in this video, we will see one family of such cuts, that can be actually derived from the algorithm. In integer optimization, the same feasible set can actually be characterized by several different polyhedr
