A Note on the MIR Closure

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed integer linear programs. In 1998, Wolsey defined MIR inequalities differently. In some sense these definitions are equivalent. However, this note points out that the natural concepts of MIR closures derived from these two definitions are distinct. Dash, Günlük and Lodi made the same observation independently.