Mingling: mixed-integer rounding with bounds (Q964180)

Mixed-integer rounding (MIR) inequalities are effective for mixed-integer programming problems with unbounded variables. The authors describe a simple procedure, called mingling, which strengthens MIR inequalities by using the information on bounds of the variables. It is shown that facets of the mixed-integer knapsack set, previously derived by subadditive lifting techniques, can be obtained by the mingling procedure. Mingling inequalities subsume the (reverse) continuous cover inequalities of \textit{H. Marchand} and \textit{L. A. Wolsey} [Math. Program. 85, No.1(A), 15--33 (1999; Zbl 0956.90021)], and the continuous integer knapsack cover and pack inequalities of \textit{A. Atamtürk} [Math. Program. 98, No. 1-3 (B), 145--175 (2003; Zbl 1082.90073)]. In some cases, mingling inequalities generalise also the two step MIR inequalities of \textit{S. Dash} and \textit{O. Günlük} [Math. Program. 105, No. 1(A), 29--53 (2006; Zbl 1085.90034)]. Mingling inequalities can easily be implemented using MIR routines. They appear to be particularly powerful after aggregating the constraints of a mixed-integer programming problem.