On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs

We compare the relative strength of valid inequalities for the integer hull of the feasible region of mixed integer linear programs with two equality constraints, two unrestricted integer variables and any number of nonnegative continuous variables. In particular, we prove that the closure of Type 2 triangle (resp. Type 3 triangle; quadrilateral) inequalities, are all within a factor of 1.5 of the integer hull, and provide examples showing that the approximation factor is not less than 1.125. There is no fixed approximation ratio for split or Type 1 triangle inequalities however. ∗Research of this author was supported in part by a Mellon Fellowship. †Research of this author was supported in part by NSF grant CMMI1024554 and ONR grant N00014-091-0033. ‡Research of this author was supported in part by a Discovery Grant from NSERC and ONR grant N0001412-1-0049. §Research of this author was supported in part by a Discovery Grant from NSERC and ONR grant N0001412-1-0049.