On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation

In Speakman and Lee (Math Oper Res 42(4):1230-1253, 2017), we analytically developed the idea of using volume as a measure for comparing relaxations in the context of spatial branch-and-bound. Specifically, for trilinear monomials, we analytically compared the three possible double-McCormick relaxations with the tight convex-hull relaxation. Here, again using volume as a measure, for the convex-hull relaxation of trilinear monomials, we establish simple rules for determining the optimal branching variable and optimal branching point. Additionally, we compare our results with current software practice.