ILOG CPLEX 11.0 User's Manual > Discrete Optimization > Early Tardy Scheduling > Transforming the Problem

When ILOG CPLEX extracts disjunctive constraints and piecewise linear functions, it transforms them to produce a MIP with linear constraints and possibly SOS constraints over integer or continuous variables. The tightness of the transformation depends on the bounds set on the variables.

In this example, the Horizon is set to 10000, but if you have information about your problem that indicates that a good or even optimal solution exists with a tighter horizon (say, 2000 instead) then the linear formulation of disjunctions will be tighter with that tighter horizon.

That kind of tightening often leads to a better lower bound at the root node and to a reduction of the solving time.