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.

It is also important to note that the piecewise linear expressions in this example are convex and their sum needs to be minimized. Therefore, this part of the problem does not lead to a MIP formulation, but instead it gives rise to an LP. This advantage is detected automatically by ILOG CPLEX, and it does not introduce any integer variable to transform this part of the problem.