In TEV minimization, we have introduced the big-M constraint

linking the continuous variable to the binary variable . Here, M should be a suitably large constant, such that the constraint is practically ineffective when  = 1. Choosing a huge Mis no harm, in principle, but it is a bad choice computationally. To see why, observe the geometry in Fig. 15.9. The feasible set consists of the origin (corresponding to = 0), and a segment of a verticalline (corresponding to  = 1). However, the continuous relaxation corresponds to a shaded triangle, below the line with slope M. The smaller the big-M, the tighter the LP bound.

Data From Fig. 15.9

Transcribed Image Text:

x < M8,