Unit Penalty (Interval Scheduling)

Definition

Unit Penalty $U_j$

The unit penalty $U_j$ records whether job $j$ misses its due date:

$$U_j=1[C_j>d_j]=\{\begin{array}{ll}1& \text{if }{C}_j>d_j,\\ 0& \text{otherwise.}\end{array}$$

Objective

The objective ${\sum }_j{U}_j$ minimises the number of late jobs. Equivalently, it maximises the number of jobs completed on time.