Makespan ($C_{\max }={\max }_j{C}_j$)

The time at which all work in a scheduling instance has finished, equivalently the largest completion time measured from a common start. For divisible job sizes $t_i\ge 0$ and positive machine speeds $s_j$, when each machine's completion time is its total assigned size divided by its speed, the minimum makespan is ${\sum }_i{t}_i/{\sum }_j{s}_j$. The lower bound follows from total processing capacity; assigning the fraction $s_j/{\sum }_h{s}_h$ of each job to machine $j$ attains it.