Let $C_j$ denote the completion time of job $j$. The objective field has the values

• makespan, $C_{\max} = \max_j C_j$,
• maximum lateness, $L_{\max} = \max_j (C_j - d_j)$,
• total completion time, $\sum_j C_j$,
• total weighted completion time, $\sum_j w_j C_j$,
• total tardiness, $\sum_j T_j$ with $T_j = \max(0, C_j - d_j)$,
• total weighted tardiness, $\sum_j w_j T_j$,
• number of late jobs, $\sum_j U_j$ with $U_j = 1$ if $C_j > d_j$ and $U_j = 0$ otherwise,
• weighted number of late jobs, $\sum_j w_j U_j$,
• number of jobs that are not just in time, $\sum_j (1 - Z_j)$ with $Z_j = 1$ if $C_j = d_j$ and $Z_j = 0$ otherwise, and its weighted version $\sum_j w_j (1 - Z_j)$,
• total flow time, $\sum_j F_j$ with $F_j = C_j - r_j$ for the release date $r_j$, and its weighted version $\sum_j w_j F_j$,
• maximum flow time, $F_{\max} = \max_j F_j$, and its weighted version $\max_j w_j F_j$.

Maximizing the number of jobs that are on time, or just in time, is minimizing the number of jobs that are not.

Two values restrict the due dates: total weighted tardiness with a common due date, $d_j = d$, and the weighted number of late jobs with due dates at most $k$ after the release dates, $d_j \le r_j + k$. Each is a special case of the unrestricted value, and a smaller $k$ of a larger one.

A value carries weights $w_j$ exactly if it is weighted and due dates $d_j$ exactly if it measures lateness, tardiness or being just in time. The makespan is the maximum lateness with $d_j = 0$; the maximum over an empty set of jobs is taken to be $0$. The four values measuring completion time or tardiness are the single expression $\sum_j w_j \max(0, C_j - d_j)$, with $w_j = 1$ where weights are absent and $d_j = 0$ where due dates are absent; the two values counting late jobs are $\sum_j w_j U_j$ with the same convention for the weights.

A value is a special case of another value of the same kind that carries at least the same data.

Theorem. Over every kernel, the objective field is sound.