The parameters in which the zoo states results, as functions of the instances.

On the operations family and the batching family: the number $n$ of jobs, the number $m$ of machines, the largest processing time $p_{\max}$ and weight $w_{\max}$, the numbers $\#p$, $\#r$, $\#w$, $\#d$ of distinct processing times, release dates, weights and due dates, the total weight $W$ and the total processing time $P$. The processing time of an operation is its time on the first machine, as in the field of processing times, and that of a job the sum over its operations. A weight is $1$ and a due date $0$ when the objective has none.

On the operations family also:

• the number of kinds of machines (Knop and Koutecký): machines of one kind have the same processing time for every operation, so this is the number of distinct columns of the matrix $(p_{ij})$;
• the rank of that matrix over the rationals (Chen, Marx, Ye and Zhang);
• $q_{\max}$, the largest processing time of the last operation of a job (and the predicate that every job has a last operation of positive length), and $\chi$, the largest number of jobs whose last operations, ending at their due dates, overlap at one instant — for jobs completed just in time the intervals $[d_j - q_j, d_j)$ (Heeger, Hermelin, Itzhaki, Schieber and Shabtay; $\omega$ there);
• the largest communication delay $c$;
• the speed ratio $s_{\max}/s_{\min}$ of uniform machines, the least over the speeds that represent the instance;
• the width of the precedence order, the largest number of pairwise incomparable jobs;
• the number $\tau$ of forbidden times, the instants at which no job may start or end;
• $n_{\max}$, the largest number of operations of a job;
• the number $g$ of batches into which batch setups group the jobs;
• with the threshold $D$: the gap $D - \mathrm{LP}$ to the optimum $\mathrm{LP}$ of the linear relaxation [CS-LP] of the vertex-cover formulation of Correa and Schulz, as in Ambühl and Mastrolilli (2009). With $P$ the transitive closure of the precedence relation and $i \parallel j$ for different jobs related in neither direction, it minimizes $\sum_j p_jw_j + \sum_{(i,j) \in P} p_iw_j + \sum_{i \parallel j} \delta_{ij}p_iw_j$ over $\delta \ge 0$ with $\delta_{ij} + \delta_{ji} \ge 1$ for $i \parallel j$, $\delta_{ik} + \delta_{kj} \ge 1$ for $(i, j) \in P$, $j \parallel k$, $k \parallel i$, and $\delta_{il} + \delta_{kj} \ge 1$ for $(i, j), (k, l) \in P$, $j \parallel k$, $l \parallel i$. Its optimum equals those of the relaxations of Potts and of Chudak and Hochbaum (their Theorems 2 to 4); the parameter is $\lceil D - \mathrm{LP} \rceil$, and $0$ when negative;
• with the threshold $D$: the time window of job $j$ runs from its release date to its deadline, and also ends at $D$ for the makespan and at $d_j + D$ for the maximum lateness, since the decision version asks for that. The pathwidth $\mathrm{pw}(I)$ of the interval graph of the windows is the largest number of windows containing one instant, minus one, and the maximum slack is the largest window length minus processing time (Hanen and Munier Kordon). A window without end has length $0$ here; it occurs only without deadlines and with another objective.

On the batching family also $\mathrm{pw}(I)$ and the maximum slack, with the same windows.

On single-machine scheduling with rejection: $n$, $\#p$, $p_{\max}$, the number $\#e$ of distinct rejection costs, the largest rejection cost $e_{\max}$, and the number of accepted jobs, read as an instance quantity: the least number of jobs a feasible solution accepts, $n$ minus the most jobs whose rejection costs fit the budget. On $P \mid\mid C_{\min}$: $n$ and $m$.