An instance consists of $n$ clients and $m$ days. Every client submits one job on every day: client $j$'s job on day $i$ has a processing time $p_{i,j} \ge 1$ and a due date $d_{i,j} \ge p_{i,j}$. The schedule is just-in-time, so that job occupies exactly the interval $(d_{i,j} - p_{i,j},\, d_{i,j}]$, and two jobs of the same day conflict if their intervals intersect. One machine is available on each day, so a schedule selects, for every day, a set of clients whose day's jobs are pairwise non-conflicting; the jobs of the clients left out are rejected that day.

Write $Z_{i,j}$ for the indicator that client $j$'s job is executed on day $i$. The objective is the fairness of the schedule, $\min_j \sum_i Z_{i,j}$: the decision problem $1 \mid \mathrm{rep} \mid \min_j \sum_i Z_{i,j}$ asks, given a fairness parameter $k$, whether some schedule serves every client on at least $k$ of the $m$ days. In the generalization $1 \mid k_j, \mathrm{rep} \mid \min_j \sum_i Z_{i,j}$ every client $j$ carries its own parameter $k_j$ and must be served on at least $k_j$ days.

Three restrictions of the instance recur. The processing times are day-independent if $p_{i,j} = p_j$ for all $i$, the due dates are day-independent if $d_{i,j} = d_j$ for all $i$, and the processing times are unit if $p_{i,j} = 1$ throughout.