An instance consists of $n$ jobs and $m$ identical second-stage machines. Job $j$ has a preprocessing time $p_j \in \mathbb{N}$, a processing time $q_j \in \mathbb{N}$, a due date $d_j \in \mathbb{N}$ and a weight $w_j \in \mathbb{N}$. It is run in two operations, in this order and without preemption: a preprocessing operation of length $p_j$ on the single first-stage machine, and a processing operation of length $q_j$ on one of the $m$ identical second-stage machines. Job $j$ is completed just in time when its second operation finishes exactly at $d_j$, and the objective is to maximize the total weight of the just-in-time jobs. In the three-field notation the problem is $FF(1,m) \mid\mid \sum_j w_j Z_j$.

Just-in-time completion pins the second operation of $j$ to the interval $[s_j, d_j)$, where $s_j = d_j - q_j$; the first operation must therefore be finished by $s_j$, which acts as a deadline for it. Two jobs conflict when those two intervals overlap, and conflicting jobs cannot share a second-stage machine.

Since the objective counts only the just-in-time jobs, a solution is the set $Z$ of jobs completed just in time, and $Z$ is feasible when its jobs — and no others — admit a schedule completing every one of them exactly at its due date.