Scheduling problem (one machine with parallel processing capability) Suppose there is a machine, which can hold at most m parts in parallel. There is also a production schedule with n > m jobs.
An operator now allocates at most m of the n jobs to the machine. He then proceeds to work on the parts consecutively, which takes him a part-specific process time t_n $\in \mathbb{Q}$. Additionally, when he starts working on a part, a part-specific "drying time" starts, which will take td_n $\in \mathbb{Q}$.
Only if all drying times and all processing times are completed, the parts can be removed and new parts can be allocated. In a more complex scenario, t_n and t_dn could both be stochastic. In the simpler case, both times are deterministic; then an overall processing time to_n = max(t_n, td_n) can be considered.
The question is now, how the total production duration for the entire schedule can be minimized: I am looking for possible approaches, not solutions.
 A: You can solve the problem via mixed integer linear programming as follows.  Let binary decision variable $x_{ib}$ indicate whether job $i$ is assigned to batch $b$, let binary decision variable $y_{ij}$ indicate whether job $i$ precedes (not necessarily immediately) job $j$, let $s_i \ge 0$ be the start time of job $i$, and let $z_b$ be the finish time of batch $b$.  The problem is to minimize $\sum_b z_b$ subject to linear constraints
\begin{align}
\sum_b x_{ib} &= 1 &&\text{for all $i$} \tag1\label1\\
\sum_i x_{ib} &\le m &&\text{for all $b$} \tag2\label2\\
x_{ib} + x_{jb} - 1 &\le y_{ij} + y_{ji} &&\text{for all $i<j$ and $b$} \tag3\label3\\
s_i + t_i - s_j &\le M_{ij}(1-y_{ij}) &&\text{for all $i\not=j$} \tag4\label4\\
s_i + \max(t_i, td_i) - z_b &\le M'_{ib}(1-x_{ib}) &&\text{for all $i$ and $b$} \tag5\label5
\end{align}
Constraint \eqref{1} assigns each job to exactly one batch.
Constraint \eqref{2} assigns at most $m$ jobs to each batch.
Constraint \eqref{3} enforces the logical implication $(x_{ib} \land x_{jb}) \implies (y_{ij} \lor y_{ji})$.
Big-M constraint \eqref{4} enforces the logical implication $y_{ij} \implies s_i + t_i \le s_j$.
Big-M constraint \eqref{5} enforces the logical implication $x_{ib} \implies s_i + \max(t_i,td_i) \le z_b$.
This compact formulation motivates a column generation formulation with a set partitioning master problem and one column per batch.
