I am trying to find any easy-to-implement algorithms for the offline scheduling of parallel Jobs comprising ordered tasks among workers to minimize makespan in the special case where the workers are unique in what they can do (rather than the typical case where workers can do any task but may take different times) subject to the constraint that a worker must finish a task before it can move onto another.
I am more concerned with ease of implementation than computational complexity as the number of workers, jobs, and tasks per job are pretty small (orders: ~10, <10, and 10-30 respectively).
The specific property of the agents being distinct in what they can do rather than how long they take to perform a task has made it hard for me to find an algorithm (or near algorithm for me to start from). When searching for algorithm , I have tried recasting this as a tiling problem when (as it's similar to stacking Gantt charts on top of each other) and have looked into how I would cast it into a graph problem to no avail.
The closest I've found so far have been dos Santos 2019, Spegal 2019, Schulz & Skutella 2002, but these require that I cast the problem as some machines taking infinite time for mismatched operations and account for other scheduling properties that are not applicable to this problem--and I do not know enough about these algorithms to know if setting them to bypassed values would break them.
I think what you're describing is known as the (inflexible) job-shop scheduling problem (with precedence ordering and non-preemptive scheduling). If you are looking for a low barrier to implementation, I would recommend an existing module like ortools. It's even defined in a manner similar to the example you provided.