# Count this to the family of Job Shop Problem?

I will explain the problem in a simplified version.

• Three Tasks: $$T_1, T_2, T_3$$

• Four Machines: $$M_1, M_2, M_3, M_4$$

The machines $$M_2$$ and $$M_3$$ make the same processing, so they are parallel.

Tasks $$T_1$$ and $$T_3$$ must go through the machines in the following order: $$M_1 \to (M_2\, or\, M3) \to M_4$$.

Task $$T_2$$ is different, not all machines need to be run through. The order is $$M_1\to M_4$$.

My question is now if this counts to the family of job-shop problems? Because in books I always read that in the job-shop problem every task must be processed on every machine, but the order does not matter.

If this is not a job-shop problem, to which family of the shop problems does this explanation count? It would be very helpful if you can add the book/paper where this is defined, that I can obtain more info about it?

## 1 Answer

As per you have a specific route for each job, it sounds like a flexible job shop problem. In a practical situation, many times, a specific job maybe does not need to process in all stages.

For example, we have two jobs (A and B) and four stages. Job A should be processed in all four stages while job B need to be processed in the three stages. if you are willing to learn more about job shop models, the following links would be useful.

Indeed, a good reference is: