I think I have some special kind of Job Shop Problem lying at hand which I'd like to solve, however I am unsure how to correctly define it and therefore cannot search for appropriate references in order to implement adequate algorithms.
Assume two machines of type A and four machines of type B. Machines of type A can process all products, but only one product at a time. Machines of type B can process only a specific type of product but can therefore process two of the same kind at once (it is possible to process only one however as well). A product needs to be processed several times by machines of type A and B in a specific order, depending on its type. Assume I know the processing plan for each product, i.e. I know beforehand how many times and in which order a product will visit A and B.
Include scheduled donwtimes / capacities of the machines. Find an optimal schedule, where optimal may refer to either minimum total completion time or minimum completion time of some prioritized product.
What kind of problem lies at hand? I have heard read about flexible job shop problems with recirculation, but I am not 100% sure this is what i should look further into.
In addition, I am looking for references which give some examples of applied solutions to basic and advanced problems. The ones I have found so far are very theoreitcal and focused on algorithm complexity and less on application to real world problems.