A job-shop problem with one additional resource type

We consider a job-shop scheduling problem with n jobs and the constraint that at most p < n jobs can be processed simultaneously. This model arises in several manufacturing processes, where each operation has to be assisted by one human operator and there are p (versatile) operators. The problem is binary NP-hard even with n = 3 and p = 2. When the number of jobs is fixed, we give a pseudopolynomial dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS). We also propose an enumeration scheme based on a generalized disjunctive graph, and a dynamic programming-based heuristic algorithm. The results of an extensive computational study for the case with n = 3 and p = 2 are presented.