Scheduling coupled tasks on parallel identical machines

Abstract In many applications in the context of patient appointment scheduling there are recurring tasks with fixed delays between them. These commonly referred to as coupled-task jobs. settings, each job consists two whereby second task must start processing after an exact time lag following completion first task. this paper, we introduce problem a set jobs on parallel identical machines objective function minimizing makespan. We study computational complexity general problem, well its special cases. prove that majority these problems (strongly) NP-hard. Nonetheless, provide optimal policy for settings consisting An important result our work includes showing existence $$(2-\varepsilon )$$ ( 2 - ε ) -approximation algorithm implies $$P=NP$$ P = N . The latter improves recently proposed bound open-shop counterpart well.