No-Wait Open Shop Scheduling

No-wait schedules model a lack of intermediate storage to store jobs between operations or a lack of buffer for optical messages in optical networks. No-wait open shop scheduling does not rule out preemptions per se. The optimal preemptive and non-preemptive no-wait schedules may differ. We prove that preemptive no-wait scheduling to minimize makespan is NP-hard in the strong sense for two machines. We show polynomial-time tests to check whether optimal makespan is C max ≤ 3 $$C_{\max }\leq 3$$ or C max ≤ 4 $$C_{\max }\leq 4$$ for no-wait open shops. The existence of a polynomial-time test for C max ≤ 5 $$C_{\max }\leq 5$$ is an open question even for 0-1 operations. We characterize instances with negative and affirmative answer for the last problem. The problem with optimal makespan C max ≤ 6 $$C_{\max }\leq 6$$ is NP-hard in the strong sense even for open shops with all jobs of length 3 and each machine workload 6. This implies that PTAS for no-wait makespan minimization does not exist unless P = NP. A PTAS, however, exists for two-machine no-wait makespan minimization. We show how to obtain no-wait schedules from cyclic compact schedules to further exploit the results of Chap. 9 . We argue that the existing optimization and approximation algorithms for no-wait open shop scheduling have been developed under assumption that the operations are non-preemptive. Therefore, there is a room for research on the preemptive case.