Off‐line scheduling with forbidden zones

In various manufacturing and computing environments there may be certain time intervals, during which processing may continue but may not be initiated. We examine the problem of off‐line scheduling in the presence of such forbidden zones. The problem is closely related to a one‐dimensional open‐end bin packing problem. We prove that the decision version of the problem is strongly NP‐complete and then establish bounds on the asymptotic performance ratio of an $O(n\log n)$ approximation algorithm for a special case, and test it numerically. We present a further heuristic for a non‐regular case and test it empirically.