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(nlogn) approximation algorithm for a special case, and test it numerically. We present a further heuristic for a non-regular case and test it empirically.