A closed single-server system is considered in which n items are scheduled to circulate at a fixed period. Each service is recognizable and is scheduled for its individual point of time; it is non-preemptive and its length depends only on which item is being served. Aberrating from this desired schedule, some of the items start out with delays. While an item is delayed, the time between a departure it makes from the server and its next arrival at the server is shortened by an item-specific parameter. The aim is to recover the regular schedule as early as possible, or minimizing the sum of delays on services. All services must be executed even if delayed. A greedy algorithm for a tractable subproblem is given. The overall problem is proved Σ2-hard; some subproblems are proved NP-hard. For one of the latter, an approximation algorithm is given whose performance ratio approaches one if the maximum delay is large enough relative to other parameters. It is proved that without this natural restriction, there can be no algorithm with asymptotic performance ratio one.
