Scheduling of Re-Entrant Flow Shops

Abstract We propose and develop a scheduling system for a very special type of flow shop. This flow shop processes a variety of jobs that are identical from a processing point of view. All jobs have the same routing over the facilities of the shop and require the same amount of processing time at each facility. Individual jobs, though, may differ since they may have different tasks performed upon them at a particular facility. Examples of such shops are flexible machining systems and integrated circuit fabrication processes. In a flexible machining system, all jobs may have the same routing over the facilities, but the actual tasks performed may differ; for instance, a drilling operation may vary in the placement or size of the holes. Similarly, for integrated circuit manufacturing, although all jobs may follow the same routing, the jobs will be differentiated at the photolithographic operations. The photolitho-graphic process establishes patterns upon the silicon wafers where the patterns differ according to the mask that is used. The flow shop that we consider has another important feature, namely the job routing is such that a job may return one or more times to any facility. We say that when a job returns to a facility it reenters the flow at that facility, and consequently we call the shop a re-entrant flow shop. In integrated circuit manufacturing, a particular integrated circuit will return several times to the photolithographic process in order to place several layers of patterns on the wafer. Similarly, in a flexible machining system, a job may have to return to a particular station several times for additional metal-cutting operations. These re-entrant flow shops are usually operated and scheduled as general job shops, ignoring the inherent structure of the shop flow. Viewing such shops as job shops means using myopic scheduling rules to sequence jobs at each facility and usually requires large queues of work-in-process inventory in order to maintain high facility utilization, but at the expense of long throughput times. In this paper we develop a cyclic scheduling method that takes advantage of the flow character of the process. The cycle period is the inverse of the desired production rate (jobs per day). The cyclic schedule is predicated upon the requirement that during each cycle the shop should perform all of the tasks required to complete a job, although possibly on different jobs. In other words, during a cycle period we require each facility to do each task assigned to it exactly once. With this requirement, a cyclic schedule is just the sequencing and timing on each facility of all of the tasks that that facility must perform during each cycle period. This cyclic schedule is to be repeated by each facility each cycle period. The determination of the best cyclic schedule is a very difficult combinatorial optimization problem that we cannot solve optimally for actual operations. Rather, we present a computerized heuristic procedure that seems very effective at producing good schedules. We have found that the throughput time of these schedules is much less than that achievable with myopic sequencing rules as used in a job shop. We are attempting to implement the scheduling system at an integrated circuit fabrication facility.