Job Scheduling at Cascading Machines

Abstract

We consider the serial batching scheduling problem in which a group of machines can process multiple jobs continuously to reduce the processing times of the second and subsequent jobs. The maximum batch size is finite. Since all jobs in the same batch are loaded and unloaded simultaneously, a completed job has to wait for the others. We examine how to schedule all jobs to minimize the total completion time. If the batch size is only one, i.e., a single job per batch, the total processing time will be longer, since no reduction in processing time is possible. As a consequence, the total completion time will also be longer. On the other hand, if the batch size is large, the total completion time can be large. Each job has to wait until all jobs in the same batch are completed. We identify several optimality properties of the optimal batching sequence. These properties are used to develop a dynamic programming algorithm to optimize the batching sequences efficiently. The complexity of the proposed method depends only on the maximum batch size and the number of jobs. The improvement achieved with the proposed method when compared with two other batching rules is illustrated using two practical applications. Note to Practitioners — Machines with job cascading (or cluster tools) are commonly seen in semiconductor manufacturing processes. While meeting production move targets is a common goal for the nondelayed jobs, catching up with the schedule is an important task for the delayed jobs to achieve higher customer service level. From the viewpoint of scheduling, reducing the delay is equivalent to reducing completion time. Hence, we propose scheduling algorithms to reduce the completion time by taking advantage of the special structure of a cascading machine. In contrast to existing scheduling theory, the proposed algorithm can be efficient due to the small maximum batch size of real cascading machines. In addition to the theoretical contributions, this paper aims at solving practical problems through a rigorous approach. The finding and insight from this paper can be used to enhance shop floor control in a semiconductor fab.