Abstract:in Wiley Online Library (wileyonlinelibrary.com).Multistage material handling processes are broadly used for manufacturing various products/jobs, where hoists are commonly used to transport inline products according to their processing recipes. When multiple types of jobs with different recipes are simultaneously and continuously handled in a production line, the hoist movement scheduling should be thoroughly investigated to ensure the operational feasibility of every job inline and in the meantime to maximize… Show more
“…Some studies have considered a time window constraint including a no-wait time constraint in a cyclic schedule [20]- [29]. There have also been a few studies on real-time hoist scheduling [30], [31]. Lee et al [2] develop cyclic scheduling methods for a wet station.…”
We examine a non-cyclic scheduling problem of a wet station that performs cleaning processes for removing residual contaminants on wafer surfaces. Several chemical and rinse baths, and multiple robots for transporting jobs are linearly combined in a wet station. A wet station in a fab tends to have different types of jobs. Therefore, it is realistic to consider non-cyclic release of jobs into a wet station. We therefore examine a non-cyclic scheduling problem of a wet station that determines the task sequence of each robot so as to minimize the makespan of a given sequence of different jobs. We develop an efficient branch and bound procedure by examining the scheduling problem. To do this, we first develop a Petri net model for the scheduling problem. By identifying deadlock prevention conditions from the Petri net model, we eliminate partial solutions in advance that eventually will lead to a deadlock. By examining the feasible transition firings or state transition behavior of the Petri net model, we branch only feasible partial solutions or nodes that correspond to feasible state transitions or transition firings. We also develop a tight lower bound based on the bottleneck workload of the baths. We prove computational efficiency of the branch and bound procedure for practical problems.
Note to Practitioners-A wet station performs wafer cleaning processes for removing residual contaminants after a wafer fabrication process. The wafer cleaning process approximately accounts for 30% of the whole wafer fabrication process and is critical to wafer quality. A wet station consists of several cleaning and rinsing baths and several lot-handling robots, and processesmultiple different jobs concurrently. The jobs often require reentrant flows and have strict time constraints while there is no intermediate buffer. Due to such high complexity, the utilization of the baths and the throughput rate tend to be very low. For example, fabs process only two or three jobs concurrently, while the number of baths is eight or more. We developed an efficient scheduling method that can solve practical scheduling problems for wet stations and increase the throughput and utilization rate more than twice. The whole solution procedure from Petri net modeling for a given tool configuration and job flow data to finding optimal robot task sequences and schedules can be automated.Index Terms-Branch and bound algorithm, cluster tool, deadlock, no-wait, Petri nets, wet station.
“…Some studies have considered a time window constraint including a no-wait time constraint in a cyclic schedule [20]- [29]. There have also been a few studies on real-time hoist scheduling [30], [31]. Lee et al [2] develop cyclic scheduling methods for a wet station.…”
We examine a non-cyclic scheduling problem of a wet station that performs cleaning processes for removing residual contaminants on wafer surfaces. Several chemical and rinse baths, and multiple robots for transporting jobs are linearly combined in a wet station. A wet station in a fab tends to have different types of jobs. Therefore, it is realistic to consider non-cyclic release of jobs into a wet station. We therefore examine a non-cyclic scheduling problem of a wet station that determines the task sequence of each robot so as to minimize the makespan of a given sequence of different jobs. We develop an efficient branch and bound procedure by examining the scheduling problem. To do this, we first develop a Petri net model for the scheduling problem. By identifying deadlock prevention conditions from the Petri net model, we eliminate partial solutions in advance that eventually will lead to a deadlock. By examining the feasible transition firings or state transition behavior of the Petri net model, we branch only feasible partial solutions or nodes that correspond to feasible state transitions or transition firings. We also develop a tight lower bound based on the bottleneck workload of the baths. We prove computational efficiency of the branch and bound procedure for practical problems.
Note to Practitioners-A wet station performs wafer cleaning processes for removing residual contaminants after a wafer fabrication process. The wafer cleaning process approximately accounts for 30% of the whole wafer fabrication process and is critical to wafer quality. A wet station consists of several cleaning and rinsing baths and several lot-handling robots, and processesmultiple different jobs concurrently. The jobs often require reentrant flows and have strict time constraints while there is no intermediate buffer. Due to such high complexity, the utilization of the baths and the throughput rate tend to be very low. For example, fabs process only two or three jobs concurrently, while the number of baths is eight or more. We developed an efficient scheduling method that can solve practical scheduling problems for wet stations and increase the throughput and utilization rate more than twice. The whole solution procedure from Petri net modeling for a given tool configuration and job flow data to finding optimal robot task sequences and schedules can be automated.Index Terms-Branch and bound algorithm, cluster tool, deadlock, no-wait, Petri nets, wet station.
“…Zhao et al have recently developed an interesting mixed‐integer linear programming (MILP) model for real‐time hoist rescheduling in a multistage electroplating line. The system consists of a number of processing units and a single material handling hoist.…”
Section: Introductionmentioning
confidence: 99%
“…When one or multiple jobs arrive, an optimal hoist reschedule should be determined based on the current state of the jobs inline and the hoist. The objective is to minimize the time span required for processing all the jobs inline while satisfying the following three types of constraints: Hoist movement constraints. The release time for the hoist to drop any job in any unit and its corresponding lift time upon completion of processing are well defined so that the hoist is not required to handle more than one job at any time.Unit processing capacity constraints.…”
SignificanceZhao et al. have recently developed an interesting mixed-integer linear programming (MILP) model for real-time hoist rescheduling in a multistage electroplating line. In this letter, we reformulate the hoist movement constraints in their model. Due to this reformulation, we obtain a more compact MILP model in terms of the number of constraints and variables. Computational experiment shows that our improved model can be solved several times faster than Zhao et al.'s model. Such a reduction in computation time is significant in a real-time hoist rescheduling context.
This paper deals with the single-hoist and multiple-products scheduling problem. Although a mixed integer linear programming model for the problem was developed earlier, a branch-and-bound based heuristic algorithm is proposed in this paper to solve the big-size problems in real situation. The algorithm is capable of handling problems incorporating different product types, jobs in the process, and tank capacities. Using a small example problem the procedure of the heuristic algorithm is explained. To assess the performance of the heuristic we generate a bigger example problem and compare the results of the algorithm proposed in this paper with the optimal solutions derived from the mathematical model of earlier research. The comparison shows that the heuristic has very good performance and the computation time is sufficiently short to use the algorithm in real situation. †
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.