Optimal One-Wafer Cyclic Scheduling of Single-Arm Multicluster Tools With Two-Space Buffering Modules

A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots’ waiting time. Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.

Scheduling of multicluster tools has received much attention due to its complexity of interaction among cluster tools. A cluster tool comprises several modules such as processing modules, a transfer module with a single or dual-armed handling robot, and loadlock modules. A multicluster tool comprises two, three, or more cluster tools that are interconnected with each other. In this paper, we propose a deadlock prevention policy for noncyclic scheduling of dual-armed multicluster tools. The proposed deadlock prevention policy is effective for generating an efficient schedule for two or three-connected multicluster tools with a single or a dual-path flow. This is proven by analyzing the strict minimal siphon of the Petri net model. The performance of the proposed method is compared with that of a maximal permissible deadlock prevention policy. The results demonstrate that the proposed method is computationally efficient for larger state spaces and more suitable than conventional deadlock prevention policies for generating effective schedules for noncyclic scheduling of multicluster tools. Note to Practitioners —Scheduling of multicluster tools has recently attracted attention in the growing semiconductor manufacturing industry. Most conventional studies on multicluster tools focus on cyclic scheduling to minimize cycle time with swap strategy. The challenge addressed by this paper is to derive a deadlock-free schedule for multicluster tools with noncyclic operations. We propose a simple deadlock prevention policy that can be applied to large-scale timed Petri net (PN) model of general multicluster tools without enumeration of siphon computations or solution of mixed integer programming. A timed PN model is developed for noncyclic operations of dual-armed multicluster tools with a dual ath. The computational results show that the approximately 10% of the total throughput of the proposed method is better than those of the conventional methods. It enables more efficient operations for noncyclic scheduling under transient periods including cleaning operations.

Scheduling a multi-cluster tool with wafer residency time constraints is highly challenging yet important in ensuring high productivity of wafer fabrication. This paper presents a method to find an optimal one-wafer cyclic schedule for it. A Petri net is developed to model its dynamic behavior. By using this model, its schedule is found and analytically expressed as a function of robots' waiting time. In addition, this work establishes the necessary and sufficient conditions under which a feasible one-wafer cyclic schedule exists. Then, it gives efficient algorithms to find such a schedule that is optimal. These algorithms require one to determine the robots' waiting time via simple calculation and thus are efficient.

It is a great challenge to find an optimal one-wafer cyclic schedule for a single-arm multicluster tool that is widely adopted in semiconductor fabrication. Aiming to tackle this significant problem, an optimal scheduling strategy is determined first for each individual tool under the condition that the bottleneck individual tool is transport-bound. Then, by developing a Petri net model with robot waiting being explicitly described to reveal the properties of the entire system, this paper shows that to schedule such a tool optimally is to allocate the robot waiting time properly. Then, this paper presents the necessary and sufficient conditions for the existence of an optimal one-wafer cyclic schedule. Thereafter, an efficient algorithm is developed to check the given conditions and find such a schedule efficiently if existing. Finally, two industrial examples are used to verify that the proposed method is applicable and effective.

Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such singlerobot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for singlerobot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

Cyclic scheduling and operation of a residency time- constrained single-arm cluster tool with failure-prone process modules are highly challenging. In some cases, when a fail- ure occurs, there still exists a feasible cyclic schedule for the performance-degraded tool. In other cases, such a schedule no longer exists. For the latter, it is highly desired to respond to a process module failure properly such that the tool can continue working and the wafers in the tool can be completed in a feasi- ble way. This work is the first one to study this important issue. The idea is to apply Petri nets to describe the dynamic behav- ior of a single-arm cluster tool. With the developed Petri net model, this paper formulates failure response policies to control the cluster tool such that it can keep working without violat- ing any residency time constraint. The failure response policies are implemented via efficient real-time control laws. Illustrative examples are presented to show their usage. Index Terms—Wafer fabrication, Cluster tools, Petri net, Scheduling, Failure response.

Artificial neural networks (ANN's) are highly parallel and distributed computational structures that can learn from experience and perform inferences. Petri nets, on the other hand, provide an effective modeling framework for distributed systems. The basic concepts of Petri net are utilized to develop ANN-like multilayered Petri net architectures of distributed intelligence having learning ability. A Petri net model of single neuron is presented. A two-layer Petri net model-neural Petri net (NPN)-that uses this neuron model as a building block is described. A new class of Petri nets called the fuzzy neural Petri net (FNPN) is defined. The FNPN can be used for representing a fuzzy knowledge base and for fuzzy reasoning. Some application examples for the two Petri net based models are given. >

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

ABSTRACTTo improve the efficiency of wafer fabrication, this work addresses the scheduling and control problems of mixed-processing with multiple wafer types in cluster tools. Then, based on a developed Petri net (PN) model, it presents a general model for cluster tools with multiple wafer types and the conventional swap strategy. By analyzing the coordination mechanism between wafers processing and robot tasks, necessary and sufficient conditions are established to check the schedulability of the system that is operated by using the conventional swap strategy. If the system is not schedulable checked by such schedulability conditions, a constraint-guided heuristic algorithm and a conflicts-avoiding algorithm are developed to obtain a reasonable schedule. Finally, illustrative examples are presented to show the applications of the proposed method.

In this work, a novel hybrid modeling approach for HVAC control system design in Intelligent Buildings is introduced. In order to achieve building system integration, a characterization of HVAC system as hybrid is required. The proposed approach is a top-down modeling method based on Petri net. Starting from abstract models designed using the Production Flow Schema, Petri net based models are built by successive refinements. The discrete part of the system is modeled using Place-Transition Petri nets and the continuous part is modeled using differential equation systems. The interface between these two parts is provided by Differential Predicate Transition Petri nets.

A PN-based approach to the high-level synthesis of digital systems

The main challenge in scheduling multi-cluster tools in semiconductor manufacturing is the interactions among clusters. These interactions create a k-unit optimal production that do not exist in single-cluster tools. This paper analyzes optimal scheduling of k-unit cycle production of multi-cluster tools with single-blade robots. A resource-based method is used to analytically derive closed-form expressions for the minimal cycle time of a multi-cluster tool. Conditions for decoupling multi-cluster tools and optimality conditions for the widely used pull schedule are also presented. An example from industry production is used to illustrate the derived formula and decoupling conditions.