Noncyclic Scheduling for Timed Discrete-Event Systems With Application to Single-Armed Cluster Tools Using Pareto-Optimal Optimization

Cluster tools, each of which consists of multiple processing modules, one material handling robot, and loadlocks, are widely used for wafer fabrication processes, such as lithography, etching, and deposition. There have been many approaches and algorithms for cyclic scheduling of cluster tools in which the robot repeats a specified sequence for processing identical wafers. However, the lot order size has recently been decreasing due to the larger wafer size and circuit width reductions. In modern fabs, each wafer lot can have different flow patterns and process times for the same process step, and heterogeneous lots are processed consecutively in a tool. Even some tools in a fab have idle time waiting for wafer lots depending on the work-in-process fluctuations. Such different wafer lots and frequent tool state changes cannot be handled with cyclic scheduling methods, and accordingly noncyclic scheduling methods for such cases are required. Therefore, we develop an efficient branch and bound (B&B) procedure for noncyclic scheduling problems of cluster tools to minimize the makespan. Since a timed Petri net (TPN) is known for its powerful modeling ability and analysis capability, the algorithm is developed based on a TPN. We verify the efficiency of the B&B procedure with various cluster tool scheduling problems.

Scheduling of time-constrained single-arm cluster tools with purge operations in wafer fabrications

The primary objective of maintenance tasks for manufacturing system is to assurance the quality of the produced work-in-process (WIP) and the final product. With the continuous improvement of system performance and increasingly complex composition structure, the probability of failure of the entire manufacturing system is increasing rapidly, meanwhile the maintenance cost and difficulty also increase. In order to comprehensively optimize the maintenance efficiency and effect of the manufacturing system, this paper introduces Quality maintenance principle of Total Productive Maintenance (TPM) theory into the maintenance optimization of the manufacturing system, and establishes a quality maintenance model based on mission reliability and Dynamic Bayesian network. As the quality maintenance principle and mission reliability connotation are expounded regarding manufacturing system. The mission reliability of manufacturing system is established by using the Dynamic Bayesian network, and a TPM oriented quality maintenance approach based on mission reliability for manufacturing system is proposed. Proposed approach is verified by an example. The final results show that the proposed approach can guarantee the healthy operation state of the manufacturing system and the reliability of the manufactured products to a certain extent.

Joint production and preventive maintenance controls for unreliable and imperfect manufacturing systems

In this paper, we develop a multi-objective model to optimally control the lead time of a manufacturing system, using goal attainment method. The manufacturing system is modelled as a new queueing system based on the failure rate of products, in which the products may have quality problems and need to be repaired in each service station. It is assumed that the product order arrives according to a Poisson process. In each service station, there is only one server (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The maintenance time of manufacturing and assembly operations is exponentially distributed. By using the total probability decomposition and Markov process method, the Queue Length Distribution, the recursion expression of the equilibrium distribution and the mean waiting time are obtained. Then, we develop a multi-objective optimal control problem, in which the average lead time, the maintenance costs and the operating costs of the system per period are minimized using goal attainment method.

Proposal for a Dynamic Scheduling Architecture and Method Using an Holonic Approach

As wafer circuit widths shrink down, wafer fabrication processes require stringent quality control. Therefore, fabs recently tend to clean a chamber after processing each wafer, in order to remove chemical residuals within the chamber. Such chamber cleaning, called purge operation, increases scheduling complexity in robotized cluster tools. In this paper, we examine scheduling problems of single-armed cluster tools with purge operations for series-parallel chambers. By extending the wellknown backward sequence, we propose a backward(z) sequence that allows partial loading for parallel chambers, where vector z specifies how many chambers zi of each process step i are kept empty for cleaning. We then propose a way of finding optimal vector z* and identify when backward(z*) achieves the minimum cycle time among all possible sequences. We present experimental results on the accuracy of backward(z*).

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

A two-level hedging point policy for controlling a manufacturing system with time-delay, demand uncertainty and extra capacity

Petri net (PN) is a classical tool for modeling, simulation, and analysis. With the emergence of distributed manufacturing system (DMS), PN has been evolved into different forms such as colored PN (CPN) and timed PN (TPN). To fulfill the practical requirements, CPN has been extended to a larger and more complex model. Meanwhile, DMS becomes an important issue for industry, and how to model a complex manufacturing network for better throughput needs further investigation. A simple single type of PN only cannot fulfill all contemporary requirements at the same time. This paper proposes a new concept for a new PN-hierarchical timed CPN (HTCPN), which can be a powerful tool for modeling, simulation, and analysis for current large complex distributed manufacturing system. This paper presents a general structure of DMS and uses HTCPN to model the manufacturing system as discrete event with dynamic behavior. The proposed approach shows superiority on modeling large complex manufacturing system as it represents the material flow and transitions clearly and provides overview and detailed description for DMS.

Semiconductor production scheduling and industrial economic coordination based on deep learning and heat loss optimization

We present a scheme for dissipatively preparing bipartite Knill–Laflamme–Milburn (KLM) entangled state in a neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the coherent population trapping, is actively exploited to engineer a steady KLM state from an arbitrary initial state. Instead of commonly used antiblockade dynamics of two Rydberg atoms, we particularly utilize the Rydberg–Rydberg interaction as the pumping source to drive the undesired states so that it is unnecessary to satisfy a certain relation with laser detuning. The numerical simulation of the master equation signifies that both the fidelity and the purity above 98% is available with the current feasible parameters, and the corresponding steady-state fidelity is robust to the variations of the dynamical parameters.

The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful resource for quantum information processing [Nature409, 46 (2001)]. For atomic KLM states, several schemes have been put forward based on the time-dependent unitary dynamics, but the dissipative generation of these states has not been reported. This work discusses the possibility for creating different forms of bipartite KLM states in neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the Rydberg antiblockade mechanism, is actively exploited to engineer a steady KLM state from an arbitrary initial state. The numerical simulation of the master equation signifies that a fidelity above 99% is available with the current experimental parameters.

Density matrix of a quantum field in a particle-creating background

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications