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Mengchu Zhou - One of the best experts on this subject based on the ideXlab platform.
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optimal one wafer Cyclic Scheduling of time constrained hybrid multicluster tools via petri nets
IEEE Transactions on Systems Man and Cybernetics, 2017Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:Scheduling a multicluster 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 the dynamic behavior of the tool. By this model, a schedule of the system is analytically expressed as a function of robots’ waiting time. Based on this model, this paper presents 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 determining the robots’ waiting time via simple calculation and thus are efficient. Examples are given to show the application and effectiveness of the proposed method.
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optimal one wafer Cyclic Scheduling and buffer space configuration for single arm multicluster tools with linear topology
Systems Man and Cybernetics, 2016Co-Authors: Liping Bai, Mengchu ZhouAbstract:This work studies the Scheduling problem of a single-arm multicluster tool with a linear topology and process-bound bottleneck individual tool. The objective is to find a one-wafer Cyclic schedule such that the lower bound of cycle time is reached by optimally configuring spaces in buffering modules that link individual cluster tools. A Petri net (PN) model is developed to describe the dynamic behavior of the system by extending resource-oriented PNs such that a schedule can be parameterized by robots’ waiting time. Based on this model, conditions are presented under which a one-wafer Cyclic schedule with the lower bound of cycle time can be found. With the derived conditions, an algorithm is developed to find such a schedule and optimally configure buffer spaces. The algorithm requires only simple calculation to set the robots’ waiting time and buffer size. Illustrative examples are presented to demonstrate the proposed method.
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schedulability and Scheduling analysis of dual arm cluster tools with wafer revisiting and residency time constraints based on a novel schedule
Systems Man and Cybernetics, 2015Co-Authors: Yan Qiao, Mengchu ZhouAbstract:Some wafer fabrication processes require a wafer to visit some processing modules in a cluster tool multiple times, leading to a wafer revisiting process. They may pose wafer residency time constraints, i.e., a wafer can stay in a module for a limited time after it is processed. Although techniques exist for Scheduling cluster tools with either wafer residency time constraints or wafer revisiting, it is much more challenging to schedule tools with both of them. Considering that atomic layer deposition is a typical wafer revisiting process, this paper intends to schedule a dual-arm cluster tool dealing with it. Based on the analysis of such a tool's properties, a novel Scheduling strategy called modified 1-wafer Cyclic Scheduling is derived. With this strategy, necessary and sufficient schedulability conditions are presented. If schedulable, highly efficient Scheduling algorithms are developed to obtain a feasible and optimal schedule together with a way to implement the obtained one. Illustrative examples are given to show the application of the proposed approach.
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optimal one wafer Cyclic Scheduling of single arm multicluster tools with two space buffering modules
Systems Man and Cybernetics, 2014Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer Cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer Cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method.
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Petri Net-Based Optimal One-Wafer Cyclic Scheduling of Hybrid Multi-Cluster Tools in Wafer Fabrication
IEEE Transactions on Semiconductor Manufacturing, 2014Co-Authors: Fajun Yang, Yan Qiao, Naiqi Wu, Mengchu ZhouAbstract:In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on Scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the Scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method.
Yan Qiao - One of the best experts on this subject based on the ideXlab platform.
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Polynomial approach to optimal one-wafer Cyclic Scheduling of treelike hybrid multi-cluster tools via Petri nets
IEEE CAA Journal of Automatica Sinica, 2018Co-Authors: Fajun Yang, Yan QiaoAbstract: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.
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optimal one wafer Cyclic Scheduling of time constrained hybrid multicluster tools via petri nets
IEEE Transactions on Systems Man and Cybernetics, 2017Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:Scheduling a multicluster 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 the dynamic behavior of the tool. By this model, a schedule of the system is analytically expressed as a function of robots’ waiting time. Based on this model, this paper presents 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 determining the robots’ waiting time via simple calculation and thus are efficient. Examples are given to show the application and effectiveness of the proposed method.
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schedulability and Scheduling analysis of dual arm cluster tools with wafer revisiting and residency time constraints based on a novel schedule
Systems Man and Cybernetics, 2015Co-Authors: Yan Qiao, Mengchu ZhouAbstract:Some wafer fabrication processes require a wafer to visit some processing modules in a cluster tool multiple times, leading to a wafer revisiting process. They may pose wafer residency time constraints, i.e., a wafer can stay in a module for a limited time after it is processed. Although techniques exist for Scheduling cluster tools with either wafer residency time constraints or wafer revisiting, it is much more challenging to schedule tools with both of them. Considering that atomic layer deposition is a typical wafer revisiting process, this paper intends to schedule a dual-arm cluster tool dealing with it. Based on the analysis of such a tool's properties, a novel Scheduling strategy called modified 1-wafer Cyclic Scheduling is derived. With this strategy, necessary and sufficient schedulability conditions are presented. If schedulable, highly efficient Scheduling algorithms are developed to obtain a feasible and optimal schedule together with a way to implement the obtained one. Illustrative examples are given to show the application of the proposed approach.
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optimal one wafer Cyclic Scheduling of single arm multicluster tools with two space buffering modules
Systems Man and Cybernetics, 2014Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer Cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer Cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method.
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Petri Net-Based Optimal One-Wafer Cyclic Scheduling of Hybrid Multi-Cluster Tools in Wafer Fabrication
IEEE Transactions on Semiconductor Manufacturing, 2014Co-Authors: Fajun Yang, Yan Qiao, Naiqi Wu, Mengchu ZhouAbstract:In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on Scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the Scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method.
Ignacio E Grossmann - One of the best experts on this subject based on the ideXlab platform.
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Optimal synthesis of multiproduct batch plants with Cyclic Scheduling and inventory considerations
2018Co-Authors: V. T. Voudouris, Ignacio E Grossmann, Carnegie Mellon University.engineering Design Research Center.Abstract:Abstract: "This paper addresses the problem of determining the optimal configuration and Cyclic operation of batch plants in which all the products require the same processing sequence. In particular, the problem can be stated as follows. Given are demands of a number of products, as well as technical information on the processing tasks (size factors, processing times, clean-up times) which are not restricted to a zero-wait policy. Given are also cost data for investment and product inventories, a list of candidate equipment and a list of candidate storage vessels with standard sizes. The problem then consists in determining the following items: number, type and size of equipment, as well as their allocation to one or multiple tasks and possible parallel operation; location and size of intermediate storage vessels; the length of the production cycle including the sequence of production of the products; levels of product inventories. The objective is to maximize the net present value. The major complication of this design problem lies in the many trade-offs that are involved, as for instance the merging of tasks versus its impact on the schedule, and length of production cycle versus inventory levels. By using a novel representation for Cyclic schedules and exact linearization schemes, it is shown that this problem can for [sic] formulated as a mixed- integer linear programming problem, and solved rigorously to global optimality. An efficient computational scheme is proposed for this purpose. Compared to the previous work by Birewar and Grossmann (1990), the proposed model provides a significant extension of the scope of the operational problem, while at the same time yielding an optimization problem that does not involve nonlinearities. Several example problems are presented to illustrate the capability of this method.
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simultaneous Cyclic Scheduling and control of tubular reactors parallel production lines
Industrial & Engineering Chemistry Research, 2010Co-Authors: Antonio Florestlacuahuac, Ignacio E GrossmannAbstract:In this work, we propose a simultaneous Scheduling and control optimization formulation to address both optimal steady-state production and dynamic product transitions in continuous multiproduct tu...
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dinkelbach s algorithm as an efficient method to solve a class of minlp models for large scale Cyclic Scheduling problems
Computers & Chemical Engineering, 2009Co-Authors: Fengqi You, Pedro M Castro, Ignacio E GrossmannAbstract:Abstract In this paper we consider the solution methods for mixed-integer linear fractional programming (MILFP) models, which arise in Cyclic process Scheduling problems. We first discuss convexity properties of MILFP problems, and then investigate the capability of solving MILFP problems with MINLP methods. Dinkelbach's algorithm is introduced as an efficient method for solving large-scale MILFP problems for which its optimality and convergence properties are established. Extensive computational examples are presented to compare Dinkelbach's algorithm with various MINLP methods. To illustrate the applications of this algorithm, we consider industrial Cyclic Scheduling problems for a reaction–separation network and a tissue paper mill with byproduct recycling. These problems are formulated as MILFP models based on the continuous time Resource-Task Network (RTN). The results show that orders of magnitude reduction in CPU times can be achieved when using this algorithm compared to solving the problems with commercial MINLP solvers.
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simultaneous Cyclic Scheduling and optimal control of polymerization reactors
Aiche Journal, 2007Co-Authors: Sebastian Terrazasmoreno, Antonio Florestlacuahuac, Ignacio E GrossmannAbstract:The simultaneous solution of the optimal sequencing and optimal dynamic transitions of two multigrade polymerization continuous stirred-tank reactors (CSTRs) is presented. The simultaneous formulation leads to a mixed-integer dynamic optimization (MIDO) problem. The profiles of the state variables during dynamic transitions are discretized using orthogonal collocation on finite elements, transforming the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The objective of this formulation is to maximize the profit of the manufacturing operation, considering polymer sales, inventory costs and transition costs. The transition cost term is determined by the duration of the transition stages and the manipulated variable profile during transitions. Two industrial reaction systems are used to analyze the optimal solution and compare it to other solutions obtained using different methods. Finally, a sensitivity analysis is carried out to describe the impact of changes in certain problem parameters. © 2007 American Institute of Chemical Engineers AIChE J, 2007
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simultaneous Cyclic Scheduling and control of a multiproduct cstr
Industrial & Engineering Chemistry Research, 2006Co-Authors: Antonio Florestlacuahuac, Ignacio E GrossmannAbstract:In this work, we propose a simultaneous Scheduling and control formulation by explicitly incorporating into the Scheduling model process dynamics in the form of differential/algebraic constraints. The formulation takes into account the interactions between Scheduling and control and is able to handle nonlinearities embedded into the processing system. The simultaneous Scheduling and control problems is cast as a mixed-integer dynamic optimization (MIDO) problem where the simultaneous approach, based on orthogonal collocation on finite elements, is used to transform it into a mixed-integer nonlinear programming (MINLP) problem. The proposed simultaneous Scheduling and control formulation is tested using three multiproduct continuous stirred tank reactors featuring difficult nonlinearities.
Fajun Yang - One of the best experts on this subject based on the ideXlab platform.
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Polynomial approach to optimal one-wafer Cyclic Scheduling of treelike hybrid multi-cluster tools via Petri nets
IEEE CAA Journal of Automatica Sinica, 2018Co-Authors: Fajun Yang, Yan QiaoAbstract: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.
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optimal one wafer Cyclic Scheduling of time constrained hybrid multicluster tools via petri nets
IEEE Transactions on Systems Man and Cybernetics, 2017Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:Scheduling a multicluster 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 the dynamic behavior of the tool. By this model, a schedule of the system is analytically expressed as a function of robots’ waiting time. Based on this model, this paper presents 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 determining the robots’ waiting time via simple calculation and thus are efficient. Examples are given to show the application and effectiveness of the proposed method.
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optimal one wafer Cyclic Scheduling of single arm multicluster tools with two space buffering modules
Systems Man and Cybernetics, 2014Co-Authors: Fajun Yang, Yan Qiao, Mengchu ZhouAbstract:A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer Cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer Cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method.
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Petri Net-Based Optimal One-Wafer Cyclic Scheduling of Hybrid Multi-Cluster Tools in Wafer Fabrication
IEEE Transactions on Semiconductor Manufacturing, 2014Co-Authors: Fajun Yang, Yan Qiao, Naiqi Wu, Mengchu ZhouAbstract:In a multi-cluster tool, there may be both single and dual-arm cluster tools. Such a multi-cluster tool is called hybrid multi-cluster tool. To operate such a multi-cluster tool, one needs to coordinate different types of robots for accessing the shared buffering modules. Aiming at finding a one-wafer periodic schedule such that the lower bound of cycle time can be reached, this paper conducts a study on Scheduling a hybrid multi-cluster tool with its bottleneck tool being process-bound. The tool is modeled by a kind of timed Petri net model. With this model, the Scheduling problem is reduced to determining the robots' waiting time. Then, the conditions under which a one-wafer periodic schedule exists such that the lower bound of cycle time can be reached are presented. Based on them, a closed-form algorithm is given to check whether such a one-wafer periodic schedule exists. If so, it is found via simple calculation. Examples are given to show the application of the proposed method.
Jose M Pinto - One of the best experts on this subject based on the ideXlab platform.
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global optimization for the Cyclic Scheduling and operation of multistage continuous plants
Industrial & Engineering Chemistry Research, 2004Co-Authors: A Alle, Jose M PintoAbstract:This work addresses the global optimization of the simultaneous problem of the Cyclic Scheduling and operation of multistage continuous plants. In this problem, production rates and yields are additional optimization variables for plant Scheduling. The representation proposed for this problem is a mixed-integer nonlinear programming (MINLP) model that has a nonconvex feasible region and a nonconvex objective function. To address nonconvexity, a spatial branch-and-bound global optimization algorithm is developed to solve the model. An illustrative example shows that the global approach is effectively able to yield a more profitable solution than a local optimization algorithm. Moreover, it is shown that modifications in the steps of the global optimization algorithm, such as preferential branching at a variable, can significantly improve its performance. Results also show that local optimization can provide very good estimates for the global solution when processing conditions have narrow variability range...
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a mathematical programming approach for Cyclic production and cleaning Scheduling of multistage continuous plants
Computers & Chemical Engineering, 2004Co-Authors: A Alle, Jose M Pinto, Lazaros G PapageorgiouAbstract:The objective of this paper is to address the Cyclic Scheduling of cleaning and production operations in multiproduct multistage plants with performance decay. A mixed-integer nonlinear programming (MINLP) model based on continuous time representation is proposed that can simultaneously optimize the production and cleaning Scheduling. The resulting mathematical model has a linear objective function to be maximized over a convex solution space thus allowing globally optimal solutions to be obtained with an outer approximation algorithm. Case studies demonstrate the applicability of the model and its potential benefits in comparison with a hierarchical procedure for the production and cleaning Scheduling problem.
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optimal Cyclic Scheduling of multistage continuous multiproduct plants
Computers & Chemical Engineering, 1994Co-Authors: Jose M Pinto, Ignacio E GrossmannAbstract:Abstract This paper addresses the problem of optimizing Cyclic schedules of multiproduct continuous plants that consist of a sequence of stages each involving one production line that are interconnected by storage tanks. The problem involves a combinatorial part (sequencing of products) and a continuous part (duration of production runs and inventory levels). The problem is formulated as a large scale mixed-integer nonlinear program (MINLP) model that involves nondifferentiabilities in the inventory levels for the storage tanks. Binary variables and mixed-integer constraints are used to remove these nondifferentiabilities. A solution method based on variants of the generalized Benders decomposition and outer approximation is proposed for this Scheduling problem. The method consists of an MINLP subproblem in which cycle times and inventory levels are optimized for a fixed sequence, and an MILP master problem that determines the optimal sequence of production. Examples are presented to compare the proposed decomposition method with the direct solution of the MINLP using an augmented penalty version of the outer-approximation method. The results show that the computational requirements can be greatly reduced in problems involving several hundred 0–1 variables, and several thousand continuous variables and constraints.
