Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs SRC/ISMT FORCe: Factory Operations Research Center Task NJ-877 Michael Fu, Director Emmanuel Fernandez Steven I. Marcus Atlanta, GA, Oct. 21-22, 2003 1 SRC/ISMT Factory Operations Research Center CONTENTS 1. Project Overview: Michael Fu 2. Summary of Completed Tasks: Emmanuel Fernandez • • Interaction with Industry Deliverables • • • • • • • Models, Algorithms, and Software Tools Simulation Case Studies Documentation submitted to SRC website Other documentation Software implementation: PMOST (Jose Ramirez) Integration with fab schedulers: collaboration with ASU Students trained 3. Summary of Doctoral and Master Theses: Students 4. Continuing and Future Research: Emmanuel Fernandez 5. Conclusions: Michael Fu 2 SRC/ISMT Factory Operations Research Center Summary Michael Fu Robert H. Smith School of Business & Institute for Systems Research University of Maryland 1. Project Overview 3 SRC/ISMT Factory Operations Research Center Research Plan (Proposed) (1) Develop, test, and transfer software tools for optimal PM planning and scheduling; (2) Research and validate the models, methods and algorithms for software development in (1); (3) Facilitate the transfer of models, algorithms and tools to 3rd party commercial software vendors. 4 SRC/ISMT Factory Operations Research Center Executive Summary • Deliverables (reports) completed: January and July 2002; SRC Pub P005269, P006317 • Best Paper in Session, TECHCON 2003 (X.Yao presenter): “Optimal preventive maintenance policies for unreliable production systems with applications to semiconductor manufacturing” • Paper submitted for publication IEEE-Trans. Semiconductor Mfg: – • 5 “Incorporating Production Planning into Preventive Maintenance Scheduling in Semiconductor Fabs” INFORMS 2003 Annual Meeting: invited talks and an invited session organized and chaired within Applied Probability Cluster. SRC/ISMT Factory Operations Research Center Executive Summary • software tool (PMOST): – – 6 Generic Scheduling Simulation Engine Generic Implementation of PM Scheduling Algorithm • summer internships (AMD & Intel) • Ph.D. dissertations supported: He, Yao, Hu, Ramirez MS dissertations supported: Crabtree, Jagannathan • commercialization feasibility discussions: Adexa, Ibex Processes. • NIST internship via Swee Leong SRC/ISMT Factory Operations Research Center Industrial Liaisons • • • • • • • • • • • • • • • • • • • 7 Matilda O'Connor, Nipa Patel, Ying Tat Leung, Wayne F. Carriker, Robin L. Hoskinson, Ben-Rachel Igal, Mani Janakiram, Madhav Rangaswami, Sidal Bilgin, Russell Whaley, Ramesh Rao, Jan Verhagen, Shekar Krishnaswamy, K.J. Stanley, Gurshaman S. Baweja, Jason Wang, James Yang, Giant Kao, Jacky Fan, AMD AMD (sign in SRC list) IBM Intel Intel Intel Intel Intel LSI (sign in SRC list) LSI (sign in SRC list) National Semiconductor Philips (sign in SRC list) Motorola (sign in SRC list) Motorola (sign in SRC list) TI TSMC (ISMT) TSMC (ISMT) TSMC (ISMT) TSMC (ISMT) SRC/ISMT Factory Operations Research Center Research Personnel Faculty: – Michael Fu, Maryland – Steve Marcus, Maryland – Emmanuel Fernandez, Cincinnati Students: – Xiaodong Yao, Maryland (PhD final defense Nov.2003) – Ying He, Maryland (PhD completed, summer 2002) – Jiaqiao Hu, Maryland (3rd year PhD) – Jason Crabtree, Cincinnati (MS completed, summer 2003) – Jose Ramirez, Cincinnati (3rd year PhD) – Sumita Jagannathan, Cincinnati (3rd year MS) 8 SRC/ISMT Factory Operations Research Center Task Description (Proposed) Year 1 - Implementing the PM scheduling algorithm; developing, distributing, and analyzing PM practice survey to drive PM planning models and algorithms; literature review of research on analytical and simulation-based models for PM planning with production considerations. Year 2 - Developing generic implementation platform for PM scheduling algorithm to facilitate possible transfer to 3rd party software provider; developing, testing, and validating PM planning models and algorithms. Year 3 – Implementing PM planning models and algorithms, validating and testing; training workshop to facilitate transfer to 3rd party software vendor. 9 SRC/ISMT Factory Operations Research Center Deliverables to Industry (Proposed) 1. Survey of current PM practices in industry (Report) (P:15-DEC-2001) 2. Models and algorithms to cover bottleneck tool sets in a fab (Report) (P:31-MAR-2002) 3. Simulation engine implemented in commercially available software, with case studies and benchmark data (Report) (P:30-SEP-2002) 4. PM planning/scheduling software tools, with accompanying simulation engine (Software, Report) (P:30-JUN-2003) 5. Installation and evaluation, workshop and consultation (Report) (P:31-DEC-2003) MORE DETAILS later in presentation 10 SRC/ISMT Factory Operations Research Center Emmanuel Fernandez, Ph.D. ECECS Department University of Cincinnati 2. Summary of Completed Tasks 11 SRC/ISMT Factory Operations Research Center Summary of Completed Tasks We summarize here the accomplishments in the project up to this point: •Interactions with industry •Deliverables •Models, Algorithms, and Software Tools •Case Studies •Documentation submitted to SRC website •Other documentation •Software Implementation: PMOST •Integration with fab schedulers: collaboration with ASU •Students trained 12 •(Doctoral and Master Theses) SRC/ISMT Factory Operations Research Center Interactions with Industry 13 SRC/ISMT Factory Operations Research Center Interaction with Industry • Interactions with industry have been fundamental in guiding our research efforts: • These facilitated the design, implementation, and proof of concept of our algorithms, models and software tools. • Interactions have taken place in the form of: • Summer internships for our students from 2000 through 2002. • Direct collaboration to exchange ideas and formulate problems and solutions, e.g: • Survey on best practices of PM scheduling; • Visits to fabs to interview and obtain feedback from tool managers and operators. • Periodic teleconferences with MC liaisons. •Co-authored publications derived from the research work. 14 SRC/ISMT Factory Operations Research Center Interaction with Industry •Summer Internships During the project, a total of four summer internships were completed at two member companies (2000 to 2002): •X. Yao, 2000, AMD, Austin, TX: data collection and simulation of one case study. •X. Yao, J. Crabtree, 2001, AMD, Austin, TX: software implementation of algorithms and models; built interfaces to integrate to fab systems. •J. Crabtree, 2002, Intel, Chandler, AZ: data collection, software implementation, and two simulation studies. •J.A. Ramírez, 2002, AMD, Austin, TX: data collection and modeling for wafer to calendar-based conversion of PM schedules, and two simulation studies. 15 SRC/ISMT Factory Operations Research Center Deliverables: Models, Algorithms, and Software Tools 16 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms, and Software Tools Here we summarize the Models and Algorithms produced by the research team representing the theoretical/academic contributions and basis for implementation in software tools: -Hierarchical Model for Optimal PM Scheduling. -MIP formulation of the PM scheduling problem. -Conversion of wafer to calendar-based PM schedules. - X. Yao Doctoral work. 17 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms Hierarchical Model for Optimal PM scheduling Objective Failure Dynamics Upper MDP PM Policy Demand Pattern Lower MIP PM Schedule WIP Constraints 18 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Objective: l l l max bi Vi (t ) - Ci I i (t ) - Ci ai (t ) a (t ) t =1 i =1 i =1 N 19 M ri SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Constraints: nil (i) ail (t ) = 1 t =1 for those PM tasks required to begin by period nil mil (ii) ail (t ) = 0 t =1 for those PM tasks prohibited from l beginning before period mi N (iii) 20 ail (t ) 1 t =1 for all PM tasks in general SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Constraints: (iv) Vi (t ) = f ( a i (t ), b (t )) i "i , t where a i (t ) is the set of PM decisions across all PM tasks, and b i (t ) is a dummy variable holding the value of a i (t ) from the previous period, i.e. b i (t + 1) = a i (t ) 21 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Constraints: (v) I i (t + 1) = I i (t ) - X i (t ) + d i (t ) "i, t = 1,..., N - 1 where di(t) is amount of incoming wafers at tool i in period t, and Xi(t) is the quantity of wafers processed on tool i in period t. (vi) X i (t ) K i Vi (t ) "i, t where Ki is the wafer throughput coefficient for tool i. 22 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Constraints: (vii) I i (t ) Li "i, t where Li is the maximum allowed inventory at tool i. (viii) rk (t ) = g (a i (t ), b i (t )) "k , t where rk (t ) is the resource requirement variable for resource k in period t. 23 SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms - MIP Formulation Constraints: (ix) rk (t ) Rk (t ) "k , t where Rk(t) is the amount of resource k available in period t. k ( ) 0 ( ) 0 ( ) 0 (x) Vi t , Ii t , Xi t , ri (t ) 0 (xi) a il (t ) = 0 or 1 24 "k , i, t "i, l , t SRC/ISMT Factory Operations Research Center Deliverables Models and Algorithms Conversion of Wafer to Calendar-based PM Schedules PM window (W: warning, D: due, L: late) Wl ij ij ij C t1 C t2 C t2 to t1 t2 t3 C ij C tij + rij tij + tij k k -1 = ijk ij C t k + rij t k Dl ... ij C t0 ij t k +1 ij ij ... ... Ct tW if ij tk ij + t k -1 ij ... ij Ct D (Wafer counts/period) D +1 ... t D t D +1 tD ij ij ij tk Dl = Dl - C t ij ij ij ij capacity at chamber j , tool i . k rij : Throughput rate in chamber ij C t : Cumulative D tD = tD + Dl ij t : Maximum (Time period) tL Dl if t k + t k -1 t k ij ij Ll 1 r rij ij j , tool i . amount of wafers produced (estimated ), chamber j , tool i . Estimated due time (date) k ij D l : Due amount t : Estimated ij of wafers for PM, chamber incomming WIP at chamber k r : Throughput ij 25 rate proportion at chamber j , tool i . j , tool i , period t k . j , tool i . SRC/ISMT Factory Operations Research Center Deliverables: Simulation Case Studies 26 SRC/ISMT Factory Operations Research Center Simulation Case Studies • Objectives – Validate PM optimization through simulation studies with real fab data – Simulation studies conducted to compare model-based optimized PM schedule and baseline or historical (“best in practice”) PM schedules. – Lay groundwork for integration of PM optimization into production environment 27 SRC/ISMT Factory Operations Research Center Simulation Case Studies • Five case studies with real fab data. Calendar and/or wafer based PM’s. – – – – – 28 Case 1: Metal Deposition process (11 tools, 7days); Best in Practice vs. Optimized Schedule Case 2: Photolithography process (25 tools, 7 days); Best in Practice vs. Optimized PM schedule Case 3: Metal Deposition process (29 tools, 7 days); Baseline vs. Optimized PM Schedule Case 4: Photolithography process (12 tools, 7days); Baseline vs. Optimized PM schedule Case 5: Thin films process (28 tools, 21 days); Best in Practice vs. Optimized PM schedule. SRC/ISMT Factory Operations Research Center Simulation Case Studies • Results: Optimization made logical decisions and showed good performance gains. – – – – – 29 Case 1: up to 14% gain in throughput for one tool. Case 2: Matched tool availability throughput for “Best-inPractice” schedule. Case 3: about 1% average gain in tool availability for entire tool group; 1.7% average gain in total throughput for entire tool group. Case 4: 1% average gain in tool availability for entire tool; 2.2% average gain in total throughput for entire tool group. Case 5: up to 6% gain in tool availability for one tool; 0.7% average gain in tool availability for entire tool group; 1% average gain in total throughput for entire tool group. SRC/ISMT Factory Operations Research Center Deliverables: Documentation Submitted to SRC Website 30 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website The following is the list of all the documentation produced by the research team and available at the SRC website: Annual review presentations •Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; Crystal City, MD, December 13-14, 2001, Pub P003262. •Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; Tempe, AZ, April 9-10, 2002, Pub P007441. •Intelligent Preventive Maintenance Scheduling in Semiconductor Manufacturing Fabs; San Jose, CA, November 20-21, 2002, Pub P005082. Reports •Survey of Current PM Practices in Industry, Conducted Via Web and Electronic Mail; E. Fernandez, M. Fu and S. Marcus; Univ. of Maryland; 17-Jan-2002; 19pp.; Pub P003461. Abstract: The researchers present the results of survey on the practices employed in the semiconductor manufacturing industry for scheduling Preventive Maintenance (PM) tasks. The survey was distributed by the middle of October 2001, and responses were received until the middle of December 2001. •Report on Models and Algorithms to Cover Major Bottleneck Tool Sets in a Semiconductor Manufacturing Fab; X. Yao, M. Fu, S. Marcus and E. Fernandez; Univ. of Maryland; 29-Jul-2002; 4pp.; Pub P004304. Abstract: The researchers have developed models and algorithms for optimal PM scheduling based on calendar information of time since last PM, and the time window within which the next PM needs to fall. A computationally tractable mixed Integer/Linear Programming (IP/LP) model for short-term planning horizon, e.g., 1-3 weeks, has been developed, tested and implemented to do the day-to-day actual scheduling of PM tasks across tools within a given family. 31 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Reports •Preventive Maintenance Optimal Scheduling Tool (PMOST): Ver. 1.0; J. Crabtree, J. Ramirez, E. Fernandez, X. Yao, M. Fu and S. I. Marcus; Univ. of Maryland; 21-Jan-2003; 8pp.; Pub P005269. Abstract: The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (programmed in C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. •Preventive Maintenance Optimal Scheduling Tool (PMOST): Ver. 1.1; J. Crabtree, J. Ramirez, E. Fernandez, X. Yao, M. Fu and S. I. Marcus; Univ. of Maryland; 10-Jul-2003; 10pp.; Pub P006317. Abstract:The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (programmed in C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. PMOST v. 1.1 includes conversion of wafer-based to calendar-based PM schedules. •Preventive Maintenance Scheduling Model and Generic Implementation, Mathematical Programming Modeling Languages and Solvers; J. Crabtree, J. Ramirez, E. Fernandez; Univ. of Cincinnati; 29-Jul-2002; 6pp.; Pub P004306. Abstract: This report present a survey on Mathematical Programming Modeling Languages (MDL) and Solvers that can be used in optimization of PM schedules. Papers •Optimization of Preventive Maintenance Scheduling for Semiconductor Manufacturing Systems: Models and Implementation; X. Yao, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 17-Dec-2001; 5pp.; Pub P003267. Abstract: In this paper, the researchers present a two-layer hierarchical modeling framework for addressing the PM optimization problem for cluster tools, i.e., a Markov Decision Process (MDP) model at the higher level, and a mixed Linear Programming (LP) model at the lower level. Production planning data such as WIP levels are incorporated in these models. Paper presented at the 2001 IEEE International Conference on Control Applications, Mexico City, Mexico, 2001. •Incorporating Production Planning into Preventive Maintenance Scheduling in Semiconductor Fabs; X. Yao, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 29-Jul-2002; 6pp.; Pub P004305. Abstract: In this paper, a general mathematical model aiming at the optimization of preventive maintenance (PM) scheduling is proposed. The researchers formulate the problem as a finite-horizon Markov decision process (MDP) that incorporates equipment dynamics and production system dynamics. Paper presented at MASM 2002 Conference, Tempe, AZ, 2002. 32 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Papers (cont.) •Optimal Preventive Maintenance Policies for Unreliable Queueing/Production Systems with Applications to Semiconductor Manufacturing; Xiaodong Yao, X. Xie, M. Fu, S. Marcus and E. Fernandez; Univ. of Maryland; 6-Jun-2003; 5pp.; Pub P006072. Abstract: The reliability of equipment is critical to fab's operational performance, and Preventive Maintenance (PM) scheduling is a very challenging task in semiconductor manufacturing. In this paper, the researchers will study optimal PM policies under the context of unreliable queueing systems. Presented at TECHON 2003 (Awarded as "Best Paper in Session") , August 25-27, 2003, Dallas, TX. •Optimal Importance Sampling in Securities Pricing; Y. Su and M. C. Fu; Univ. of Maryland; 21-Jun-2002; 29pp.; Pub P004145. Abstract: To reduce variance in estimating security prices via Monte Carlo simulation, the researchers formulate a parametric minimization problem for the optimal importance sampling measure, which is solved using infinitesimal perturbation analysis (IPA) and stochastic approximation (SA). •Convergence of Simultaneous Perturbation Stochastic Approximation for Nondifferentiable Optimization; Y. He, M. C. Fu and S. I. Marcus; Univ. of Maryland; 22-May-2003; 5pp.; Pub P005903. Abstract: This paper considers Simultaneous Perturbation Stochastic Approximation (SPSA) for function minimization. The standard assumption for convergence is that the function be three times differentiable, although weaker assumptions have been used for special cases. However, all previous work appears to at least require differentiability. This paper relaxes the differentiability requirement and proves convergence using convex analysis. Presentations •Preventive Maintenance in Semiconductor Manufacturing Fabs; M. Fu; Univ. of Maryland; 15-May-2001; 41pp.; Pub P002234. Abstract: FORCe Kick-off meeting presentation, Seatle, WA, April 26-27, 2001. •Optimal Preventive Maintenance Policies for Unreliable Queueing/Production Systems with Applications to Semiconductor Manufacturing Fabs; Xiaodong Yao, X. Xie, M. Fu, S. Marcus and E. Fernandez-Gaucherand; Univ. of Maryland; 8-Sep-2003; 13pp.; Pub P006866. Abstract: The reliability of equipment is critical to fab's operational performance, and Preventive Maintenance (PM) scheduling is a very challenging task in semiconductor manufacturing. In this paper, the researchers will study optimal PM policies under the context of unreliable queueing systems. Presented at TECHON 2003 (Awarded as "Best Paper in Session"). 33 SRC/ISMT Factory Operations Research Center Deliverables Documentation submitted and currently available at SRC website Other documentation Software Description: Preventive Maintenance Optimal Scheduling Tool (PMOST); SMITLab University of Cincinnati; Univ. of Maryland; 30-Jun-2003; 2pp.; Pub P006313. Abstract: The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a (C-language) software tool for optimal scheduling of Preventive Maintenance tasks in Semiconductor Fabs. PMOST accepts a set of parameters related to the PM optimization process, e.g. planning horizon, number of resources for the PM tasks, cost coefficient related to the PM tasks, etc.. PMOST obtains an optimal solution for that problem via the use of mathematical programming solvers for Linear Programming/Mixed Integer Programming problems. The PMOST system was designed to work with different types of mathematical programming solvers, such as IBM OSL and CPLEX. The system requires a set of data files, defined under specific (standard) formats, used in the optimization process. Thesis-MS: Optimal Preventive Maintenance Scheduling in Semiconductor Fabs; J. Crabtree; Univ. of Cincinnati; 10-Oct-2003; 84pp.; Pub P007381. Abstract: This thesis is spawned from the research project, "Preventive Maintenance in Semiconductor Fabs", sponsored by the Semiconductor Research Corporation (SRC) and International SEMATECH. The project proposes a two-level hierarchical optimization structure that considers important factors such as the work-in-progress (WIP) at a tool and the complex relationships between the chambers of a cluster tool. This thesis focuses on the lower level of the aforementioned hierarchy that deals with PM scheduling. It expands on the work accomplished thus far in the project, specifically analyzing and fixing current issues with the PM scheduling algorithm and creating a software implementation of the scheduling algorithm. 34 SRC/ISMT Factory Operations Research Center Deliverables: Other Documentation 35 SRC/ISMT Factory Operations Research Center Deliverables Other Documentation (not posted yet at SRC web site) Papers •Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing, X. Yao; E. Fernandez-Gaucherand; M.C. Fu; S.I. Marcus; submitted for publication to IEEE Transactions on Semiconductor Manufacturing, 2003. •An Algorithm to Convert Wafer to Calendar-Based Preventive Maintenance Schedules for Semiconductor Manufacturing Systems, J.A. Ramírez-Hernández and E. Fernández-Gaucherand., to appear in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, December, 2003. •Optimal PM Scheduling in Semiconductor Manufacturing Systems: Case Studies, Univ. Cincinnati, Univ. Maryland, AMD, Intel. In preparation. •Survey of Best Practices of PM Scheduling in Semiconductor Manufacturing Systems, J.A. Ramírez, J. Crabtree, E. Fernandez, X. Yao , M. Fu and S.I. Marcus. In preparation. •Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems, X. Yao, X. Xie, M. Fu, and S. Marcus. In preparation. Presentations •Suppliers Teleconference Presentation: Commercialization, M. Fu, E. Fernandez, S.I. Marcus, J. Crabtree, J.A. Ramírez, X. Yao, September 4th,, 2003, SEMATECH Webex teleconference system. 36 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST 37 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST Software implementation of models and algorithms is an objective that has been accomplished with the design and coding of the software Preventive Maintenance Optimal Scheduling Tool (PMOST). The following are the versions produced up to this point: •PMOST ver. 1.0: first version of PMOST coded in C-language, running over MSWindows platforms (Windows 2000 and up). Include a basic text-mode user interface, link with Optimization Library Solutions (OSL) solver from IBM, and generates Mathematical Programming System (MPS) files describing the MIP problem. •PMOST ver. 1.1: includes same characteristics of version 1.0 plus the conversion algorithm for wafer-based to calendar-based PM schedules. An installer for MS-Windows is included in this version. •PMOST ver. 1.2: first Graphical User Interface (GUI) for PMOST, includes all characteristics of verions 1.0 and 1.1. MS-Windows platform (Windows 2000 and up). 38 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST Block Diagram pmost_ui.exe main.c START User Interface pmost.exe read_data_file.c read_fam_file.c read_sch_file.c read_wip_file.c -Planning horizon -Tools family -Number of Technicians utils.c General functions used in different parts of the system. -Tool/PM data files: *.fam, *.data -Conversion to calendar-time PMs data files Read Input Data write_sch_file.c -PM schedule: files *.sch -Estimated WIP data files: files *.wip ASAP conv2cal (.exe, .c, .h) -Debugging file: debug.txt -Converted Schedule File: *.csch Conversion to calendar-time PMs create_pm_vectors.c write_set_val_files.c write_mps_file.c write_debug_file.c Write MPS file -Output data: *.set, *.val files -MPS file: *.mps .mps file main.c calls the solver (OSL, CPLEX, etc) LP/MIP SOLVER solution file (text file) parse_osl_solution.c parse_cplexl_solution.c write_solution_file.c write_pm_order_file.c 39 Output: pm_order.txt Parse Solution pm_solution.txt SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.2 with GUI, Demo Movie 40 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •The input data used for this exercise was artificially created for illustration purposes only. •The user executes the file pmost.exe and the following prompt will be shown: 41 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •After that, the user will define the “Start Date” and “End Date” in the format requested in the following screenshot: 42 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •Finally, PMOST will ask for the number of technicians assigned to each period in the planning horizon defined by the “Start Date” and the “End Date”, as follows: 43 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •PMOST will then produce the MPS file, and finally it will communicate this MPS to the solver selected. The solver will compute the optimal solution that will be decoded by PMOST and written in the output_files directory. The messages presented by PMOST are as follows: 44 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •For this example in particular, the pm_solution.txt file will looks as follows: Tool Name PM Name CT01 7 DAY PM CT02 14 DAY PM CT03 28 DAY PM CT04 56 DAY PM CT04 PMCH1 CT05 PMCH4 CT06 PMCH5 CT07 PMCH2 CT08 PMCH3 CT09 KIT CH2 CT10 KIT CH3 CT02 7 DAY PM CT04 14 DAY PM CT01 28 DAY PM CT05 56 DAY PM CT01 PMCH1 CT10 PMCH4 CT04 PMCH5 CT06 PMCH2 CT05 PMCH3 CT03 KIT CH2 CT09 KIT CH3 45 Old Due Date 01/06/2002 07:00:00 01/05/2002 07:00:00 01/04/2002 07:00:00 01/03/2002 07:00:00 01/01/2002 07:00:00 01/02/2002 07:00:00 01/03/2002 07:00:00 01/04/2002 07:00:00 01/02/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/02/2002 07:00:00 01/03/2002 07:00:00 01/04/2002 07:00:00 01/01/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/02/2002 07:00:00 01/05/2002 07:00:00 01/03/2002 07:00:00 01/02/2002 07:00:00 01/01/2002 07:00:00 Optimal Due Date 01/05/2002 07:00:00 01/06/2002 07:00:00 01/02/2002 07:00:00 01/03/2002 07:00:00 01/03/2002 07:00:00 01/03/2002 07:00:00 01/06/2002 07:00:00 01/06/2002 07:00:00 01/04/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/01/2002 07:00:00 01/03/2002 07:00:00 01/05/2002 07:00:00 01/03/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/03/2002 07:00:00 01/06/2002 07:00:00 01/03/2002 07:00:00 01/02/2002 07:00:00 01/01/2002 07:00:00 SRC/ISMT Factory Operations Research Center Software Implementation: PMOST PMOST 1.1 with text-mode user interface, screen captions •Also, a pm_order.txt file can be generated for use it in AutoSched AP simulations as PM orders: PMORDER order1 order2 order3 order4 order5 order6 order7 order8 order9 order10 order11 order12 order13 order14 order15 order17 order18 order19 order20 order21 order22 46 STN CT01 CT02 CT03 CT04 CT04 CT05 CT06 CT07 CT08 CT09 CT10 CT02 CT04 CT01 CT01 CT10 CT04 CT06 CT05 CT03 CT09 DUEDATE 01/05/2002 07:00:00 01/06/2002 07:00:00 01/02/2002 07:00:00 01/03/2002 07:00:00 01/03/2002 07:00:00 01/03/2002 07:00:00 01/06/2002 07:00:00 01/06/2002 07:00:00 01/04/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/01/2002 07:00:00 01/03/2002 07:00:00 01/05/2002 07:00:00 01/05/2002 07:00:00 01/01/2002 07:00:00 01/03/2002 07:00:00 01/06/2002 07:00:00 01/03/2002 07:00:00 01/02/2002 07:00:00 01/01/2002 07:00:00 PTIME 8.000000 12.000000 55.000000 55.000000 48.000000 5.000000 5.000000 50.000000 50.000000 24.000000 24.000000 8.000000 12.000000 55.000000 48.000000 5.000000 5.000000 50.000000 50.000000 24.000000 24.000000 PTUNITS hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr hr SRC/ISMT Factory Operations Research Center Integration with Fab Schedulers: Collaboration with ASU 47 SRC/ISMT Factory Operations Research Center Integration of Fab Schedulers: Collaboration with ASU •Collaboration is under way with the ASU Team with the objective of integrating fab scheduling and optimal PM scheduling in semiconductor fabs. – The goal is integrate both fab scheduling and preventive maintenance to evaluate long-term performances in semiconductor manufacturing systems via simulation analysis. – The research teams have identified the requirements for such integration as well as proposed a work plan to complete the task. – Currently, both teams are working to close the gap in the software implementation and start experiments using simple models (e.g., minifab) for proof of concept. – Integration involves communication between simulation software (customization of ASAP) and the corresponding schedulers (jobs and PMs). 48 SRC/ISMT Factory Operations Research Center Students Trained 49 SRC/ISMT Factory Operations Research Center Students Trained The following students have participated in the research tasks for this project, and have received substantial training in different topics (e.g., ASAP training, courses in stochastic modeling and decision, simulation analysis and modeling): – Ph.D. Students: • • • • Ying He, Maryland (Ph.D. completed, graduated on summer 2002) Jiaqiao Hu, Maryland (3rd year Ph.D.) José Ramírez, Cincinnati (3rd year Ph.D.) Xiaodong Yao, Maryland (Ph.D., will graduate in December 2003) – M.Sc. Students: • Jason Crabtree, Cincinnati (M.Sc. completed, graduated September 2003) • Sumita Jagannathan, Cincinnati (continuing M.Sc.) 50 SRC/ISMT Factory Operations Research Center (Students) 3. Summary of Doctoral and Master Theses 51 SRC/ISMT Factory Operations Research Center Summary of Doctoral and Master Theses M.Sc. Thesis on Electrical & Computer Engineering & Computer Science Title: Optimal Preventive Maintenance Scheduling in Semiconductor Fabs Author: Jason Crabtree, SMITLab, University of Cincinnati. Defense/submission date: August 4th 2003. Abstract: This thesis is spawned from the research project, "Preventive Maintenance in Semiconductor Fabs", sponsored by the Semiconductor Research Corporation (SRC) and International SEMATECH. The project proposes a two-level hierarchical optimization structure that considers important factors such as the work-in-progress (WIP) at a tool and the complex relationships between the chambers of a cluster tool. This thesis focuses on the lower level of the aforementioned hierarchy that deals with PM scheduling. It expands on the work accomplished thus far in the project, specifically analyzing and fixing current issues with the PM scheduling algorithm and creating a software implementation of the scheduling algorithm. (See SRC Publication P007381) 52 SRC/ISMT Factory Operations Research Center Summary of Doctoral and Master Theses Research Proposal Ph.D. on Electrical & Computer Engineering & Computer Science Title: Reinforcement Learning (Neuro-Dynamic Programming) Approach for Production Control of Semiconductor Manufacturing Re-Entrant Lines Author: José A. Ramírez, SMITLab, University of Cincinnati. Defense/submission date: proposal to be defended in December 2003. Description: Semiconductor fabs are complex systems characterized by re-entrant lines in the manufacturing process. The scheduling of jobs (control) in this type of systems is a challenging task. Finding optimal scheduling policies, via analytical procedures, is a difficult problem. Generally, it is intractable given the complexity and high dimensionality of such systems. We propose the use of a novel approach in control of high-dimensional and complex systems: Reinforcement Learning (Neuro-Dynamic Programming). 53 SRC/ISMT Factory Operations Research Center Summary of Doctoral and Master Theses Research Proposal Ph.D. on Electrical & Computer Engineering & Computer Science Jose A. Ramírez – SMITLab – University of Cincinnati Description (cont.): •Reinforcement Learning (RL) (Neuro-Dynamic Programming (NDP)) has been successfully used to find suboptimal (near to the optimal) policies in complex systems, where the curse of dimensionality is presented as a serious constraint to apply Dynamic Programming approaches for optimization and control. RL and NDP are new and very promissory approaches for a wide spectrum of applications. •RL and NDP methods are based in learning from the interaction with the system of interest (e.g., learn an (sub) optimal scheduling policy) or its corresponding model (simulation). From this interaction we maximize the long-term returns (performance index) given the actions (control) applied to the system, and derived from the learning process. •Semiconductor manufacturing systems have the essential characteristics to apply these type of approaches: simulation models are available, but analytical modeling is too complex in large scale systems and stochastic events are present (e.g., tool failures, tool maintenance). 54 SRC/ISMT Factory Operations Research Center Summary of Doctoral and Master Theses Xiaodong Yao, Ph.D. Student, University of Maryland, Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems 55 SRC/ISMT Factory Operations Research Center Overview 1. 2. 3. 56 In literature preventive maintenance (PM) and production control have been treated independently. Recent work Boukas and Liu (2001) (continuous flow model) Iravani and Duenyas (2002) (propose and analyze a heuristic policy of “double-threshold” policy) Sloan and Shanthikumar (2002, 2000) (integrated production dispatching and maintenance scheduling in semiconductor manufacturing) Our objective characterization of optimal joint policies for unreliable production systems with either time-dependent failures operation-dependent failures SRC/ISMT Factory Operations Research Center Systems with time-dependent failures u [0,P] d, constant demand • The machine experiences time-dependent failures: Machine deteriorates over calendar time, and can fail while idle. (e.g., calendar-based PMs) • flexible production rate, u [0,P], P is the maximal production rate • inventory consumed by a constant demand d, and backlog allowed • Upon machine failures, repair has to be initiated with cost cr, and time for repair r is a r.v. • Before machine failures, PM can be applied with cost cp, and time for PM p is a r.v. as well. • inventory holding cost g(·), piecewise linear function of inventory level • Objective: find PM / production policy to minimize discounted cost 57 SRC/ISMT Factory Operations Research Center Markov-Decision Process Formulation Consider the discrete-time model: state st , it , nt where st = inventory level 2 : if machine in PM it = 1 : if machine in working state 0 : if machine in repair nt = time periods since the last change of machine state i PM : to do PM control ut = , while machine in working state, i.e., it = 1. u 0 , P : to produce conditiona l probabilit ies : f n = Pr it +1 = 0 it = 1, nt = n , pn = Pr it +1 = 1 it = 2, nt = n , rn = Pr it +1 = 1 it = 0, nt = n . 58 SRC/ISMT Factory Operations Research Center Bellman Equations The optimal cost functions satisfy: when machine in repair : J s,0, n = g s + b rn J s - d ,1,0 + b 1 - rn J s - d ,0, n + 1, when machine in PM : J s,2, n = g s + b pn J s - d ,1,0 + b 1 - pn J s - d ,2, n + 1, when machine in working state : J s,1, n = min Q where Q PM PM s,1, n ; min Q s,1, n , u u = 0 ,, P s,1, n = c p + J s,2,0, Q s,1, n = g s + b f n cr + J s + u - d ,0,0 u + b 1 - f n J s + u - d ,1, n + 1. 59 SRC/ISMT Factory Operations Research Center Characterization of optimal policy Theorem 1: J(s,0,n), J(s,1,n), J(s,2,n) are decreasing function in s, for s 0. Remark: This implies that when there is backlog, if choose not to do PM, then optimal production rate is at least as large as demand rate. Theorem 2: J(s,1,n) is an increasing function in n, if the following conditions are satisfied: (1) the machine has IFR; (2) cr cp; (3) times for repair and PM are stochastically equivalent or machine failure rate is constant. Corollary: For fixed inventory level, the optimal joint policy has control-limit form w.r.t. machine age. Theorem 3: There exists s* such that "s > s*, *(s,1,n) = 0 or PM, for all n. Remark: This is an intuitive observation, such that at high inventory level, it’s not optimal to produce. 60 SRC/ISMT Factory Operations Research Center Numerical Study Example: the machine lifetime ~ Weibull (4,5), time for PM ~ U(0,3), time for CM ~ U(0,6), d = 1, P =3, cp = 50, cr = 2 * cp, c+ = 1, c- = 10, b = 0.95. Fig. 1: the optimal policy Fig. 2: The relative difference of cost function under the joint optimal policy and independently optimized policy. diff = (Jind – J*)/J* 100%. 61 Fig. 2 SRC/ISMT Factory Operations Research Center Operation-Dependent Failures u {0,1} 1, with prob. q • • • • Operation-dependent failures: Machine deteriorates only when it is producing, and can’t fail while idle. (e.g., wafer-count-based or operation-history based PMs) Random demand: unit demand in each period with prob. q Machine can produce at rate either 0 or 1, u {0,1} Upon machine failures, repair has to be initiated with cost cr, and time for repair r is a r.v. • Before machine failures, PM can be applied with cost cp, and time for PM p is a r.v. as well. • • 62 inventory holding cost g(·), piecewise linear function of inventory level Objective: find PM / production policy to minimize discounted cost SRC/ISMT Factory Operations Research Center Bellman Equations The optimal cost functions satisfy: when machine in repair : J s,0, n = g s + b q rn J s - 1,1,0 + q1 - rn J s - 1,0, n + 1 + b (1 - q )rn J s,1,0 + 1 - q 1 - rn J s,0, n + 1, when machine in PM : J s,2, n = g s + b q p n J s - 1,1,0 + q 1 - p n J s - 1,2, n + 1 + b (1 - q ) p n J s,1,0 + 1 - q 1 - p n J s,2, n + 1, when machine in working state : J s,1, n = min Q where Q Q PM 0 PM s,1, n ; Q 0 s,1, n ; Q1 s,1, n , s,1, n = c p + J s,2,0, s,1, n = g s + b q J ( s - 1,1, n) + (1 - q) J ( s,1, n), Q ( s,1, n) = g ( s ) + b q f n cr + J s,0,0 + q1 - f n J s,1, n + 1 1 + b (1 - q ) f n cr + J s + 1,0,0 + 1 - q 1 - f n J s + 1,1, n + 1 63 SRC/ISMT Factory Operations Research Center Characterization of optimal policy Theorem 4: J(s,1,n) is an increasing function in n, if the following conditions are satisfied: (1) the machine has IFR; (2) cr cp; (3) r st. p. Corollary: For fixed inventory level, the optimal joint policy has control-limit form w.r.t. machine age. Theorem 5: There exists s* such that "s > s*, *(s,1,n) = 0, for all n. 64 SRC/ISMT Factory Operations Research Center Numerical Example Example: the machine lifetime ~ Weibull (4,5), time for PM ~ U(0,3), time for CM ~ U(0,6), q = 0.8, cp = 50, cr = 2 * cp, c+ = 1, c- = 10, b = 0.95. Fig. 3: the optimal policy 65 SRC/ISMT Factory Operations Research Center Conclusions The big picture: Hierarchical Framework for PM planning and scheduling. High Level: objective: to derive optimal PM policies methodology: Markov-decision processes Low Level: objective: to obtain optimal PM schedules methodology: Mathematical programming 66 SRC/ISMT Factory Operations Research Center 4. Continuing and Future Research 67 SRC/ISMT Factory Operations Research Center Continuing and Future Research Finishing and submission of papers for publication •Optimal PM Scheduling in Semiconductor Manufacturing Systems: Case Studies, J. A. Ramírez, J. Crabtree, E. Fernandez, M. Fu, X. Yao, S.I. Marcus, Advanced Micro Devices, Corp., Intel, Corp., in preparation. •Survey of Best Practices of PM Scheduling in Semiconductor Manufacturing Industry, J.A. Ramírez, J. Crabtree, E. Fernandez, X. Yao , M. Fu and S.I. Marcus, to be submitted for publication. •Optimal Joint Preventive Maintenance and Production Control Policies for Unreliable Production Systems, X. Yao, X. Xie, M. Fu, and S. Marcus, in preparation. •Conversion of Wafer-Based PM Schedules into Calendar-Based for Optimal PM Scheduling in Semiconductor Manufacturing, J.A. Ramírez, E. Fernandez, in preparation. 68 SRC/ISMT Factory Operations Research Center Continuing and Future Research Commercialization Continue working with suppliers… Collaboration with other research groups •Continue task for integration of job and PM scheduling algorithms in a pilot study with ASU Team. •Analysis of simulations from integration of fab and PM scheduling algorithms. • Other •Xiaodong Yao, Ph.D. Dissertation defense and submission. •No cost extension through August 2004. 69 SRC/ISMT Factory Operations Research Center 5. Conclusions 70 SRC/ISMT Factory Operations Research Center Conclusions 71 SRC/ISMT Factory Operations Research Center

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# PM Optimization for Cluster Tools