Optimal Preventive Maintenance Scheduling in ... - Semantic Scholar

IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 23, NO. 3, AUGUST 2010

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Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing Systems: Software Tool and Simulation Case Studies José A. Ram´ırez-Hernández, Member, IEEE, Jason Crabtree, Xiaodong Yao, Member, IEEE, Emmanuel Fernandez, Senior Member, IEEE, Michael C. Fu, Fellow, IEEE, Mani Janakiram, Steven I. Marcus, Fellow, IEEE, Matilda O’Connor, and Nipa Patel

Abstract—This paper presents the architecture and implementation of a preventive maintenance optimization software tool (PMOST), based on algorithms for the optimal scheduling of preventive maintenance (PM) tasks in semiconductor manufacturing operations. We also present results from four complex simulation case studies, based on real industrial data and employing full fab models, to illustrate the use, data needs and outcomes produced by PMOST. These results demonstrate significant improvements in tool production and consolidation of PM tasks. We give a description of the different software modules that compose PMOST, to provide guidelines as well as a template for other implementations of the PM optimization algorithms utilized by PMOST. Index Terms—Optimal preventive maintenance (PM) scheduling, simulation case studies, software tool.

Manuscript received May 14, 2007; revised November 8, 2009; accepted February 6, 2010. Date of publication June 1, 2010; date of current version August 4, 2010. This work was supported in part by the Semiconductor Research Corporation and International Sematech, within the Factory Operations Research Center, under Grant Task NJ 877.001. J. A. Ram´ırez-Hernández and E. Fernandez are with the Department of Electrical and Computer Engineering, University of Cincinnati, Cincinnati, OH 45221-0030 USA (e-mail: [email protected]; [email protected]). J. Crabtree is with Integral Analytics, Inc., Cincinnati, OH 45202 USA (e-mail: [email protected]). X. Yao is with SAS Institute, Inc., Cary, NC 27513-8617 USA (e-mail: [email protected]). M. C. Fu is with the Robert H. Smith School of Business and the Institute for Systems Research, A. James Clark School of Engineering, University of Maryland, College Park, MD 20742 USA (e-mail: [email protected]). S. I. Marcus is with the Institute for Systems Research and the Department of Electrical and Computer Engineering, A. James Clark School of Engineering, University of Maryland, College Park, MD 20742 USA (e-mail: [email protected]). M. Janakiram is with Intel Corporation, Chandler, AZ 85248-4907 USA, and with the Thunderbird School of Global Management, Glendale, AZ 853066000 USA (e-mail: [email protected]). M. O’Connor was with Advanced Micro Devices, Inc., Austin, TX 78741 USA. She is currently with Bits, Bytes & Bots Computer Adventures, Austin, TX 78798 (e-mail: [email protected]). N. Patel is with GLOBALFOUNDRIES, Inc., Austin, TX 78746 USA (email: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSM.2010.2051731

I. Introduction

I

N SEMICONDUCTOR manufacturing systems, preventive maintenance (PM) is performed by taking off-line a specific tool to apply a prescribed maintenance task. PM increases the overall operational reliability while decreasing unanticipated (expensive) down-time from tool failures. The importance of the PM operations in the semiconductor industry is clearly illustrated by the large costs of the tools utilized in the fabrication process. For instance, a new fab using technology for 300 mm wafers can cost in excess of $3 billion [1], [2]. PM properly applied is a necessity in the fab to maintain and improve productivity, and to justify enormous capital investments of this industry. In addition, PM operations are usually based on heuristic methods, e.g., cumulative experience obtained by the engineers from the fab operations. The application of optimization methods in this problem is a topic that has received significant attention recently [3]–[5]. The objectives of this paper are as follows. First, to present the architecture and implementation of a software tool called preventive maintenance optimization software tool (PMOST), based on the PM scheduling optimization algorithm for semiconductor manufacturing operations proposed in [3], [4], and [5]. This software tool receives operational data and baseline PM schedules to generate an optimized PM schedule. Second, to present the architecture and implementation of PMOST, in order to provide guidelines and a template, as well as experimental data, that can help in the adoption of these by others, and also perhaps serve as the basis for generic third-party commercial tools. Third, to present a set of four complex simulation case studies, based on real industrial data and using full fab models, to illustrate the use, data needs and outcomes produced by PMOST. Both the PM optimization algorithms reported in [3], [4], and [5] and PMOST are the result of research supported by the semiconductor research corporation and International Sematech within the factory operations research center program. The project was justified by the fact that neither algorithms nor software tools for PM scheduling optimization in semiconductor

c 2010 IEEE 0894-6507/$26.00

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manufacturing operations were available previous to this research. The case studies presented in this paper consisted of simulations of four different tool groups in photolithography, metal deposition, and thin films processes on which the impact of optimized PM schedules, obtained with PMOST, vs. heuristic and baseline PM schedules was evaluated. The simulation experiments were performed in two fabs from different semiconductor companies. For the experiments, the companies allowed the utilization of industrial data as well as the full factory simulation models. Moreover, the simulations were conducted under the strict supervision of the personnel in charge of factory simulations, and according to the simulation practices utilized by each company. We also studied the problem of incorporating noncalendarbased PM schedules into the PM scheduling optimization. As a result, a conversion algorithm [6], [7] was designed to provide estimates of the equivalent calendar-time PM schedules for PM tasks defined under other noncalendar time units, e.g., number of wafers processed or processing-time elapsed since last PM task. The algorithm reported in [6] and [7] utilizes as input the projections of the work-in-process (WIP) and the system’s parameters (e.g., tool throughput rate, number of chambers), and then yields estimates of the dates for which the corresponding tool could receive a prescribed noncalendar time type of PM task. In addition to the fact that calendartime PM schedules are easy to use and to implement, in terms of the optimization algorithm given in [3], [4], and [5], calendar-time schedules are preferred because the search space for the optimization problem may be smaller when compared to the use of other units used to describe the PM schedules. Specific details of the conversion algorithm are provided in [6], and [7]. Moreover, in [7] an overview of how the calendartime PM schedules generated by the conversion algorithm are incorporated in the PM optimization with PMOST is presented, as well as a case study with real industrial data that demonstrates the accuracy of the conversion algorithm. The organization of this paper is as follows: Section II presents an overview of the optimal PM scheduling framework utilized by PMOST. This is followed by a description of PMOST in Section III that describes the data utilized by the software tool and how optimization results are provided. An overview of the simulation studies and the corresponding optimization and simulation results are given in Section IV and V, respectively. Finally, conclusions are presented in Section VI. II. Overview of PM Scheduling Optimization PMOST is based on the modeling framework for optimization of PM schedules given in [3], [4], and [5]. This framework is described as a two-level hierarchical model [3], with a Markov decision process (MDP) [4] at the higher level and a mixed integer programming (MIP) formulation [3], [4], [5] at the lower level, as depicted in Fig. 1 below. The long-term PM planning policies are produced by the MDP, which employs “the available information in a way that provides a trade-off between immediate and future benefits and costs, and that utilizes the fact that observations will be

Fig. 1. Two-level hierarchical framework for PM planning and scheduling (adapted from [3]–[5]).

available in the future” [8]. In the lower level, a MIP formulation [3]–[5] generates the optimized PM schedules according to an optimization objective, projections of the WIP, and these are subjected to several constraints. It is this PM scheduling optimization algorithm that is implemented by PMOST, and the PM planning policy, or frequency for performing the different PM tasks, is obtained from the baseline, or nominal, schedule employed in daily fab operations. This frequency is determined by the semiconductor fab operations, and based on recommendations from the tool’s manufacturer. Next we present some notation and details on the optimization models and algorithmic solutions, presented previously in [3], [4], and [5], which are utilized in PMOST. As presented in [3], [4], and [5], the objectives utilized for the lower level MIP model are as follows:

max

Tp M

MIP Objective 1

bi · Vi (t) −

ciI

· Ii (t) −

t=1 i=1

ρi

cil

·

ail (t)

(1)

l=1

MIP Objective 2 Tp M ρi l l max bi · Xi (t) − ci · ai (t) t=1 i=1

(2)

l=1

where, using the same notation as in [3], [4], and [5], Tp represents the number of time units or periods in the PM scheduling horizon, M is the number of tools (or tool chambers), Vi (t) is availability of tool i in period t, bi is the profit coefficient for availability of tool i, Ii (t) is the workload level (i.e., WIP) for tool i in period t, ciI is the cost coefficient for inventory in tool i, ρi is the number of PM tasks on tool i, ail (t) is a binary decision variable (1: do PM, 0: do not do PM) for PM task l on tool i in period t, and cil is the cost of performing PM task l on tool i. Moreover, in MIP Objective 2 the quantity Xi (t) represents the wafer throughput of tool i in period t and bi is the profit coefficient for throughput on tool i. The above MIP objectives (1) and (2) would be optimized under constraints such as inventory levels, availability of resources (e.g., maintenance technicians per period), tools availability and throughput. Notice that each

´ RAMÍREZ-HERNANDEZ et al.: OPTIMAL PREVENTIVE MAINTENANCE SCHEDULING

Fig. 3.

Fig. 2.

Calendar-time-based PM windows.

objective aims to maximize two different performance indices in a tool group. In MIP Objective 1 the goal is to maximize the availability of tools while minimizing inventory and PM task costs. For MIP Objective 2, the goal corresponds to maximize the tool throughput while minimizing the PM costs. The PM scheduling optimization considers a scheduling horizon where PM tasks are specified by "PM windows" and are delimited by a warning, due and late date, or by the amount of units completed (e.g., wafers, kilowatt-hours), see Fig. 2. Thus, the range of time or units completed, as indicated by a PM window, represents the interval of time or production when a PM task can be applied. The warning represents the earliest moment when a PM should be conducted, and the due and late dates are the suggested and latest time to perform a PM task, respectively. The optimization algorithm assigns the occurrence of these tasks within the associated PM windows. Thus, PM tasks have a nominal frequency to be performed; for example, every 30 d or every 15 000 wafers since the last PM task was completed. The frequency is determined by the semiconductor fab operations and based on recommendations from the tool’s manufacturer. The optimization increases tool throughput and availability by determining due dates of PM tasks, within the scheduling horizon, e.g., by avoiding periods of high-incoming WIP, and by consolidating PM tasks. Consolidating PM tasks involves scheduling PM tasks to occur synchronously, if those tasks can be performed concurrently on the tool, thus reducing the total time to complete all the tasks and increasing overall tool availability. When a consolidation is obtained, PM tasks with the longest repair time are selected. Scheduling PM tasks by avoiding periods of high-incoming WIP helps ensure that the tools are not down for maintenance during times when these are most needed. In the next section, we present a description of the software tool PMOST, which implements the PM scheduling optimization algorithm. III. Preventive Maintenance Optimal Scheduling Tool (PMOST) Different operational data from the process is required to formulate the MIP problem (e.g., estimated WIP, tool parameters, and scheduling horizon). The optimization algorithm [3]–[5] was originally designed to use PM tasks based on calendar-time schedules because of ease of use of data in this

479

Data inputs and outputs for the PM optimization algorithm.

format and dimensionality of the MIP. When noncalendarbased PM schedules are considered (e.g., processing-timebased PM tasks), these need to be converted into calendar-time format by using, e.g., the conversion algorithm in [6] and [7]. The data inputs and outputs for the optimization algorithm are illustrated in Fig. 3 below. As presented, the algorithm receives as data inputs a set of tools, an initial PM schedule, a scheduling horizon, projected incoming WIP, cost parameters and constraints, as well as the available resources. As data outputs, it generates the optimized schedule, the estimated tool availability and the estimated WIP when the optimized PM schedule is utilized. The preventive maintenance optimal scheduling tool (PMOST) is a comprehensive software tool designed to implement the PM scheduling optimization model presented in [3], [4], and [5] (see also [9]). This software tool was developed as a joint effort of the systems modeling and information technology laboratory at the University of Cincinnati, Cincinnati, OH, and the Institute for Systems Research at the University of Maryland, College Park. In the same way as the optimization algorithm [3]–[5], PMOST accepts a set of input parameters and data related to the PM optimization process, e.g., scheduling horizon, number of available resources for the PM tasks, cost coefficients related to the PM tasks (see Fig. 3), via data files and user input. The data files consist of both static and dynamic data. Static data is information that does not generally change from run to run of the optimization, e.g., mean duration of a PM task. This data is generally entered manually into text files. Dynamic data is information that changes from run to run of the optimization, e.g., upcoming due date of a PM task. Thus, PMOSTs static data files include information of the tool family, PM tasks per tool, and a file with a mapping of the effective throughput of tools with multiple chambers. The dynamic data files include data of the initial or baseline PM schedule for the tool group, the projected WIP levels per tool at each period in the scheduling horizon, and the number of technicians available per period in the scheduling horizon. Regarding the length of the periods for the scheduling horizon, it is a common practice in the industry to utilize scheduling horizons of one or two weeks, with periods of one day or one shift, i.e., half day. Also, data projections of WIP levels at each tool can be obtained from scheduling tools such as the realtime dispatcher [10]. Moreover, the collection of the dynamic data could be automated by linking the necessary input files to the different fab information systems, e.g., manufacturing execution system (MES) [10], enterprise resource planning. PMOST assembles the input data into a mathematical programming system (MPS) file [11], [12], which contains the objective function, constraints, and all input data. The MPS file

480


Fig. 5.

Fig. 4.

PMOST flow diagram.

format, created by IBM in the 1960s, is a standard for defining linear programming (LP) problems, and is widely accepted by commercial LP solvers [13]. Although PMOST does not need a modeling description language (MDL) [13], [14] to model the optimization process and generate the corresponding MPS file, modifications on future versions of PMOST may include interfaces with MDL software, e.g., AMPL [15] and ILOG optimization programming language (OPL) [16]. Currently, PMOST has the ability to work directly with any commercial mathematical programming solvers that accept command line executions. Solvers that have been successfully utilized with PMOST include IBM optimization solution library (OSL) [17] and ILOG CPLEX [18]. For instance, PMOST is able to generate a call to IBMs OSL, transferring the MPS file and processing the output results from the solver. The parsed solution from the IBMs OSL can be easily read and displayed, or used to create a PM order file for simulation purposes, e.g., in AutoSched AP [19], [20]. The core of PMOST was written in C [21], which allows portability across different platforms or operating systems. For the current version of PMOST, we also developed a User Interface (UI) in C++ [22] which works under Microsoft Windows platforms. Fig. 4 below depicts the flow diagram of PMOST with the different processes that are executed by this software tool. As illustrated in the figure, the program “pmost ui.exe,” which corresponds to the UI application, includes the process utilized to gather information manually from the user, such as the scheduling horizon, tool family information, and number of technicians. The UI application is also utilized to manually start the PM optimization process. Also, the application “conv2cal.exe” implements the conversion algorithm reported in [6] and [7] for the conversion of noncalendar time PM schedules, e.g., wafer-based PM tasks. Within the

PMOST user interface screenshot, tool/PM data file.

user interface is the core application, “pmost.exe,” which uses as input the data collected by reading the static and dynamic information contained in multiple data files. The core application then generates the corresponding MPS file that is passed to the LP/MIP solver to generate the PM optimization. Once the solver finds a feasible solution according to the input data provided, then the solution is properly parsed into a calendar-time format that can be used by the fab simulation model, or for direct use in the PM operations. In the work described here, the simulation models utilized were those in use at the industrial sites, which were implemented utilizing commercial software, e.g., AutoSched AP [19], [20]. The current version available for PMOST is version G2.0. Several screenshots from the user interface of this version are found below. Fig. 5 shows a screenshot of a Tool/PM data file open for editing. This file contains the general parameters for the tool group. Fig. 6 shows a screenshot that illustrates the progress of the optimization process during a run. After a successful optimization run, the user can open and view the optimal PM schedule in a text file. The screenshot in Fig. 7 shows a solution file that contains the optimal PM schedule from the optimization run. The optimal PM schedule is given alongside the initial PM schedule. In the next section, we present an overview of the simulation studies, including the general conditions for the simulation experiments, as well as additional terminology utilized in the subsequent sections. Each case study described in the following sections utilized PMOST, together with IBMs OSL or CPLEX, to obtain the optimized PM schedules.

IV. Simulation Studies Overview Four simulation case studies were performed for three relevant semiconductor manufacturing operations: photolithography, metal deposition, and thin films. In previous work, presented in [3] and [5], another simulation case study is provided for which a group of 11 tools in a thin films


Fig. 6. PMOST user interface screenshot, progress of optimization process during a run.

Fig. 7.

PMOST user interface screenshot, optimal PM schedule file.

operation was considered. That case study also considered the optimization objectives given in (1) and (2), and the results reported in [3] and [5], demonstrated an increase of tool throughput of up to 13.9%. In this paper, we present results from simulation experiments conducted in two fabs, each from a different semiconductor companies. Moreover, the metal deposition and thin films operations case studies presented here included both calendar-time and wafer-based PM tasks. Similarly to the study reported in [3] and [5], the results presented in this paper indicate that a maximum increase of 14.2% was observed in tool throughput for the thin films operations. All the case studies presented in this section were conducted utilizing industrial data and the corresponding full factory simulation models, including modeling of unscheduled tool downtimes due to failures, from the two fabs that participated in the study. The simulation experiments were performed under strict supervision of the personnel in charge of factory simulations at each company, and by following the simulation practices

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utilized at each fab. In addition, the different data required for modeling and the optimization process was collected in meetings with personnel in each fab, from technicians to tool/process managers. It is important to mention that the types of simulation case studies described in this section are difficult to perform. These experiments are costly, in terms of the time invested by qualified personnel in charge of factory simulation, the need that they be conducted over a limited time period, the experiments involve very sensitive data related to the simulation model, and the complexity of the corresponding implementation of the experiments. Therefore, in this section we present as much information as possible from our onsite research at the fabs and companies that participated in the study. As indicated earlier, these simulation case studies were done in two different industrial settings. Therefore, the two sets of simulation studies conducted differ in terms of the factory simulation model utilized, and some simulation parameters, e.g., number of replications, simulation lengths, warm-up periods which were done as per common practices utilized by the different industrial groups. Unfortunately, not all the numerical results presented in this paper are given in the same format because of the difficulties mentioned above and because of the different simulation practices utilized at each fab. In the case of the photolithography process, two different groups of tracker/stepper tools were selected. These tools are utilized to expose wafers with the circuit patterns, which are later etched into the wafers. Steppers are good candidates for optimization because of their high cost, and these are common bottlenecks in the manufacturing process. Increasing the throughput of a set of steppers through optimization, can alleviate the bottleneck condition and possibly allow a fab to reduce equipment costs by obtaining the same productivity from a smaller amount of tools. Tracks are responsible for preparing the wafers for the steppers. This preparation involves coating the wafers with photoresist and spinning them to evenly distribute it. The tracks were considered in the simulation studies because these are physically connected to the steppers, and thus PM activities performed on them affect the operation of the steppers. The tools in the thin films and metal deposition processes are utilized to deposit thin layers of material on the wafers (e.g., metallic layers, silicon oxide). As with the tracker/steppers, these tools are good candidates for optimization because they are common constraints (e.g., bottlenecks) in the fab. The four simulation case studies are organized below. 1) Case I: Considered a PM schedule with only calendartime-based PM tasks in a tracker/stepper tool group for a photolithography process. 2) Case II: This case included a PM schedule with only calendar-time-based PM tasks and was performed on a second tracker/stepper tool group for a photolithography process. 3) Case III: Utilized PM schedules with only wafer-based PM tasks on a set of metal deposition tools.

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4) Case IV: Applied a PM schedule of both calendar and wafer-based PM tasks for a thin films tool group. From the previous list, notice that although the Case Studies I and II utilized the same type of tools and process, we preferred to differentiate these because each case was conducted in a different fab, and thus under significant data and simulation settings differences. The pairs of Case Studies {I, III}, and {II, IV} were performed in different industrial settings. Therefore, these two sets of experiments differ in terms of the factory simulation model utilized and the simulation experiments parameters, e.g., number of replications, simulation lengths, warm-up periods, etc., as per common practices utilized by the different industrial groups. The simulations were performed by using actual fab simulation models built in AutoSched AP [19], [20]. For each of the four case studies, two schedules were simulated for multiple replications: one generated by applying a heuristic or baseline PM schedule employed by the fab, and the other obtained through the PM optimization algorithm. Performance was compared between the optimized and nonoptimized schedules. Through the next sections, we use the following terminology for PM schedules. 1) Baseline is defined as the nominal PM schedule that contains the raw PM due dates based on PM frequencies. These frequencies are suggested by the tool manufacturers and fab operations. The baseline schedules can be specified in calendar-time, wafer, or processing time formats. 2) Initial is a strictly calendar-time version of the baseline schedule, where all noncalendar PM tasks (e.g., wafer based) have been converted to equivalent calendar-based PM tasks. The initial PM schedule is the input schedule for PMOST. 3) Heuristic is defined as a PM schedule generated and implemented by fab engineers. In general, this type of schedule is created manually from a baseline schedule. 4) Optimal schedule is obtained from the PM scheduling optimization algorithm implemented in PMOST. The following are common conditions considered in the four case studies. 1) The semiconductor fab operated 24 h a day, seven days of the week. 2) The statistics of interest collected from the simulation studies were: percentage of tool availability, tool utilization, and tool throughput (production). 3) Actual heuristic PM schedules were obtained by collecting historical operational data from the fab information systems. The data include the baseline PM schedules for the scheduling horizon that were based on the assigned frequencies for each PM task. The next subsections, describe the specific conditions considered in each case. Cases I and II are presented together because of the similarity of their conditions, while Cases III and IV are described independently.

A. Case Studies I and II: Optimal Scheduling of CalendarTime PM Tasks on Photolithography Process Tools Cases I and II considered stepper and track tools in a photolithography process. In both cases, the PM activities were strictly calendar based, thus, no conversions were needed to feed the PM tasks into the optimization algorithm (i.e., the PM optimization works in calendar time only). The simulation studies were conducted under the following conditions. 1) Case I conditions are as follows. a) The scheduling horizon considered was 8 d. b) PM tasks were only calendar-time based. A total of 12 single-chambered tools were considered in the simulation study, of which only eight tools had their PM windows in the scheduling horizon. c) PM tasks were performed with different frequencies since the last PM (e.g., every week, month), from 7 to 90 d. d) A baseline PM schedule, in calendar-time format, was obtained from the fab information systems, e.g., MES, in-house customized systems. It was directly used as an initial schedule by PMOST. e) Estimated incoming WIP, from the fab’s lot scheduling system, e.g, real-time dispatcher (RTD) [10], was specified in hours of processing-time. 2) Case II conditions are as follows. a) The scheduling horizon was one week (7 d). b) The simulation study involved 25 steppers and 25 tracks, e.g., each stepper and track combination modeled as a single tool. Of these tools, 13 had PM tasks due within the scheduling horizon. c) The baseline PM schedule was in calendar-format; thus it was utilized as an initial schedule by PMOST. d) Additional data, such as a WIP snapshot for the fab at the beginning of the week and the wafer starts for the week, were gathered to ensure an accurate simulation. For Case II, a WIP snapshot was used to initialize the fab at the beginning of the scheduling horizon. The snapshot indicated the amount of WIP at each tool and processing step at the horizon start. The wafer starts data indicated the amount of new wafers started during the scheduling horizon. Coupled with the WIP snapshot, this data enabled the simulation to accurately reflect the WIP conditions in the fab. In particular, for Case II, since each stepper and track combination was modeled as a single tool, PM activities were scheduled on the whole tool as opposed to being scheduled on the tool’s chambers. However, since each stepper and track were physically linked together, taking one tool down for maintenance disabled the other tool. Thus, the steppers and tracks were each considered chambers of a twochambered tool. Treating each stepper-track combination as a two-chambered tool allowed the optimization algorithm to take advantage of potential PM consolidations, where if a PM task was scheduled on one chamber, then a second PM task could be scheduled to occur concurrently on the second chamber.


In contrast, the tools in Case I were considered as singlechambered. In general, by scheduling PM tasks to occur concurrently, the total time to complete the tasks may be reduced. That is, by consolidating several PM tasks for a tool, the number of times that the tool needs to be taken down is reduced as compared with the case in which the PM operations are not performed concurrently. The immediate benefit from PM consolidations is then an increase in tool availability. That is, consolidating PM tasks helps to minimize the total maintenance time that a tool experiences, which in turn, helps to maximize both tool availability and throughput. B. Case Study III: Optimal Scheduling of Wafer-Based PM Tasks on Metal Deposition Tools The third case study focused on scheduling strictly waferbased PM tasks on a group of tools for a metal deposition process. To optimally schedule wafer-based PM tasks, the conversion algorithm in [6] was applied to obtain an equivalent baseline PM schedule in calendar-time format. This was used as an initial PM schedule in PMOST. The simulation study considered the following conditions. 1) The scheduling horizon was 8 d. 2) Four different wafer-based PM tasks were considered. 3) Although a total of 29 tools were included in the simulation study, only five tools had their PM windows in the scheduling horizon. These five tools were then considered for the PM optimization process. 4) The due amounts of wafers required to perform each PM task were in the order of thousands of wafers. 5) Estimated incoming WIP, from the fab’s lot scheduling system, e.g, RTD [10], was given in hours of processing time. In addition to comparing the performance of optimized and nonoptimized PM schedules, a related goal was also to utilize this case study to validate the integration of noncalendar-based PM schedules into the PM optimization process. Moreover, the accuracy of the conversion algorithm was evaluated by comparing historical data against the estimated calendar-time PM schedules. In general, a satisfactory performance was obtained as it is reported in [7]. However, an important conclusion from this experience is that accurate projections or estimates of the incoming WIP are required to improve the accuracy of the equivalent calendar-time PM schedules. For instance, in the evaluations of the conversion algorithm reported in [7], it was observed that the accuracy in the estimations is affected by projected WIP levels that are far from the PM window targets, i.e., warning, due, and late dates. In practice, the engineers in charge of the factory simulations at the fabs prefer to utilize WIP projections of no more than two weeks for the scheduling horizons. In doing so, the goal is to provide accurate simulations that are then utilized in different planning of operations in the fab, including PM. Moreover, accurate estimates of the incoming WIP will directly affect the PM optimization process. For instance, MIP Objective (1) depends directly on the projected incoming WIP; therefore, the solution obtained by solving the MIP will

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reflect the operational conditions assumed by using the WIP projections. C. Case Study IV: Optimal Scheduling of Mixed-Type PM Tasks on Thin Films Tools The fourth simulation study was performed on a group of thin films tools, which are responsible for depositing a layer of dielectric material ("glass") on wafers. The simulation study was conducted under the following conditions. 1) The scheduling horizon was 22 d. 2) The simulation study involved 28 thin films tools. Of these tools, 16 had PM tasks due within the scheduling horizon. 3) The thin films tools employed both calendar and waferbased PM tasks. The thin films tools were chosen because these were true parallel tools, which is what the PM scheduling optimization is best suited for. Parallel refers to the fact that multiple chambers of the tool can perform the same functions. This ability allows the tool to still operate, at a reduced throughput, while a chamber is taken down for maintenance. In addition, these tools are also common bottlenecks in the fab, because they are subject to large amounts of reentrant flow, where a wafer comes back to the same tool type for further processing. In principle, these tools are good candidates for the optimization. Each tool in the group was comprised of three processing chambers along with a main transfer chamber, where a robot transfers wafers from one processing chamber to the next, as well as initially transferring wafers from the load docks to the first processing chamber. However, chamber-specific data was not made available to us at the time of the study, and thus for the purpose of the PM scheduling optimization, the entire tool was considered as one chamber. Also included in the optimization were subfab PM activities. The term subfab refers to the pumps and other equipment that lie beneath the floor, under the tools. These PM tasks were included because their execution also requires that the tool be taken down for the duration of the PM operation. The subfab was considered as an additional chamber of the tool. For the PM optimization, the tools had to be modeled as two-chambered tools, with the entire tool representing the first chamber and the subfab representing the second one. This simplification reduced the possibility of the optimization finding PM consolidations. However, as the results show, some consolidations were made, and slight improvements in performance were then achieved. In addition, since the optimization works in terms of calendar time, the wafer-based PM windows needed to be converted to equivalent calendar-based PM windows. Because historical data was being used for the simulation study, this was not a difficult task since the wafer counts of each tool could be matched up with their corresponding calendar times. Thus, by looking at historical production data, the wafer counts corresponding to the PM windows could be matched up with calendar dates. The next section presents the results from the simulation case studies.

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TABLE I Comparison of Baseline and Optimal PM Schedules for Case Study I

PM Name STR1 PMC1 STR2 PMC1 STR3 PMC2 STR4 PMC3 STR5 PMC4 STR6 PMC2 STR7 PMC5 STR8 PMC3

PM Schedule (Day) Baseline Optimal 1 2 1 2 4 4 1 2 8 Do Not Perform PM 3 4 5 6 7 Do Not Perform PM

V. Optimization and Simulation Results This section presents the results from the PM scheduling optimization and simulation studies. The results for each case study are described independently and organized by subsections. In addition, each subsection presents a comparison between the initial and optimized PM schedules, as well as the percentage change observed in the performance statistics for the tool group when a baseline or a heuristic PM schedule was replaced by an optimized PM schedule. A. Results for Case Study I: Scheduling of Calendar-Time PM Tasks on Photolithography Process Tools. A comparison between the optimal and baseline PM schedules is shown in Table I. In this table, the label STR# PMC# represents the PM name that is associated to each pair of tools and PM tasks. These labels are utilized instead of the actual names for proprietary reasons. For instance, STR1 PMC1 corresponds to the PM task "PMC1" at tool "STR1". As presented in Table I, the only PM operation that was not modified by the optimization process is STR3 PMC2. Moreover, the optimal PM schedule indicates to not perform the PM tasks STR5 PMC4 and STR8 PMC2 within the corresponding PM scheduling horizon. Statistical results for this simulation study are presented in Table II. These results correspond to average values for the entire group of twelve tools when three replications were generated using the baseline and optimal schedules. While the first column lists the performance statistics considered, the second and third show the maximum and minimum percentage change for a single tool in the group, respectively, when the baseline is replaced by an optimized PM schedule. Similarly, the last column indicates the average change in the statistic over the entire group of tools when the baseline is replaced by an optimized PM schedule. The first statistic in Table II corresponds to the average number of wafers completed (WCOMPS). Results indicate that when the optimized PM schedule was applied, the group of tools produced on average 1.64% more wafers as compared with the baseline PM schedule. Notice, however, that the PM tasks STR5 PMC4 and STR8 PMC3, which require several hours to be completed, were not performed under the optimized PM schedule and these were then expected to be scheduled earlier in the next scheduling horizon.

TABLE II Performance Results From Case Study I: Percentage Change for Baseline Versus Optimal PM Schedule Statistic WCOMPS AVAIL UTIL

Max. (%) 96.85 54.15 53.10

Min. (%) −38.01 −34.56 −34.74

Avg. (%) 1.64 1.02 1.68

Min., Max.: Minimum and maximum change in a single tool. Avg.: Average change over the entire tool group.

The results also indicate that the positive change in WCOMPS is due to better PM scheduling provided by the optimization algorithm rather than the nonscheduling of PM operations in the tools STR5 and STR8. In fact, the increase in WCOMPS for the tool group under the optimal PM schedule is due to production increases in the tools that received PM operations within the scheduling horizon, some of them yielding an increase of up to 97% in production. Interestingly, the results indicate that the tools STR5 and STR8 decreased their WCOMPS by about 20% under the optimal PM schedule. Nevertheless, in other case studies presented in this paper we also observed an increase in WCOMPS when the optimized schedule was utilized and all the PM tasks were properly scheduled within the PM scheduling horizon. As can be seen in Table II, by solely looking at the numbers, the percentage improvement obtained with the optimal PM schedule is relatively small. However, even such small changes in the tool group performance, e.g., average WCOMPS, may represent substantial increases in marginal profits in the semiconductor manufacturing business. The results from this case study also indicate slight but positive differences of 1.02% and 1.68% in average tool availability (AVAIL) and average tool utilization (UTIL), respectively, by applying the optimal PM schedule. Although the statistics for some single tools obtained a significant increase while for other tools the statistics decreased, it was observed that the average performance of the entire tool group was improved when the optimized PM schedule was utilized. B. Results for Case Study II: Scheduling of Calendar-Time PM Tasks on Photolithography Process Tools. The results of the optimization for this case are given in Table III. In this table, the optimal PM schedule is given alongside the heuristic schedule. The first column of the table provides the PM names, which have been also modified from the actual names. Each PM name is comprised of the tool name (Tool#) and a chamber name (CH#). Chamber one (CH1) refers to the stepper, and chamber 2 (CH2) refers to the track. The symbols †, , and ♦ indicate the dates with consolidations of PM tasks in a tool. By consolidation we mean conducting two or more different PM tasks in the same tool. From Table III, notice that several PM tasks are consolidated in both the heuristic and optimal PM schedules, e.g., PM tasks on the stepper (CH1) and track (CH2) of Tool13. The way in which the heuristic PM schedule is presented indicates that fab engineers performed consolidations of PM tasks as appropriate


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TABLE III

TABLE V

Comparison of Initial (Baseline) and Optimal PM Schedules for Case Study II

Comparison of Baseline and Optimal PM Schedules for Case Study III

PM Schedule (Day) Heuristic Optimal 2 2 5 2 1 3 3 1 1 2 4 6 2† 3† 2† 3† 6 3 6 2 3 7 3 7 ♦ 5 1♦ ♦ 5 1♦ 1 2 4 4 4 4

PM Name Tool1 CH1 Tool2 CH1 Tool8 CH1 Tool10 CH1 Tool11 CH1 Tool12 CH1 Tool13 CH1 Tool13 CH2 Tool14 CH1 Tool17 CH1 Tool18 CH1 Tool18 CH2 Tool19 CH1 Tool19 CH2 Tool20 CH1 Tool25 CH1 Tool25 CH2

†, , ♦: Dates with consolidated PM tasks in a tool. TABLE IV Performance Results From Case Study II: Heuristic Versus Optimal PM Schedule Statistic WCOMPS AVAIL UTIL

Change (%) 0 0.03 0.01

due to the physical interrelationships between the steppers and trackers described in Section IV. This interdependence between steppers and trackers was also indicated to the PM optimization algorithm as constraints. As a result, the PM optimization algorithm preserved the PM task consolidations, while changing the dates when the tasks were scheduled. Thus, any improvements in tool throughput made by the optimization algorithm would therefore be left to scheduling the PM tasks around periods of high-incoming WIP. The simulation results for the tool group are given in Table IV. These results show the percentage change for the total number of WCOMPS when the heuristic PM schedule was replaced by an optimized schedule. Table IV also lists the percentage change for the AVAIL and UTIL. The results represent the average statistics from ten simulation replications. The results in Table IV show very minor improvements in tool availability and tool utilization made by the PM optimization. These gains were most likely due to scheduling the PM tasks around periods of high-incoming WIP, since the PM consolidations, made by the optimization, were also made by fab engineers. Evidently, the fab engineers did a very good job at scheduling PM tasks in this instance, but accomplishing this may be a very time-consuming job and highly sensitive to the ability of the particular individual(s) performing the scheduling. Fig. 8 illustrates a WIP profile for

PM Name MDep1 PMW1 MDep1 PMW2 MDep2 PMW3 MDep2 PMW1 MDep3 PMW3 MDep3 PMW1 MDep4 PMW3 MDep5 PMW3

PM Schedule (Day) Baseline Optimal 1 2† 2 2† 3 4 5 4 5 2♦ 3 2♦ 4 2 7 5

†, , ♦: Dates with consolidated PM tasks in a tool.

the tool group during the scheduling horizon, taken from the simulation results. The figure shows that highest WIP level occurred on Day 5 and the lowest on Day 2. Referring to the PM schedules in Table III, the PM optimization avoids scheduling PM tasks on Day 5 and schedules several tasks on Day 2. The results of this simulation study validate the PM scheduling optimization. While the PM optimization does not make major gains in this simulation study, it does show that it can capture the major decision factors in the PM scheduling process and perform as well as the best heuristic policies. An argument in favor of the use of such software tool is that it would yield optimized schedules every time, guiding fab engineers to the best schedule and thus avoiding any potential gross inefficiencies due to human error. The optimization would also be of value in efforts to automate the PM scheduling process. Automating the PM scheduling process would not only save time to engineers who manually generate the PM schedules, but could also lead to more sophisticated lot scheduling in the fab. C. Simulations Results for Case Study III: Scheduling of Wafer-Based PM Tasks on Metal Deposition Tools. In this case study, an optimized schedule was obtained for wafer-based PM tasks. Table V shows both the initial and optimal PM schedules. In the first column of Table V, the label MDep# PMW# identifies the PM name that is associated with the pair of tools and PM tasks. The second and third columns list the baseline and optimal schedules, respectively. The baseline PM schedule was estimated by using the conversion algorithm in [6]. It should be noted from Table V that consolidations of PM tasks are produced in three out of the five tools considered in the optimization. Consolidations of PM tasks in the tools are highlighted in bold and properly identified with the symbols †, , and ♦ in Table V. For instance, before the optimization the PM tasks PMW1 and PMW2 were scheduled on different days for the tool MDep1. After the PM scheduling optimization, these PM operations for MDep1 were consolidated and scheduled on the same date (Day 2). Moreover, notice that for this simulation experiment the tools considered did not have the physical constraints observed for the steppers and trackers of Case Study II. Thus, in this case the PM optimization

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Fig. 8.


Sample WIP profile for Case Study II optimization results.

TABLE VI

TABLE VII

Performance Results From Case Study III: Percentage Change for Baseline Versus Optimal PM Schedule

Comparison of Heuristic and Optimal PM Schedules for Case Study IV

Statistic WCOMPS AVAIL UTIL

Max. (%) 14.52 5.83 6.34

Min. (%) −8.09 0 −2.65

Avg. (%) 2.19 1.04 0.75

Min., Max.: Minimum and maximum change in a single tool. Avg.: Average change over the entire tool group.

algorithm provided PM task consolidations that both improved the overall scheduling and were not due to physical constraints in the tools. The statistical results from the simulation are presented in Table VI. The value of these percentages of change in the statistics represent an average of three replications and considered the entire tool group. In addition, the minimum and maximum change for a single tool is indicated. As seen in this table, the optimal PM schedule produces a positive effect in AVAIL; an average of 1.04% improvement was obtained. Also, the total number of WCOMPS was increased in 2.19% by utilizing the optimal schedule. Similarly, note that some single tools obtained either substantial increases or decreases in the statistics when the optimized PM scheduled is applied, while the percentage change over the entire tool group remains positive. In this case, it is clear that the consolidation of PM tasks produced a significant positive effect in tool availability and throughput. Two objectives were accomplished with this case study. First, it validated the PM optimization algorithm by presenting positive improvements in the tools’ production. And second, the case study served as proof of concept for the integration of the conversion algorithm [6], [7] for noncalendar time schedules and the PM scheduling optimization algorithm. D. Simulations Results for Case Study IV: Scheduling of Mixed-Type PM Tasks on Thin Films Tools. Table VII presents the results of the optimization for this case study. In the table, the optimal PM schedule is given

PM Name Tool5 CH1 Tool6 CH1 Tool6 CH2 Tool7 CH2 Tool8 CH2 Tool10 CH1 Tool19 CH1 Tool20 CH1 Tool21 CH1 Tool21 CH2 Tool22 CH2 Tool31 CH2 Tool32 CH2 Tool33 CH2 Tool34 CH1 Tool34 CH2 Tool35 CH1 Tool37 CH1 Tool39 CH1 Tool39 CH2

PM Schedule (Day) Heuristic Optimal 17 16 12 10† 5 10† 5 3 16 2 9 6 3 4 3 1 16 14 6 14 6 16 1 8 1 11 17 8 9 10‡ 17 10‡ 8 6 2 1 15 12♦ 8 12♦

†, , ‡, ♦: Dates with consolidated PM tasks in a tool.

alongside the heuristic schedule. The resulting PM task consolidations in the tools are highlighted in bold in the third column and marked with the symbols †, , ‡, and ♦, respectively. The first column of the table provides the modified PM names. Each PM name is comprised of a tool name (Tool#) and chamber name (CH#). Chamber one (CH1) refers to the tool and chamber 2 (CH2) refers to the subfab. The results from the simulation for the entire tool group are given in both Table VIII and Fig. 9. In Table VIII, the percentage change in the statistics represents the average from ten simulation replications. As it can be seen in this table, both the amount of wafers completed and the utilization of the tool group was increased about 1% by the optimal PM schedule and with respect to the heuristic PM schedule. The availability of the tool group was also increased in 0.68%.


Fig. 9.

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Tool utilization/availability (U/A) improvement using Baseline and Optimal PM schedules, Case Study IV.

TABLE VIII Performance Results From Case Study IV: Heuristic Versus Optimal PM Schedule Statistic WCOMPS AVAIL UTIL

Change (%) 0.94 0.68 1.00

Evidently, the fab engineers did a very good job at scheduling PM tasks in this instance also, but again, accomplishing this may be a very time-consuming job, and highly sensitive to the ability of the particular individual(s) performing the scheduling. Fig. 9 illustrates the ratio of utilization to availability (U/A) for each tool obtained for this simulation case study. As depicted in this figure, in most of the cases when an optimized PM schedule is utilized a lower value of the ratio U/A is observed (i.e., lower level bar), indicating an increase in tool availability; therefore, an improvement in production performance. In this case, PM consolidations made by the optimization resulted in an average of 4.77% increase in tool availability among the four tools that experienced consolidation, with a maximum 6% availability increase for one tool. This simulation study showed good results. Tool availability was increased significantly for several tools, with a maximal increase of 6%. These benefits are due mostly to the consolidation of subfab and normal PM tasks. It is worth mentioning that simplifications were needed to specify the tool parameters for the purpose of the PM optimization. As indicated in the overview of this case study given in Section IV, the tools studied had three processing chambers. However, specific data for each chamber was not available. Thus, for PM optimization purposes these three chambers were specified as one while the subfab represented the second chamber. These necessary simplifications reduced the possibility of finding PM

consolidations and thus limited the full potential of the PM scheduling optimization algorithm. VI. Conclusion The architecture and implementation of the software tool PMOST, which utilizes a PM optimization algorithm for semiconductor manufacturing operations, has been described. To demonstrate how PMOST can be utilized in practice to improve PM operations, we presented results from four complex simulation case studies, based on real industrial data, that were conducted on groups of semiconductor manufacturing tools, located at two separate fabs. Results from these simulation experiments demonstrated that the PM optimization performed as well as, if not better than, the heuristic PM policies obtained by the fab engineers, and in Studies III and IV it performed noticeably better than the available fab’s baseline PM schedules. Software implementations of PM optimal scheduling algorithms as PMOST, are therefore shown to be a valuable decision support tool, which can be used by fab engineers to aid in PM scheduling, as well as a component in efforts to automate the PM scheduling process. Results presented here also demonstrated an increase in tool production. As such, the utilization of a PM optimization algorithm can lead to significant improvements in marginal profits. By presenting here an architecture and the corresponding software implementation of the PM optimization algorithm, i.e., PMOST, we also aimed to provide guidelines and a template, as well as experimental data, that can help in the adoption of these by others, and also perhaps serve as the basis for generic third-party commercial tools. Moreover, the current version of PMOST is subject to further improvements. For instance, PMOST currently does not use a MDL for the optimization model and to generate the corresponding MPS file used by the LP/MIP solver. However,

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future versions or modifications of PMOST could include interfaces with MDL software to facilitate implementation and portability. References [1] M. Venables, “Small is beautiful: Small, low-volume semiconductor manufacturing plants,” IEE Rev., vol. 51, no. 3, pp. 26–27, Mar. 2005. [2] J. Blau, “News analysis: Europe’s semiconductor makers are back in the game,” IEEE Spectr., vol. 40, no. 2, pp. 18–19, Feb. 2003. [3] X. Yao, M. C. Fu, S. I. Marcus, and E. Fernandez-Gaucherand, “Optimization of preventive maintenance scheduling for semiconductor manufacturing systems: Models and implementation,” in Proc. IEEE Int. Conf. Control Applications, 2001, pp. 407–411. [4] X. Yao, M. C. Fu, S. I. Marcus, and E. Fernandez-Gaucherand, “Incorporating production planning into preventive maintenance scheduling in semiconductor fabs,” in Proc. Int. Conf. MASM, 2002, pp. 84–89. [5] X. Yao, E. Fernandez-Gaucherand, M. C. Fu, and S. I. Marcus, “Optimal preventive maintenance scheduling in semiconductor manufacturing,” IEEE Trans. Semicond. Manuf., vol. 17, no. 3, pp. 345–356, Aug. 2004. [6] J. A. Ram´ırez-Hernández and E. Fernandez-Gaucherand, “An algorithm to convert wafer to calendar-based preventive maintenance schedules for semiconductor manufacturing systems,” in Proc. 42nd IEEE Conf. Decision Control, 2003, pp. 5926–5931. [7] J. A. Ram´ırez-Hernández, E. Fernandez, M. O’Connor, and N. Patel, “Conversion of noncalendar to calendar-time-based preventive maintenance schedules for semiconductor manufacturing systems,” J. Quality Maintenance Eng., vol. 13, no. 3, pp. 259–275, 2007. [8] S. Bhatnagar, E. Fernandez-Gaucherand, M. C. Fu, Y. He, and S. I. Marcus, “A Markov decision processes model for capacity expansion and allocation,” in Proc. 38th IEEE Conf. Decision Control, 1999, pp. 1380–1385. [9] J. Crabtree, “Optimal preventive maintenance scheduling in semiconductor fabs,” M.S. thesis, Dept. Elect. Comput. Eng., Univ. Cincinnati, Cincinnati, OH, 2003. [10] Real-Time Dispatcher. Applied Materials, Inc. [Online]. Available: http://www.appliedmaterials.com/products/rt dispatch 2.html [11] D. Applegate, W. Cook, S. Dash, and M. Mevenkamp. (2009). Mps Format [Online]. Available: http://www2.isye.gatech.edu/ wcook/qsopt/hlp/ff mps format.htm [12] I. Maros, Computational Techniques of the Simplex Method. Boston, MA: Kluwer Academic, 2003. [13] R. Fourer. (2005). Linear Programming: Software Survey [Online]. Available: http://www.lionhrtpub.com/orms/orms-6-05/frsurvey.html [14] R. Fourer, D. M. Gay, and B. W. Kernighan, “A modeling language for mathematical programming,” Manage. Sci., vol. 36, no. 2, pp. 519–554, 1990. [15] R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming. Belmont, CA: Duxbury Press Brooks Cole Publishing Company, 1993. [16] OPL Studio. ILOG, Inc. [Online]. Available: http://www.ilog.com/ products/oplstudio/ [17] D. G. Wilson and B. D. Rudin, “Introduction to the IBM optimization subroutine library,” IBM Syst. J., vol. 31, no. 1, pp. 4–10, Jan. 1992. [18] CPLEX Optimizers. ILOG, Inc. [Online]. Available: http://www.ilog.com/products/cplex/ [19] AutoSched AP. Applied Materials, Inc. [Online]. Available: http://www.appliedmaterials.com/products/autosched ap 2.html [20] T. Phillips, “Autosched AP by autosimulations,” in Proc. Winter Simulation Conf., 1998, pp. 219–222. [21] B. W. Kernighan and D. M. Ritchie, The C Programming Language, 1st ed. Englewood Cliffs, NJ: Prentice Hall, 1978. [22] B. Stroustrup, The C++ Programming Language, special ed. Reading, MA: Addison-Wesley, 2000. José A. Ram´ırez-Hernández (S’93–M’08) received the B.S., the Licenciatura and M.S. degrees (both with honors) in electrical engineering from the University of Costa Rica, San Jose, Costa Rica, in 1995, 1996, and 1999, respectively. Currently, he is pursuing the Ph.D. degree from the Department of Electrical and Computer Engineering, University of Cincinnati, Cincinnati, OH. From 1996 to 2001, he was an Adjunct Professor in the School of Electrical Engineering, University of Costa Rica. Since 2001, he has been with the Systems Modeling and Information Technology Laboratory, University of

Cincinnati. His current research interests include Markov decision processes, dynamic programming, simulation-based optimization, artificial intelligence, and computational biology. Prof. Ram´ırez-Hernández is a member of INFORMS and the Omega Rho honor society. Jason Crabtree received the B.S. degree in mechanical engineering, the M.S. degree in electrical engineering, and the M.S. degree in quantitative analysis all from the University of Cincinnati, Cincinnati, OH, in 2000, 2003, and 2004, respectively. From 2001 to 2003, he was a Research Assistant with the Systems Modeling and Information Technology Laboratory, University of Cincinnati. He currently works as a Project and Technical Operations Manager with Integral Analytics, Cincinnati. Xiaodong Yao (S’00–M’04) received the B.S. and M.S. degrees in automation and control from Tsinghua University, Beijing, China, and the Ph.D. degree in electrical engineering from the University of Maryland, College Park, in 1992, 1995, and 2003, respectively. From 1995 to 1998, he was a Lecturer in the Department of Automation and the State Computer Integrated Manufacturing Systems-Engineering Research Center, Tsinghua University, Beijing, China. He has been with the SAS Institute, Inc., Cary, NC, since 2004, and is currently an Analytical Solutions Manager with the Advanced Analytics Division. His current research interests include revenue management and pricing optimization, with applications to the retail, hospitality, and other industries. Emmanuel Fernandez (S’84–M’91–SM’96) received the Bachelors degree in electrical engineering from the University of Costa Rica, San Jose, Costa Rica, in 1983, the M.S. degrees in electrical engineering and applied mathematics from the University of Oklahoma, Norman, in 1985 and 1986, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Texas, Austin, in 1991. From 1991 to 2000, he was with the Department of Systems and Industrial Engineering, University of Arizona, Tucson, first as an Assistant Professor and then as an Associate Professor, and was on sabbatical leave at the University of Maryland and Texas A&M University from 1998 to 1999. Since 2000, he has been an Associate Professor in the Department of Electrical and Computer Engineering, University of Cincinnati, Cincinnati, OH, and the Director of the Systems Modeling and Information Technology Laboratory. His research areas of expertise include stochastic models, decision, and control processes, and mathematical and computational operations research. His current research interests include manufacturing, operations, management, telecommunication, logistics, algorithms, and software tools. Dr. Fernandez is a member of the IIE, INFORMS, and Society for Industrial and Applied Mathematics, as well as the honor societies Eta Kappa Nu, Omega Rho, and Tau Beta Pi. He has served as an Associate Editor for SIAM Journal on Control and Optimization. He was a co-recipient of the 1995 David Rist Prize from the Military Operations Research Society, and was named the 1993–1994 Professor of the Year by the Arizona Alpha chapter of Tau Beta Pi.

Michael C. Fu (S’89–M’89–SM’06–F’08) received the S.B. and S.M. degrees in electrical engineering, the S.B. degree in mathematics from the Massachusetts Institute of Technology, Cambridge, in 1985, and the M.S. and Ph.D. degrees in applied mathematics from Harvard University, Cambridge, MA, in 1986 and 1989, respectively. He is a Ralph J. Tyser Professor of Management Science with the Robert H. Smith School of Business, with a joint appointment in the Institute for Systems Research and Affiliate Faculty in the


Department of Electrical and Computer Engineering, A. James Clark School of Engineering, all at the University of Maryland, College Park. He is coauthor of Conditional Monte Carlo: Gradient Estimation and Optimization Applications (Kluwer, 1997) and Simulation-Based Algorithms for Markov Decision Processes (Springer, 2007), as well as co-editor of Perspectives in Operations Research (Springer, 2006), Advances in Mathematical Finance (Birkhauser, 2007), and Encyclopedia of Operations Research and Management Science, (Springer, forthcoming 2011, 3rd ed.). His current research interests include simulation and applied probability modeling, particularly with applications toward manufacturing systems, supply chain management, and financial engineering. Dr. Fu has served as the Simulation Area Editor for Operations Research, as Stochastic Models and Simulation Department Editor for Management Science, and on the Editorial Boards for INFORMS Journal on Computing, Mathematics of Operations Research, IIE Transactions, and Production and Operations Management. He was also a guest co-editor of a special issue on simulation optimization for the ACM Transactions on Modeling and Computer Simulation.

Mani Janakiram received the Ph.D. and M.S. degrees in industrial and systems engineering from Arizona State University, Tempe, the MBA degree from the Thunderbird School of Global Management, Glendale, AZ, and the B.S. degree in mechanical engineering. He is a Principal Engineer and the Supply Chain Research Program Manager with Intel, Chandler, AZ, and in his 10+ years with Intel, he has delivered several projects in supply chain, modeling, capacity planning, process control, analytics, and research. His expertise is in integrating business needs with analytics and software to provide effective solutions to the customers. He has 20+ years of experience, published 50+ papers, and has two patents. He is a Six Sigma Master Black Belt, and served on several committees including ITRS FI, Stanford AIM, ISMI, NSF research panels, and Factory Systems of Semiconductor Research Corporation. He is also an Adjunct Professor with the Thunderbird School of Global Management.

Steven I. Marcus (S’70–M’75–SM’83–F’86) received the B.A. degree in electrical engineering and mathematics from Rice University, Houston, TX, in 1971, and the S.M. and Ph.D. degrees in electrical engineering from the Massachusetts Institute of Technology, Cambridge, in 1972 and 1975, respectively. From 1975 to 1991, he was with the Department of Electrical and Computer Engineering, University of Texas, Austin, where he was a L.B. (Preach) Meaders Professor in Engineering. He was the Associate

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Chairman of the department from 1984 to 1989. Since 1991, he has been with the University of Maryland, College Park, as a Professor in the Department of Electrical and Computer Engineering and the Institute for Systems Research. He was the Director of the Institute for Systems Research from 1991 to 1996 and the Chair of the Department of Electrical and Computer Engineering from 2000 to 2005. His current research interests include stochastic control, estimation, hybrid systems, and optimization. Dr. Marcus is a Fellow of the Society for Industrial and Applied Mathematics.

Matilda O’Connor received the B.S. and M.S. degrees in industrial engineering from Stanford University, Stanford, CA, in 1986 and 1987, respectively, the MBA degree from the Kellogg Graduate School of Management, Northwestern University, Evanston, IL, and the Masters of Engineering Management from the McCormick School of Engineering, Northwestern University, in 1992. She was in the semiconductor and high-tech manufacturing industry from 1987 to 1990 and from 1992 to 2007. Her experience includes materials management, production planning and scheduling, demand planning and forecasting, supply chain management, capacity planning, simulation modeling, operations management, and organizational development. She is with Advanced Micro Devices, Inc., Austin, TX, and currently as the President with Bits, Bytes and Bots Computer Adventures, Austin, offering technology education programs for children.

Nipa Patel received the B.S. degree in industrial engineering from Mississippi State University, Starkville, and the M.E. degree in systems engineering from the University of Virginia, Charlottesville. She has a background in industrial engineering with a focus on simulation modeling, cost modeling, and supply chain planning as applied to the semiconductor industry. She was with SEMATECH in the Department of Operational Modeling and Statistical Methods. She was with Advanced Micro Devices in Manufacturing Systems Technology and the Strategic Planning groups. She is currently with GLOBALFOUNDRIES, Inc., Austin, TX, in supply chain planning.