Read the full paper (word file)


Published on

Published in: Business, Technology
  • Be the first to comment

  • Be the first to like this

No Downloads
Total views
On SlideShare
From Embeds
Number of Embeds
Embeds 0
No embeds

No notes for slide

Read the full paper (word file)

  1. 1. An Adaptive Distributed Simulation Framework for a Server Fulfillment Supply Chain Eamonn Ambrose and Vincent Yan Chen, John Fowler, Teresa Wu Thomas Callarman Hargaden Dept. of Industrial Engineering China Europe International Quinn Business School Arizona State University Business School University Collage Dublin Tempe, AZ, United States Shanghai, China Dublin, Ireland {jennychen, john. fowler, teresa.wu {eamonn.ambrose, ,thomas.callarman} vincent.hargaden} Abstract – Supply chains that produce and distribute . configuration, the servers wait on the docks to be computer servers are globally dispersed and have a transported to customers. high degree of uncertainty. To excel at servicing customers, a supplier must be highly skilled in Wafers IC s matching the assets in the system with customer demand. Discrete event simulation has been proven Assembly IC Customers valuable for system state estimation of supply chains. Wafer Fabrication &Test However, irregularities and disruptions occurring at any site along the system and the resulting bullwhip Server Fulfillment Servers effects can lead to significant departures of simulation- Center based estimation from the performance of the real system. These departures reduce the ability of the Server model to assist in making correct decisions. In this Customers paper, we propose an adaptive distributed simulation framework for a server fulfillment supply chain, and a Peripheral Warehouse Kalman filter to improve our estimates of job completion times. Fig 1. Scope of the Server Fulfillment Supply Chain Index Terms – Simulation, Server fulfillment supply chain For end-customers, good service means on-time receipt of parts ordered and the required quantities [1]. In this server fulfillment supply chain, each manufacturing facility I. INTRODUCTION faces a big challenge to meet the quota at the end of the Computer server fulfillment supply chain studied in this each quarter. The cost of unfulfilled orders can run into work is illustrated in Figure 1. It consists of 6 main millions of dollars. Two things in this server fulfillment elements: a wafer fabrication facility; an assembly and test supply chain make the task above challenging. The first is facility; a server fulfillment center; a peripheral warehouse; the scope of the problem, which includes complex end-customers for Integrated Circuits (ICs); and end- manufacturing flow and long cycle time in wafer customers for servers. Two types of products are produced fabrication, globally dispersed locations of the wafer in this system: integrated circuits (ICs) and configured fabrication, assembly and test facilities, and the server servers. fulfillment center. The second is irregularities and The core material transformation flow in this supply disruptions occurring at any point in the system without chain is wafers to ICs to servers. The wafers go through an warning due to the dynamic nature of a supply chain. elaborate process in a wafer fabrication facility in which Discrete event simulation has been proven valuable as a thousands of circuits are fabricated on the wafers. Once the practical tool for representing complex interdependencies, wafers are completed, they are then cut, packaged and evaluating alternative designs and policies, and analysing tested to create integrated circuits in an assembly and test performance tradeoffs for supply chain systems [2, 3, 4, 5, facility. After that, ICs are shipped to either IC customers 6, 7]. Jain et al. [8] describe a simulation study on the or the server fulfillment center depending on demand. In supply chain for a large logistics operation. The results the server fulfillment center, the ICs go through a series of indicate that improvement in forecast accuracy can provide panel assemblies and system tests with other peripherals larger savings than process automation changes. from a warehouse to configure ordered servers. After Applicability of distributed simulation for decision-making in semiconductor manufacturing has been demonstrated by Lendermann et al. [9]. Its popularity is also reflected in . industry applications. IBM developed a supply chain 1
  2. 2. simulator, which has a mix of simulation and optimization The High Level Architecture (HLA), which is a framework functions, to model and analyse its own supply chain developed by the Defense Modeling and Simulation Office issues [10]. IBM also used its own simulation-based supply (DMSO), provides the necessary infrastructure for large- Fig 2. Interaction between Federates in Distributed Simulation System chain analyzer to visualize and quantify the effects of scale distributed simulation. In HLA, a federate can be making changes on a hypothetical supply chain, and the viewed as a component simulation model that is taking part impact of the changes on system performance [11]. in a large simulation [14]. A federation consists of a set of Further, the need for executing supply chain simulations federates. For instance, in the case of supply chain based on a full-detailed model has also been pointed out: simulation, federates can be embodied factories or Jain et al. [12] compared two models with different levels suppliers and the federation is then the entire supply chain of detail for semiconductor manufacturing supply chains. itself. The result shows that simulations incorporating detailed In our distributed simulation framework, the federation models are required when attempting to determine the includes 6 federates. correct inventory levels for maintaining desired customer 1. IC demand generator responsiveness. In these cases, abstracted models can give 2. Server demand generator inaccurate results that may subsequently lead to erroneous 3. Wafer fabrication facility decisions. Venkateswaran et al. [5] drew similar 4. Assembly & Test facility conclusions in their paper. 5. Server fulfillment center In this paper, we describe how a distributed, detailed 6. Peripheral warehouse simulation model is built as a prototype for the server Each federate is a sub-model which executes on fulfillment supply chain above to be studied. Meanwhile, separate process in workstations and can be geographically we notice that irregularities and disruptions occurring at distributed. It improves the simulation execution speed, any site along the system and their resulting bullwhip supports reusability of existing simulation models and effects can make significant departures of simulation-based interoperability between different simulation packages. estimates about the system state from the real situation, The simulation model is composed of the basic elements which subsequently impairs its functionality in making of a supply chain [12]. These elements include correct decisions. To address this issue, we propose a manufacturing, transportation, business processes and Kalman filter based approach to calibrate the estimates for customer orders as depicted in Figure 2. entry and exit times at the wafer fabrication, the assembly Three successive stages of material transformation, and test facility, the server fulfillment center and the wafers to ICs to servers, are modeled. The transportation peripheral warehouse. Some preliminary work has been among wafer fabrication facility, assembly and test facility, done for the server fulfillment center only [13]. server fulfillment center and peripheral warehouse are modelled. So is the shipment to end-customers. II. DISTRIBUTED SIMULATION MODEL OF SERVER FULFILLMENT Forecasting, production and inventory planning that are SUPPLY CHAIN related to business processes are incorporated in the model. Customer orders are generated with the actual rate allowed The distributed simulation test bed used in our study is to be different from the forecasted rate so as to simulate an HLA-based discrete event simulation system that real life situations. The major components in this originated from a semiconductor supply chain simulator distributed simulation framework and their interaction are developed in C++ under a joint project between Singapore summarized in Figure 2. The federates interact with each Institute of Manufacturing Technology and the School of other through information and material flow. The Computer Engineering at Nanyang Technological information flow is represented using dashed lines while University, Singapore [12]. The test bed is implemented the material flow using solid lines. Each of the federates is using the Run Time Infrastructure (RTI), which is an described below. implementation of the HLA Interface Specification [14]. 2
  3. 3. A. IC Demand Generator (D/G) The manufacturing process in the server fulfillment center is shown in Figure 3. The chips provided by the The IC D/G generates orders for integrated circuits daily A&T facility along with other peripherals are put on the based on a predefined demand profile. These orders are boards in panel assembly. Then the assembly is tested at then fed to the assembly and test facility. The volume for this stage. Next, the tested assembly is put together with the orders of ICs can be varied each week by altering the additional peripherals to form a basic untested server demand profile. Each order is randomly assigned a system. This basic untested server system then goes for customer weight and due dates are randomly assigned to system test. After the test, the server system is each customer order, based on a uniform distribution. disassembled (Dekit) and the resulting tested components are put into storage to fulfill a future customer order. Once B. Server Demand Generator (D/G) a customer order is issued by the server demand generator, The server D/G generator works similarly to the IC servers are configured depending on the actual D/G. Server orders are produced daily based on another requirements. The configured customer servers are then predefined demand profile. The volume can be varied each tested and sent for packing and shipping. week by altering the demand profile. Each order is The production of servers before the point of fulfillment randomly assigned a customer weight and due dates are assembly is based on a make-to-stock strategy driven by randomly assigned to each customer order, based on a forecast, whereas the production starting after the uniform distribution. fulfillment assembly is based on a make-to-order strategy. The server fulfillment center releases multiple chip C. Wafer Fabrication modules and other peripherals into production based on the product’s work-in-progress level in the factory and in The production of wafers in the wafer fabrication transit, the inventory level in storage, the desired safety facility is based on a make-to-stock strategy driven by stock level and the forecasted demand for the server. At forecast, whereas the production of ICs in the assembly this moment, only one type of server is considered in this and test facility is based on a make-to-order strategy. The study. W/F facility releases wafer lots into production based on Once the orders from the server D/G are issued, based the product’s work-in-progress level in the factory and in on the availability of factory capacity and inventory, the transit, the inventory level of the wafer product in the server fulfillment center assigns orders to fulfillment warehouse of the A&T facility, the desired safety stock assembly. Meanwhile, it re-evaluates its stock level and level and the forecasted demand of the product. For further generates IC demand for Assembly and Test and peripheral details, refer to the paper by Chong et al. [15]. On a daily demand for warehouse, if necessary. basis, wafer fabrication ships completed wafers to the A&T warehouse with a shipment delay of one day. The wafer fabrication plant data is based on factory Start Panel Assembly Assembly Test Fab Assembly data from Sematech dataset 1, which is available through the Internet [16]. It produces two wafer products, which go through 210 and 245 process steps respectively. There are 32 operator groups in the dataset. The primary dispatching Customer rules for machines are FIFO and Setup Avoidance (only Requir. for the medium and high current implantation machines). D. Assembly and Test (A&T) Fulfillment Assembly Test Dekit Storage Assembly The orders from IC D/G and the demand from the server fulfillment center are fed to the assembly and test facility. Based on the availability of factory capacity and wafer inventory, the A&T facility assigns lots to orders and releases the lots into the facility. Customer System Packing Shipping End Test The data for the assembly and test facility is based on previous projects the authors have had with the Fig 3. Manufacturing Process in Server Fulfillment Center semiconductor industry. The data, particularly volume release and factory capacities, has been adapted to ensure F. Peripheral Warehouse that the production quantities and the utilization of facilities are consistent with what is typically found in the The peripheral warehouse supplies peripherals based on industry. Approximately 25 process steps exist in the A&T the demand issued by the server fulfillment center. A lead facility and the major dispatching rule for machines is time consistent with industrial experience is randomly FIFO. generated using a normal distribution. E. Server Fulfillment Center While the distributed simulation testbed works well to represent the operations of the real world supply chain, the 3
  4. 4. uncertainties inherent to supply chains, (such as where Gnxn is the system state matrix that relates the state at unpredictable environmental changes, unpredictable the previous time step k-1 to the present step k, and Hmxn failures, and emergent behaviour) impose significant relates the system states to the measurements. The random challenges on supply chain management and on supply variables εk and ηk represent the process and measurement chain simulation, which have been designed, planned, and noise respectively. They are assumed to be white noise controlled based on a static, deterministic paradigm of data with normal distributions: p (εk) ∼ N (0, Qk) and p (ηk) ∼ N acquisition and decision-making, and an (essentially) open- (0, Rk). The equations for the Kalman filter fall into two loop mode of control. Often, decisions on SC models groups: time based equations (Equation 1 and 2), applied cannot be changed until the gap between the planned to obtain the current system state, and measurement based system state and actual system state has become equations (Equation 3-5), used to adjust the system state significant, making correction expensive. Therefore, there from the measurements. is a need for an integrated framework combines actual ˆ− xk = Gxk −1 (1) system state from the real operation and predicted system state from simulation results to narrow the gap and provide Pk− = GP k −1 G T + Qk (2) − − −1 better overall system estimation. K k = P H ( HP H + Rk ) k T k T (3) Note hardware and software technologies are developing which could enable a new paradigm of real- − ( xk = x + K k z k − Hx ˆ k − k ) (4) time decision making in supply chains. In particular, Pk = ( I − K k H ) P k − (5) technologies like RFID, GPS, grid computing, and where Kk is the Kalman gain, Pk is the error covariance, universal access to the World Wide Web promise instant availability and communication of state change data. ˆ− ˆ xk is the estimation of xk before the measurement, and xk In this study, we propose a framework integrating is the estimation of xk given measurement zk. The Kalman Kalman filter and discrete event simulation. The basics of filter assembles the two groups of equations to give the the Kalman filter are introduced in next section. best estimate of the system state. The system of measurement and transition equations can be combined III. KALMAN FILTER into an iterative process to determine the state of the system x. Kalman filters have traditionally been used for stochastic estimation and control. Recently, the Kalman IV. INTEGRATED FRAMEWORK filter has been applied in a variety of applications as well including Inertial Navigation and Guidance [17], Global In this section, we describe how to integrate the Positioning Systems [18], Target Tracking [19], Finance distributed simulation system with the Kalman filter to get [20, 21], etc. In the supply chain domain, Aviv [22] an estimate of the entry and exit time for each job at the proposes an adaptive inventory replenishment policy that wafer fabrication facility, the assembly and test facility, the utilizes the Kalman filtering technique. Wu and O’Grady server fulfillment center and the peripheral warehouse in [23] develop an integrated approach that uses Kalman the server fulfillment supply chain. filtering and a Petri Net model to obtain a better state The proposed framework is shown in Figure 4, where estimation of a supply chain system. Vensim the estimated state for each job is obtained by running the [], an optimizer tool provided by distributed simulation model. When a job is in a process, Ventana Systems, uses Kalman filtering to track the actual an emulation module provides real progress update. The inventory. Ventana Systems claim that Kalman filtering Kalman filter module will calibrate the results and provide tracks the inventory much better than either simple a more realistic estimate. simulation alone or the measured inventory alone. In this First, an estimate of when an entity will pass through work, a Kalman filter approach is proposed to take into every major process is obtained. This estimate is obtained account the measurement error to obtain a better state using simulation. The entire process is simulated for 30 estimate, namely, the estimated start and end processing replications. For each replication, the arrival time of the times of jobs at each major supply chain component. entity to the system, is kept the same. An estimate of the A Kalman filter [24, 25] is a set of mathematical queue times for all entities and an estimate of the equations that supports estimations of past, present, and processing times for all entities at every process are even future states. The power comes from the fact that it calculated by taking the average from the 30 replications. can do these estimations even when the precise nature of The standard deviation in these estimates is also calculated. the modeled system is unknown [26]. To emulate the real world, an additional simulation is Mathematically, a Kalman filter is a set of recursive run, using the same distribution and using the same equations used to estimate the state x ∈ Rn of a discrete- parameters for the processing times as used in the time controlled process such as a manufacturing process simulation with 30 replications. We call this emulation. In that is governed by a transition equation and a other words, measurements obtained from emulation are measurement equation. assumed to represent measurements obtained from the real Transition Equation: xk = G*xk-1 + εk-1, x ∈ R n world. At this point, information from the two different sources is available and both these sources have variability Measurement Equation: zk = H* xk + ηk, z ∈ R m 4 Fig 4. Proposed Framework
  5. 5. Fig 4. Proposed Framework fulfillment center). Equation (12) estimates the corrected variance in the estimate of the state when an entity will –simulation has variance in estimation and emulation has complete the last process (process at server fulfillment variance in measurement (one source of measurement center). Equation (13) estimates the next entity state from variance might be human recording errors). The Kalman the corrected current state. Finally, equation (14) estimates filter can then be applied to generate estimates by the variance in the estimate of the next entity state. optimally combining simulated predictions with measurement using equations (6) – (14). The variables in these equations are defined in Table 1. TABLE I Est ( L1 ) = E AT + TB ( E AT → L1 ) (6) Variable Definition σ 2 ( EstL1 ) = σ 2 ( E AT + TB ( E AT → L1 ) ) = σ 2 ( T B( E AT → L1 ) ) ˆ ˆ ˆ Time when entity starts or completes a process. For example, L1 refers to the start (7) Li of the first process, L2 refers to the end of the first process, L3 refers to the start of the K ( Li )σ ( Est Li ) / (σ ( Est Li ) + σ ( Msd Li ) ) ˆ 2 ˆ 2 ˆ 2 (8) second process, and so on. Cor ( Li ) = Est ( Li ) + K ( Li ) * ( Msd ( Li ) − Est ( Li ) ) (9) EAT Entity arrival time σ ( Cor ( Li ) ) = σ ( Est Li ) − K ( Li ) * σ ( Est Li ) ˆ2 ˆ 2 ˆ 2 (10) Estimate of time between entity arrival Est ( L12 ) = Cor ( Li ) + TB ( Li → L12 ) (11) TB(EAT →L1) and start time of the first process σ 2 ( Est ( L12 ) ) = σ 2 ( Cor ( Li ) ) + σ 2 ( TB ( Li → L12 ) ) ˆ ˆ ˆ (12) Estimate of time between the instant when entity is at the start of process i and the Est ( Li +1 ) = Cor ( Li ) + TB ( Li → Li +1 ) (13) end of the process. This accounts for the TB(Li →Li+1) queue time between the end and beginning σ ( Est ( Li +1 ) ) = σ ( Cor ( Li ) ) + σ ( TB ( Li → Li +1 ) ) ˆ2 ˆ 2 ˆ 2 (14) of a process and the processing time at a process. Equation (6) estimates the start time of the process at the wafer fabrication facility and equation (7) estimates the Estimate of time between the start of one TB(Li →Ln) variation in the estimate of the start time. Equation (8) process to the end of the overall process calculates the Kalman correction required to account for Est ( Li ) Estimated time for entity to be at the start the measurement error in the state. Equation (9) applies the or the end of the process Kalman correction and obtains the corrected estimates of the state. Equation (10) estimates the variance in the Msd ( Li ) Measured time for entity to be at the start corrected estimate of the state and equation (11) uses the or the end of the process corrected estimate for intermediate states to estimate when Corrected time for entity to be at the start Cor ( Li ) an entity will complete the last process (process at server or the end of the process K ( Li ) Kalman correction 5
  6. 6. [7] B.P. Gan, L. Liu, S. Jain, S.J. Turner, W. Cai, and W.J. Hsu. σ 2 ( Est Li ) ˆ Estimate of variance in estimated time of “Distributed supply chain simulation across enterprise boundaries.” Li Proceedings of the 2000 Winter Simulation Conference, ed. J.A. Estimate of variance in measurment of Li Joines, R.R. Barton, K. Kang and P.A. Fishwick, 1245-1251. 2000. σ 2 ( Msd Li ) ˆ [8] S. Jain, E.C. Ervin, A.P. Lathrop, R.W. Workman, L.M. Collins. (assumed to be 36) “Analyzing the supply chain for a large logistics operation using σ 2 ( Cor Li ) ˆ Estimate of variance in corrected time of Li simulation.” Proceedings of the 2001 Winter Simulation Conference, ed. B.A. Peters, J.S. Smith, D.J. Medeiros, and M.W. Rohrer, 1123-1128. 2001. Estimate of variance in estimated time [9] P. Lendermann, N. Julka, B.P. Gan, D. Chen, L.F. McGinnis, and σˆ 2 ( T B( E AT → L1 ) ) between entity arrival time and the start J.P. McGinnis. “Distributed supply chain simulation as a decision- time of the first process support tool for the semiconductor industry,” Simulation, 79(3): 126-138. 2003. Estimate of variance in estimated time ( σˆ 2 TB ( Li → Li+1 ) ) between the instance when entity is at the [10] S. Bagchi, S.J. Buckley, M. Ettl, and G.Y. Lin. “Experience using the IBM supply chain simulator,” Proceedings of the 1998 Winter start and the end of the process Simulation Conference, ed. D.J. Medeiros, E.F. Watson, J.S. Carson Estimate of variance in estimated time and M.S. Manivannan, 1387-1394. 1998. ( σ 2 TB ( Li → Ln ) ˆ ) between the start of one process and the [11] G. Archibald, N. Karabakal, and P. Karlsson. “Supply chain vs. end of the overall process supply chain: Using simulation to compete beyond the four walls,” Proceedings of the 1999 Winter Simulation Conference, ed. Farrington, H.B. Nembhard, D.T. Sturrock, and G.W. Evans, 888-896. 1999. Some preliminary work has been done with a focus on [12] S. Jain, C.C. Lim, B.P. Gan, and Y.H. Low. “Criticality of detailed the manufacturing portion of the server fulfillment center modeling in semiconductor supply chain simulation,” Proceedings in our previous research [13]. The initial experimentation of the 1999 Winter Simulation Conference, ed. P.A. Farrington, H.B. Nembhard, D.T. Sturrock, and G.W. Evans, 888-896. 1999. results show that using a Kalman filter can help in getting a [13] D. Parmar, T. Wu, J. Fowler, T. Callarman and V.Hargaden. “An more realistic estimate of when an entity is likely to come intergrated framework for responsive supply chain management,” out of the server fulfillment center. The improved The 16th International Conference on Flexible Automation and estimates are then used to sense whether an entity is on Intelligent Manufacturing, Limerick, Ireland, June, 2006. course to meet customer delivery expectations. In the [14] S.J. Turner, W. Cai, and B.P. Gan. “Adapting a supply chain simulation for HLA,” Proceedings of IEEE 4th International future, we will explore it for the entire server fulfillment Workshop on Distributed Simulation and Real Time Applications, supply chain. 71-78, San Francisco, USA. 2000. [15] C.S. Chong, P. Lendermann, B.P. Gan, B.M. Duarte, J.W. Fowler, V. SUMMARY and T.E. Callarman. “Analysis of a customer demand driven semiconductor supply chain in a distributed simulation test bed,” This paper describes a computer server fulfillment Proceedings of the 2004 Winter Simulation Conference, ed. R.G. supply chain and its modular structure in a prototype Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters.1902-1909, 2004. [16] MASMLab Test-Bed datasets [Online], maintained by Modeling distributed simulation model, and it explores the dynamics and Analysis of Semiconductor Manufacturing Laboratory, and interaction among the components across the system. Industrial Engineering department, Arizona State University, USA. In addition, a Kalman filter approach is proposed to, 2004. calibrate the system state estimate to get more realistic job [17] P. Zarrchan., "Tactical and strategic missile guidance," AIAA, Inc., Washington, DC, 1994. completion time forecasts. [18] R.P. Denaro and P.V.W. Loomis., "GPS Navigation Processing and Kalman filtering," AGARD, NO. 161, pp. 11.1-11.9, 1989. [19] C.K. Chui and G. Chen, Kalman filtering with real-time applications, Springer-Verlag, New York, 1987. REFERENCES [20] C. Wells, The Kalman filter in finance, Kluwer Academic [1] K. Fordyce, “New supply chain management applications provide Publishers, Dordrecht, 1995. better customer service: serious gets exciting,” IBM [21] P.J. Bolland and J.T. Connor, "A Constrained neural network Microelectronics, Second Quarter, 2001. Kalman filter for price estimation in high frequency financial data," [2] M. Hennessee, “Challenges facing global supply chains in the 21st International Journal of Neural Systems, Vol. 8., No. 4, August, century,” Proceedings of the 1998 Winter Simulation Conference, 1997. ed. D.J. Medeiros, E.F. Watson, J.S. Carson and M.S. Manivannan, [22] Y. Aviv: “A Time series framework for supply chain inventory 3-4. 1998. management,” Operations Research, Vol. 51, No. 2, pp. 210-227, [3] L. Chwif, M.R.P. Barretto, E. Saliby. “Supply chain analysis: 2003. Spreadsheet or simulation?” Proceedings of the 2002 Winter [23] T. Wu and P. O’Grady: “A Methodology for improving the design Simulation Conference, ed. E. Yücesan, C.-H. Chen, J.L. Snowdon, of a supply chain,” International Journal of Computer Integrated and J.M. Charnes, 59-66. 2002. Manufacturing, Vol. 17, No. 4, pp. 281-293, 2004. [4] S. Jain, N.F. Choong, and W. Lee. “Modeling computer assembly [24] R.E. Kalman, and R.S. Bucy., "New results in linear filtering and operations for supply chain integration,” Proceedings of the 2002 prediction theory," Transactions of the ASME series D: Journal of Winter Simulation Conference, ed. E. Yücesan, C.-H. Chen, J.L. Basic Engineering, 83 (3): 95 - 108, 1961. Snowdon, and J.M. Charnes, 1165-1173. 2002. [25] R.E. Kalman, "A New approach to linear filtering and prediction [5] J. Venkateswaran, Y.-J. Son, and B. Kulvatunyou. “Investigation of problems," Transactions of the ASME series D: Journal of Basic influence of modeling fidelities on supply chain dynamics.” Engineering, 82 (1): 35 - 45, 1960. Proceedings of the 2002 Winter Simulation Conference, ed. E. [26] G. Welch and G. Bishop: “An introduction to the Kalman filter,” Yücesan, C.-H. Chen, J.L. Snowdon, and J.M. Charnes, 1183-1191. Technical Report No. TR 95-041, Department of Computer Science, 2002. University of North Carolina, 1995. [6] S.T. Enns, and P. Suwanruji. “A simulation test bed for production [27] P.S. Maybeck. Stochastic Models, Estimation, and Control, and supply chain modeling,” Proceedings of the 2003 Winter Academic Press, Inc., New York, Vol 1, 1979. Simulation Conference, ed. S. Chick, P.J. Sánchez, D. Ferrin, and D.J. Morrice, 1174-1182. IEEE. 2003. 6