A Discrete-Continuous Combined Modeling Approach for Supply ...

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A Discrete-Continuous Combined Modeling Approach for Supply Chain Simulation Young Hae Lee, Min Kwan Cho and Yun Bae Kim SIMULATION 2002; 78; 321 DOI: 10.1177/0037549702078005561 The online version of this article can be found at: http://sim.sagepub.com/cgi/content/abstract/78/5/321

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A Discrete-Continuous Combined Modeling Approach for Supply Chain Simulation Young Hae Lee Min Kwan Cho Hanyang University Department of Industrial Engineering South Korea yhlee@ hanyang.ac.kr Yun Bae Kim Sungkyunkwan University School of Systems Management Engineering South Korea Supply chain management (SCM) is a strategic paradigm to coordinate cash, material, and information flows from raw material to customer. Supply chain simulation (SCS) is a strong and popular tool for designing, evaluating, and optimizing the structure of supply chains, and it requires an important task to estimate the effect of the planning to coordinate such flows in SCM. Stochastic natures existing in the supply chain can be analyzed efficiently using simulation. One uses discrete-event simulation to model a supply chain in general. However, the nature of the supply chain system is neither completely discrete nor continuous; both aspects must be considered together in developing an SCS model. In this paper, a framework of discrete-continuous combined modeling for supply chain simulation is proposed. Equations for the continuous aspects of a supply chain in this framework are included, and a simple example of the SCS model using this equation is presented. Keywords: Supply chain simulation, discrete-continuous combined modeling

1. Introduction

2. Literature Review

In the past, many companies have focused on improving their productivity and efficiency within their company, such as through computer-integrated manufacturing systems (CIMS), factory automation (FA), and flexible manufacturing systems (FMS). However, these activities have reached the limit of improving profits in varying customer needs. A new paradigm is needed to overcome this limit. SCM is the strategy coordination management of cash, material, and information flows from raw material to customers in a supply chain consisting of a manufacturer, inventory, and supplier. SCM is strategic planning to increase the efficiency and profits for the supply chain by optimizing speed and certainty and maximizing the value that is added by every related process. Each process of the supply chain works together in an effort to acquire raw materials or sources, convert these raw materials into final goods, and deliver these final goods to the retailer. These processes are characterized as the material flow, shown in Figure 1 [1].

2.1 Supply Chain Simulation

SIMULATION, Vol. 78, Issue 5, May 2002 321-329 © 2002 The Society for Modeling and Simulation International

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In existing analytical methods, the stochastic natures and elements for the supply chain could not be efficiently included, resulting in a restricted supply chain model presentation. Ingalls [2] discussed modeling and analyzing the supply chain, as well as the advantages and disadvantages for simulation compared to other analysis methodologies. Demand variance or forecast error, modeling scale, and the dramatically changing nature of the optimal answer as the slightly changing input value are a few of the reasons given for the fitness of simulation in modeling and analyzing the supply chain [2]. However, simulation is an effective analytical tool to present the supply chain, considering the stochastic natures and elements. We can locate optimum values for each supply chain component by considering the entire supply chain through simulation. SCS consists of a couple of activities: (1) designing and evaluating the model and (2) estimating the effect of planning for the supply chain and data gathering for analysis.


Lee, Cho, and Kim

2.3 Simulation Tool for the Supply Chain

Cash, Information flow

Supplier

Factory

Distributor

Retailer

Customer

Procurement, Manufacturing, Logistics Material, Product and Service flow

Figure 1. Concept of supply chain management

2.2 Simulation Models for the Supply Chain The use of simulation mainly focuses on evaluating the effects of various supply chain strategies on demand amplification. The objective of the simulation model is to determine which strategies are the most effective in smoothing demand variations. Just-in-time (JIT) and echelon removal strategies are proposed as the most effective [3]. Several strategies to improve the supply chain are applied on a three-stage reference supply chain model. This reference model consists of a single factory, distribution facilities, and retailers. The implementation of each strategy is carried out using simulation, the results of which are used to determine the effects of the various strategies on minimizing demand fluctuations. The conclusion is that the strategy to improve the information flow and separate demand into order is the most effective [4]. The applicability of our approach is reviewed, specifically by looking at (1) discrete event simulation, an event-driven approach, and (2) system dynamics (SD), a time-driven approach. It is confirmed that discrete event simulation is better at answering questions that concentrate only on system events, while system dynamics is suitable for providing insight on consequential results over time [5]. The taxonomy of research and development in SD modeling for SCM is classified as modeling for theory building, modeling for problem solving, and improvement of the modeling approach [6]. The simulation model is used to compare various strategies to manage capacity, and application completion rate, backlog levels, and total cumulative costs are included as the performance measure [4]. A large-scale discrete resource allocation problem for SCM is solved using a hybrid algorithm. This hybrid algorithm is developed to combine the nested partitions methods with the paradigm of an efficient ranking and selection technique [7]. In an uncertain environment, fuzzy modeling and simulation of a supply chain are studied. Discrete fuzzy sets are used to present various uncertainties in customer demand and external supply [8]. An order release mechanism for SCM using the simulation approach is proposed. The main focus is on improving customer service through more effective release of orders into the supply chain [9].

The supply chain analyzer (SCA) is a simulation software that can help companies make strategic business decisions for the design and operation of supply chains. It runs on a single platform and is built on SIMPROCESS. This simulator runs discrete event simulation using partial modules with enriched operations of financial transactions; it also uses an optimization program developed at IBM Research (called the Inventory Optimizer) and an optimization program (called the Supply Planning Optimizer) that schedules replenishment orders or material shipping. However, this simulator cannot be applied to distribution simulation and Web-based simulation because of the built-in standalone platform [10]. eSCA, the extended version of the SCA, has a client/server structure based on an Internet environment. eSCA supports distribution simulation through synchronous working, batch experiments, model cataloging for reusable models, and developed supply chain models. The architecture of eSCA consists of clients, a Web server, and an eServer. The salient features of eSCA are a client/server-based computing model for SCA, a parallel and distributed simulation environment, and a knowledgebased model catalog [11]. The Compaq supply chain analysis tool (CSCAT) is an ARENA discrete event simulation that allows for the easy configuration of a supply chain and the analysis of the dynamics of a supply chain. However, the CSCAT is an inconvenient supply chain simulator because it is designed for Compaq’s supply chain network and only uses the module of Compaq’s internal logic [12]. The LOGSIM simulator is a simulation analysis tool for managing the internal supply chain network of NOKIA. This simulator uses a simulation engine with PROMODEL and Visual Basic as the user interface and report generator. However, this simulator does not integrate process modeling and cost modeling into the simulator [13]. e-SCOR is based on the supply chain operations reference (SCOR) model, provided by the Supply Chain Council. The SCOR model provides a standard way of viewing a supply chain, a common set of manipulatable variables, and a set of accepted metrics for understanding the dynamic behavior of supply chains. High-level architecture (HLA) is used for distributed simulation in this tool [14]. 2.4 Decision Procedures in the Supply Chain The nature of supply chain integration is a systematic connection between the internal and external processes of the company. Most strategic decisions for integrating supply chains involve either modifying the supply chain’s structure or changing the supply chain’s policies. The following four steps can help users in deciding which techniques are appropriate for each type of decision (see Figure 2) [15]: Step 1: Network optimization Step 2: Network simulation

322 SIMULATION Volume 78, Number 5


DISCRETE-CONTINUOUS COMBINED MODELING APPROACH

Network Configuration Inventory Optimization Transport Optimization

Module Optimization Customer demand Location Associated linkage Aggregated plan Assigning resource Supplier selection

Simulation Analysis & Decision Policy Design for Robustness

Step 1: Network Optimization Step 2: Network Simulation Step 3: Analysis & Decision Policy Step 4: Design for Robustness

Figure 2. Steps for decisions in the supply chain

Step 3: Analysis and decision policy Step 4: Design for robustness 3. Simulation Process for the Supply Chain Required activities of enterprises for supply chain management can be classified into three levels: an operation level, a tactical level, and a strategic level [2]. Discrete event simulation modeling of supply chain model methodology generates the following supply chain analyst problems: • Reflecting the continuous nature of the process is not possible. • Representing the interaction that occurs among those components is not possible. • There is growing complexity in more detailed models. • There is too much simplification for small-scaled models.

A combined model is defined as an integrated model that incorporates both discrete and continuous variables within the same model. To model such systems, the system must represent both the discrete and continuous components, as well as the interactions that may occur among those components. Combined modeling gives the following supply chain analyst conveniences [16]: • • • • • •

explaining the dynamic behavior of an existing system, confirming the validity of proposed system modification, predicting new types of system behavior, benchmarking competitive improvement strategies, checking out of novel adaptive control systems, approximating a discretely changing variable by using continuously changing variables.

Continuous models are based on a defined relationship for the state of the system over time. If the state of the system is denoted by variable x, then the objective is to find a function f such that x = f (t, λ, x0 ),

where t denotes time, λ denote parameters of the model, and x0 denotes the initial conditions of the system. This relationship is known as a state equation. In most cases, the complex system’s components are not enough to provide insight to directly develop state equations for the system. However, a relationship can be developed for the rate of change of x with respect to time, called the derivative of x. In general, a continuous or combined model contains one or more state equations to describe the system state. If the model contains all state equations, then the system state is known for all time in terms of the model’s initial conditions and parameters [14]. The continuous model is mainly applied to the chemical industry. The state of each process may be presented as the state function over time, and the change rate of the state is calculated as differentiating the state function. Modeling methodology, applied to designing supply chains, varies with every level for supply chain management. At the operation level, optimal value is given by the analytical optimization method. It can be said that using discrete event simulation is an appropriate choice for the tactical level [9]. A large-sized simulation model, based on the entire supply chain, is needed for an enterprise plan at the strategic level. If this simulation model is designed to use discrete event modeling, large input data are required, and the continuous nature of the supply chain cannot be reflected. These facts have a negative influence on supply chain modeling. However, if a combined modeling approach is used, the continuous nature of the supply chain can be properly considered in designing it. The actual model of a supply chain is large scale and requires large amounts of input data. But if a combined modeling approach is used, it can represent continuous features, interactions, flow rate of the product, and information in the model simply or more precisely. Classifying elements into two groups (discrete or continuous) depends on the attributes of the element. This proposition is applied to classifying supply chain components (supplier, factory, distributor, retailer, customer, etc.) and the connection between the components. Information about customer orders, information flows in each supply chain component, and inventory levels at the distributor and at each factory for products are considered as continuous elements. Transportation is considered as a discrete element (see Figure 3). Two interactions occur between discrete and continuous elements in the combined model. The first is the changes made to the continuous components by the discrete component. This type of interaction superimposes a discrete jump on a continuous-change response variable. The second type of interaction consists of changes made to the discrete component from the continuous component. To model interactions between discrete components and continuous variables, the changing value for the continuous Volume 78, Number 5 SIMULATION 323


Lee, Cho, and Kim

Table 1. Modeling method for each level Level

Modeling Method

Model Detail

Model Scale

Operation level Tactical level

Mathematical model Optimization/discrete event simulation Combined modeling simulation

Very detailed Normal

Small Normal

Simple

Very large

Strategic level

User Interface

Forecasting

Database

Customer demand

Historical data

Configuration parameter

Location

Planning parameter

Supplier selection

Assigning resource Decision Policy Inventory Planning Aggregate plan Material planning

Output/Result Transport Planning

delay between supply chain components. These activities are controlled and constrained by management policies and the structure of the supply chain. The four components—retailer, distributor, factory, and supplier—are treated in a similar way, and their detailed flows are shown in Figures 5 to 8. Equations are developed to represent the relationships between the supply chain components. Levels are represented as variables, which measure associated quantities in equations. These levels are counted by running a simulation model. For example, in the retailer section, levels are central to the distribution and sales task and exist in the orders, information, and material flow channels. The levels appear to be as follows:

Production planning

Distributing planning

Simulation

Figure 3. Discrete and continuous portions in the supply chain

Order from customer Goods from supplier

Retailer Supplier

Factory

Distributor

Customer

Discrete part Continuous part

• Backlog of orders received from the consumer but not yet filled • Inventory of goods in stock

The major rates of flow that appear to be pertinent to the objectives are as follows: • • • • • • • • • • •

Outgoing shipping rate to customer Outgoing ordering rate from retailer to distributor Outgoing ordering rate from distributor to factory Outgoing ordering rate from factory to supplier Incoming shipping rate of goods from supplier to factory Incoming shipping rate of goods from factory to distributor Incoming shipping rate of goods from distributor to retailer Inventory level at retailer section Inventory level at distribution section Inventory level at factory section Inventory level at supplier section

Figure 4. Structure of the supply chain system

4.1 Retailer Section variables in the discrete model is assigned to the state or derivative variable [14]. 4. Structure of the Supply Chain Simulation Model We will concentrate on the material flow from supplier to consumer, as well as on the order of information flow from consumer to supplier. The considered structure of the supply chain is shown in Figure 4. The purpose of Figure 4 is not to exhibit a complete representation of all functions but rather to describe fundamental activities such as shipping delay and information

There is an unfilled order rate of the retailer at a point of time k such as shipped quantity up to time k UORk = 1 − order quantity up to time k SQRj + SQRj +1 =1− . OQRj + OQRj +1 Order quantity from the retailer to distributor is reflected by an inventory optimization module. The numerical formula is as follows: ORDk = IDRk − (IARk − UORk ),




Supplier warehouse

Supplier

Factory

Factory warehouse

Distributor

Inventory

Inventory

Inventory

Retailer

Transport delay

Inventory

Mail delay

RQR

Inventory Customer order information

IAR

Retailer

IDR

SQR

Order decision ORD

Unfilled order UOR

Goods for customer

OQR

Customer information flow product flow

Inventory Supplier warehouse

Supplier

Inventory Factory

Distributor

Product flow

Order information flow

Inventory

Inventory

Factory warehouse

Retailer

Definition

Ship delay

Order-filling delay

Information delay

Order-decision delay

Figure 5. Retailer section

where

index j : past time period k: present time period, k = j+1 Given value IDR : desired inventory level at retailer(volume) Parameter UOR : unfilled order at retailer(volume or rate) IAR : Inventory Actual level at Retailer ORD : order quantity from Retailer to Distributor. OQRj : ordered quantity from retailer, from initial time till a point of time j OQRj+1: ordered quantity from retailer, from j till a point of time k SQRj : shipped quantity from retailer, from initial time till a point of time j SQRj+1 : shipped quantity from retailer, from j till a point of time k RQRj : received quantity from distributor, from initial time till a point j

Figure 6. Distribution section

IARk (volume) = received quantity a point of time k − shipped quantity a point of time k = RQRj + RQRj +1 − SQRj + SQRj +1 , UORk (volume) = received order quantity a point of time k

In detail, MQFk

∴ ORDk = IDRk − RQRj − RQRj +1

= IDF − RQMj − RQMj +1 − SQFj − SQFj +1 − OQFj + OQFj +1 + SQFj + SQFj +1 = IDF − RQMj + RQMj +1 − OQFj + OQFj +1

+ OQRj + OQRj +1 .

= IDF − RQMj − RQMj +1 + OQFj + OQFj +1 .

− shipped quantity a point of time k = OQRj + OQRj +1 − SQRj + SQRj +1 .

4.2 Distribution Section UODk , IADk , and ODFk can be obtained by the same methods as in the retailer section.

The replenishment of MQFk is decided at the former time, and MQFk is also constrained by the capacity at the former time. Therefore, MQFk is calculated as follows:   IDF − RQMj − RQMj +1 + OQFj + OQFj +1 ,   if MQFj ≤ MC at the former time   MQFk =     MC, if MQFj > MC at the former time.

4.3 Factory Section UOFk and IAFk are obtained by the same methods as in retailer section. MQFk is decided as follows:

MQFk = IDF − (IAFk − UOFk ).

A formula for MDTk is as follows: ROMj + ROMj +1 MDTk = LT . MQFj + MQFj +1 Volume 78, Number 5 SIMULATION 325


Lee, Cho, and Kim

Transport delay

Mail delay

Transport delay

Mail delay

RQD Manufacturing MDT MC LT

RQM

Order decision

Inventory IAD

IDD

ODF

Inventory

Factory

Distributor

IAF

IDF

Manufacturer MQF

Order decision OFS

Unfilled order

SQD

UOD

SQF

Unfilled order UOF

OQD

information flow product flow

OQF information flow product flow

Definition index

Definition

j : former time k: present time, k = j+1

Given value I D D : desired inventory level at distributor (volume)

Parameter UOD : Unfilled Order at Distributor IAD : Inventory Actual level at Distributor ODF : Order quantity from Distributor to Factory OQDj : ordered quantity from retailer, from initial time till a point of time j OQDj+1 : ordered quantity from retailer, from j till a point of time k SQDj : shipped quantity from retailer, from initial time till a point of time j SQDj+1 : shipped quantity from retailer, from j till a point of time k RQDj : received quantity from distributor, from initial time till a point of time j RQDj+1 : received quantity from distributor, from j till a point of time k

Figure 7. Factory section

Given value I D F : desired inventory level at factory (volume) Constant LT : manufacturing lead time MC: manufacturing capacity Parameter UOF: unfilled order at factory (rate) I A F : actual inventory level at factory factory to supplier OFS: order quantity from MQF: manufacturing quantity at factory MDT : manufacturing delay time OQFj : ordered quantity from factory, from initial time till a point of time j OQFj+1 : ordered quantity from factory, from j till a point of time k SQFj : shipped quantity from factory, from initial time till a point of time j SQFj+1 : shipped quantity from factory, from j till a point of time k RQMj : received quantity from manufacture, from initial time till a point of time j RQMj+1 : received quantity from manufacture, from j till a point of time k MQFj : manufacturing quantity at factory, from initial time till a point of time j MQFj+1 : manufacturing quantity at factory, from j till a point of time k

Figure 8. Supplier section

4.4 Supplier Section UOSk , IASk , and MQSk can be obtained by the same methods as in the retailer section. MQSk is decided in a similar way to the factory section as follows: 

 IDS − RQSj − RQSj +1 + OQSj + OQSj +1 ,   if MQSj ≤ MC at the former time   MQSk =     MC, if MQSj > MC at the former time. A formula for MDTk is as follows: ROSj + ROSj +1 MDTk = LT . MQSj + MQSj +1 5. Experiment The purpose of the experiment is to show the benefits of combined modeling, based on the above formulas, with respect to discrete event modeling in the supply chain simulation.

In the experimental model, the retailer section is similar to the distribution section. Also, the factory section is similar to the supplier section. For the sake of experiment, the order quantity is generated from the customer. Then the fill rate, the new order quantity to the distributor, is calculated in the retailer section. For example, if the inventory level is 500, the order quantity from the customer is 300, and the desired inventory level is set as 600, then the fill rate for the customer will be 100%, and the order quantity for the distribution section will be 400 (= 600 − (500 − 300)). This quantity will then be sent to the distributor section. In the distribution section, a similar process is repeated, with 400 as the order quantity from the retailer section. For the factory section, there are two major processes regarding parameters. The first process concerns manufacturing order quantity. Manufacturing order quantity is decided by considering the capacity of the factory and the received quantity from the distributor. If the manufacturing order quantity is larger than the capacity of the factory, the factory will produce products at full capacity. Otherwise, the factory will produce products equal to the manufacturing order quantity.




Table 2. Parameters in an experimental model Supplier section

Factory section

Distributed section Retailer section

Manufacturing process time Manufacturing capacity Inventory capacity Desired inventory level

TRIA(14,16,18) 75 1600 1000

Manufacturing process time Manufacturing capacity Inventory capacity Desired inventory level Inventory capacity Desired inventory level Inventory capacity Desired inventory level

TRIA(12,14,16) 55 1600 800 1000 500 800 400

The second process concerns order quantity for the supplier. Order quantity for the supplier is calculated by considering the ratio of the final product and its parts. In general, the ratio or the relation between the product and its parts is shown in the bill of material (BOM). If the quantity of the order from the distributor is 300, the present inventory level of the factory is 500, the desired inventory level of the factory is 600, factory capacity is 700, and the products to their parts ratio is 1 to 3, then the manufacturing order quantity will be 400 (= 600 − (500 − 300)). This quantity is less than factory capacity. Therefore, the quantity of 400 should be produced. Also, the order quantity for the supplier will be 1200 (3 × 400 = 1200). The same process is applied to the supplier section. In the experimental model, the main input parameters are set as shown in Table 2. Figure 9 diagrams the inventory level using a combined model approach. The x-axis is represented as time, and the y-axis represents the inventory level. The diagrams are not drawn in a general step shape, given by discrete event modeling. However, sharp fluctuations repeatedly appear in each section, which means that all inventory levels can be reflected by continuous property in the supply chain. In this experiment, a discrete event model is developed to compare the inventory level given by a combined modeling approach. The average inventory level for each approach is shown in Table 3. The comparison of inventory levels for each approach is shown in Figure 10. In Figure 10, the inventory level given by the discrete event modeling approach is bigger than the inventory level given by the combined modeling approach. In other words, the simulation results of the discrete event modeling approach are overestimated compared with those of the combined modeling approach. This is mainly due to the difference between the discrete and continuous characteristics. These overestimated results are interpreted as unnecessary inventory, which means that the discrete event modeling approach cannot represent the actual state of the inventory level as the combined modeling approach. Unnecessary inventory is a major problem in the supply chain. Therefore, a combined modeling approach

Customer order generate; EXPO(20) Information delay; 10

Manufacturing MDT MC LT

RQS

Inventory

Supplier

IAD

IDD

SQS

Manufacture decision MQS

Unfilled order UOS OQF

information flow product flow

Definition Given value I D F : desired inventory level at factory (volume)

Constant LT : manufacturing lead time MC: manufacturing capacity

Parameter UOS: unfilled order at supplier (rate) I A S : actual inventory level at supplier MQS: manufacturing quantity at supplier MDT: Manufacturing delay time OQSj : ordered quantity from supplier, from initial time till a point of time j OQS j+1 : ordered quantity from supplier, from j till a point of time k SQSj : shipped quantity from supplier, from initial time till a point of time j SQSj+1 : shipped quantity from supplier, from j till a point of time k RQSj : received quantity from supplier, from initial time till a point of time j RQSj+1 : received quantity from supplier, from j till a point of time k MQFj : manufacture quantity at supplier, from initial time till a point of time j MQFj+1 : manufacture quantity at supplier, from j till a point of time k

Figure 9. Inventory level by combined model approach

can estimate a more accurate measure of the inventory level and is more effective in the supply chain simulation. 6. Conclusion Most supply chain simulation models have been developed using discrete event simulation. However, the nature of the supply chain system is neither completely discrete nor continuous; both aspects must be considered together in developing an SCS model. Volume 78, Number 5 SIMULATION 327


Lee, Cho, and Kim

Table 3. Average inventory level by each approach Discrete Event Model

Average inventory level

Combined Model

Retailer

Distributor

Factory

Supplier

Retailer

Distributor

Factory

Supplier

438.57

511.53

822.67

1069.92

415.54

477.44

779.06

1024.47

Figure 10. Comparison of inventory levels for each approach

In this paper, a framework of discrete-continuous combined modeling for supply chain simulation has been proposed. We have included equations for the continuous aspects of the supply chain in this framework, and a simple example for the SCS model using this equation is presented. An experiment was done to show the benefits of combined modeling, with respect to discrete event modeling, in the supply chain simulation. We suggest that further research should develop the process for generating graphical output data such that decision makers can see how the supply chain acts over time during simulations. It is also necessary to develop modeling processes in a more detailed way for specific industries. A combined simulation modeling helps managers to observe the supply chain more macroscopically and to save time in the execution of supply chain simulation models. 7. Acknowledgment This research was supported by the Brain Korea 21 Project in 2002. 9. References [1] Beamon, B. M. 1998. Supply chain design and analysis: Models and methods. International Journal of Production Economics 55 (3): 281-294. [2] Ingalls, R. G. 1998. The value of simulation in modeling supply chain.

Proceedings of the 1998 Winter Simulation Conference, pp. 13711375. [3] Towill, D. R., M. M. Naim, and J. Wikner. 1992. Industrial dynamics simulation models in the design of supply chains. International Journal of Physical Distribution and Logistics Management 22 (5): 3-13. [4] Anderson, E. G., and D. J. Morrice. 1999. A simulation model to study the dynamics in a serviced-oriented supply chain. Proceedings of the 1999 Winter Simulation Conference, pp. 742-748. [5] Kritchanchail, D., and B. L. MacCarthy. 2000. Discrete or continuous: Which is more appropriate for supply chain simulation modeling? Proceedings of the 2000 International Conference on Production Research, Bangkok, Thailand. [6] Bernhard, J. A., and C. A. Marios. 2000. System dynamics modeling in supply chain management. Proceedings of the 2000 Winter Simulation Conference, pp. 342-351. [7] Shi, L., C. H. Chen, and E. Yücesan. 1999. Simultaneous simulation experiments and nested partition for discrete resource allocation in supply chain management. Proceedings of the 1999 Winter Simulation Conference, pp. 395-401. [8] Petrovic, D., R. Roy, and R. Petrovic. 1998. Modelling and simulation of a supply chain in an uncertain environment. European Journal of Operational Research 109 (2): 299-309. [9] Chan, F. T. S., P. Humphyes, and T. H. Lu. 2001. Order release mechanisms in supply chain management: A simulation approach. International Journal of Physical Distribution and Logistics Management 31 (2): 124-139. [10] Bagchi, S., S. J. Buckley, M. Ettl, and G. Y. Lin. 1998. Experience using the IBM supply chain simulator. Proceedings of the 1998 Winter Simulation Conference, pp. 1387-1394. [11] Chen, H. B., O. Bimber, C. Chhatre, E. Poole, and S. J. Buckley. 1999. eSCA: A thin-client/server/Web-enabled system for




distributed supply chain simulator. Proceedings of the 1999 Winter Simulation Conference, pp. 1371-1377. [12] Ingalls, R. G., and S. Kasales. 1999. CSSAT: The Compaq supply chain analysis. Proceedings of the 1999 Winter Simulation Conference, pp. 1201-1206. [13] Hieta, S. 1998. Supply chain simulator with LOGSIM-simulator. Proceedings of the 1998 Winter Simulation Conference, pp. 323326. [14] Barnett, M. W. 2000. Analysis of the virtual enterprises using distributed supply chain modeling and simulation: An application of e-SCOR. Proceedings of the 2000 Winter Simulation Conference, pp. 352-355. [15] Hicks, D. A. 1999. A four step methodology for using simulation and optimization technologies in strategic supply chain planning. Proceedings of the 1999 Winter Simulation Conference, pp. 12151220. [16] Bossel, H. 1994. Modeling and simulation. Wellesley, MA: A. K. Peters, Ltd.

Korean Society of Supply Chain Management. He received his BS from Korea University and MS and PhD from the University of Illinois at Chicago in 1983 and 1986. His research interests are SCM, simulation optimization, simulation output analysis, and simulation in manufacturing and logistics. He is a senior member of IIE and INFORMS and a member of SCS. Min Kwan Cho is a PhD student in the Department of Industrial Engineering, Hanyang University, Korea. He received his BS and MS from Hanyang University. His current research interests are SCM, simulation modeling, simulation output analysis, and Optimization. Yun Bae Kim is a professor in the School of Systems Management Engineering, Sungkyunkwan University, Korea. He received his BS from Sungkyunkwan University, MS from University of Florida, and PhD from RPI (Rensselaer Polytechnic Institute).

Young Hae Lee is a professor in the Department of Industrial Engineering, Hanyang University, Korea, and a president of the

Volume 78, Number 5 SIMULATION 329
