DISCRETE-EVENT PROCESS SIMULATION FOR THE
CONTINUOUS SIMULATION MODEL BUILDER

Edward J. Williams
206-2 Engineering Computer Center, Mail Drop 3
Ford Motor Company
Dearborn, Michigan 48121-2053 U.S.A.
williame@umdsun2.umd.umich.edu
 

KEYWORDS

Continuous simulation, discrete simulation, combined simulation

ABSTRACT

Simulation models, whether discrete, continuous, or a combination of both, are characteristically built to improve the understanding of a system and the processes operating within that system. Continuous simulation models study continuous variables, amenable to analysis via mathematical techniques such as differential and difference equations. Discrete-event process simulation models study integer-valued or binary variables requiring analysis via methods of discrete mathematics, statistics, and operations research. Additionally, random, stochastic variation is frequently both a significant provocation for undertaking a discrete process simulation study and a significant challenge within that study.

After describing the similarities and differences between continuous and discrete-event process simulation, this paper discusses typical business motivations for use of discrete simulation and presents a methodology and workplan for such studies in the context of example applications. Next, we describe data characteristically needed to drive a discrete-event process simulation model and the statistical concerns and methods pertinent to analyses of both input data and output results. We conclude with a generic description of computer software tools for building discrete models and a brief presentation of three case studies from manufacturing.

1 THE SIMILARITIES OF AND DIFFERENCES BETWEEN CONTINUOUS AND DISCRETE SIMULATION

Simulation, whether continuous, discrete, or a combination of both (a "hybrid" or combined simulation), is an analytical technique directed toward understanding the behavior of a real system by building a model of that system and then experimenting with the model. Specifically, the model of the system is driven with suitable inputs and the corresponding outputs are then observed (Bratley, Fox, and Schrage 1983).

In a continuous simulation model, the input and output variables (conceptually, the independent and dependent variables) are continuous, often differentiable. Typical continuous variables studied in such models are temperature, flow (e.g., of fluid or thermal energy), pressure, stress, or quantity of a desired chemical produced by a reaction; all these variables are continuous functions of time. In a discrete simulation model, the variables of interest are integer or even binary, and hence neither continuous nor differentiable. Typical discrete variables studied in such models are number of arriving customers, number of parts on a conveyor belt, the status of a machine (available or unavailable), or the number of completed jobs shipped in an hour. This fundamental distinction between continuous and discrete simulation models may be summarized by the statement "If alterations to the model occur continuously as time varies, the model is continuous; if such changes occur only at discrete instants of time, the model is discrete" (Hoover and Perry 1989).

2 TYPICAL BUSINESS MOTIVATIONS OF DISCRETE-EVENT PROCESS SIMULATION

Discrete-event process simulation is an analytical tool attractive to managers and engineers seeking to design, understand, and improve a business process. Simulation permits study and improvement of the process design, via use of a model, without having to build, disturb, or disable the actual process. For example, use of a simulation model to detect deficiencies in a process under design is far faster, less expensive, and less committal than actual construction of the process, observance of the deficiencies, and shutdown of the process while corrective measures are implemented within the actual process. Hence, many companies rely on simulation as standard practice when planning a new facility or evaluating a process change (Harrell and Tumay 1995). The extremely broad applicability of discrete-event process simulation and consequent realization of these benefits is readily observable in the great variety of case study contexts appearing in recent technical literature. Recent illustrative uses of simulation are design of a hospital admissions scheduling system (Lowery 1996), operation of a fast-food restaurant (Farahmand and Martinez 1996), handling of containerized cargo at a seaport (Ottjes et al. 1996), fabrication of steel components being made into hand tools (Porcaro 1996), manufacture of automobile engines (Jayaraman and Agarwal 1996), assessment of multicast routine algorithms within computer networks (Jia, Pissinou, and Makki 1997), evaluating operation of a fleet of remote-controlled load-haul-dump vehicles carrying ore in a mine (Vagenas 1996), design of a job shop system (Habchi and Seneclauze 1996), crop harvest and transport at a sugar plantation (Arjona-Suárez and Salazar-Cervantes 1996), and estimation of reorder points under uncertainty in both lead time and demand (Muñoz and Garza 1996).

3 THE WORKPLAN ROAD TO SUCCESSFUL PRACTICAL APPLICATION

The technical details of discrete process simulation and the building of a model (usually with the aid of computer software [Section 5]) are one important step in, but not the centerpiece of, a successful simulation study. Successful simulation projects proceed, with discipline, through well-defined stages of opportunity and scope definition (what new knowledge and understanding will be obtained from the simulation, and what business decisions will rely on that incremental knowledge and understanding), collection of data [Section 4], building, verifying, and validating the model, undertaking extensive experimentation with the model, analyzing and implementing the results, and documenting all work (Williams 1996). Ongoing communication between the simulation analysts and the business clients, via listening to the client, providing clear milestones and frequent progress reports, being mindful of the client's perceptions, and involving key decision makers, is vital to simulation project success (Musselman 1994). Detailed, extensively annotated checklists of all steps required in simulation practice are provided in (Ülgen et al. 1994a) and (Ülgen et al. 1994b).

4 DATA AND STATISTICAL ANALYSES TYPICALLY NEEDED WITHIN A DISCRETE-EVENT PROCESS SIMULATION

Extensive data is typically needed to drive a discrete-event process simulation. First, the current or proposed process logic must be described. This description comprises all rules concerning the paths of entities moving among the locations within the simulation model. Relative to some of the broadly ranging applications cited above, these entities might be hospital patients, electronic messages, loads of ore, partly assembled automobile engines, or diners in a restaurant. In addition to a complete description of process logic, the numeric data answering the following questions are essential:

The model builder will need to collect these data from the client prior to or concurrently with the building of the simulation model. Additionally, many of these data items may be highly volatile; the modeler should make provision for quick, convenient change of these data values.

Incorporation of uncertainty and stochastic processes is of greater frequency and importance in discrete simulation than in continuous simulation. Therefore, statistical analyses of input data and output results are required. Typical sources of randomness in discrete process simulation models are variability of time to do a task (whether the task is done by a person or is automated), variability of interarrival times of entities to the model, unpredictability of downtime (both onset and duration), and variability of output ("throughput") demanded of the system, as by the marketplace.

A statistical analysis often required for input data is the fitting of an appropriate probability density function to empirical data. For example, if actual times required to repair a machine have been recorded, the analyst should examine those data to decide whether a closed-form density function (e.g., lognormal, Weibull, or gamma) characterizes the data accurately, and, if so, what parameters that density should have. Statistical tests such as the chi-square test (Pearson 1900), Kolmogorov-Smirnov test (Kolmogorov 1933), and Anderson-Darling test (Anderson and Darling 1954) supplement qualitative judgments from histograms to assist with these decisions. An excellent taxonomy of input process modeling methods appears in (Leemis 1996).

Another statistical decision common to discrete simulation is the choice of an initial "warm-up" time. The computer model typically begins execution "empty and idle." If the actual system being modeled, such as a bank or restaurant, also begins each day's operation "empty and idle," this decision is moot. However, if the actual system is one that does not close and restart, such as a hospital, telephone exchange, harbor, or airport, the analyst seeking understanding of long-term system behavior should "warm up" the computer model for a length of simulated time, discard the initial, atypical output, and continue the computer simulation run. Alternatively or additionally, the analyst may initialize system conditions to values more typical of long-term behavior than "empty and idle" (Banks, Carson, and Nelson 1996).

A single run of a stochastic simulation model is conceptually an experiment whose specific outputs vary depending on the initial position of the random number generators used to model the uncertainties within the actual system being modeled. As with any statistically analyzed experiment, a simulation model should be run for multiple replications. Consequently, the analyst can then build confidence intervals for prediction of quantitative system performance metrics, such as customers served per hour, average and maximum lengths of queues, or utilization of expensive equipment. When, as is often the case in practice, numerous input parameters having numerous possible values are to be comparatively investigated, the analyst typically designs an experiment to apply techniques of analysis of variance (ANOVA) (Montgomery 1997). By applying one of several variance reduction techniques, such as common random numbers, antithetic variates, or control variates (Law and Kelton 1991), the analyst can achieve narrower confidence bands for these predictions at a specified level of uncertainty (p-value), or confidence bands of a specified width at lower uncertainty.

Subsequently, to compare system performance under various alternatives under consideration (i.e., various scenarios), the analyst has available a variety of statistical techniques. To undertake these sensitivity analyses (i.e., to examine the sensitivity of system performance to changes in system configuration), the analyst may use multivariate analysis of variance (MANOVA), discriminant analysis, regression models and metamodels, and response surface methodology (RSM) (Noguera and Watson 1997).

5 GENERIC DESCRIPTION OF COMPUTER SOFTWARE TOOLS

Computer software tools for building discrete simulation models may be broadly subdivided into languages and packages. In general, using a language gives the modeler more explicit control of detail in the model at the expense of increasing model-building time. On the other hand, using a package confines the modeler to the conceptual constructs available in the package, but reduces model-building time and often permits constructing an animation concurrently with the simulation model itself. In practical modeling work, an animation provides valuable assistance to verifying the model, fostering communication between the analyst and the client, and achieving credibility of the model's predictions. Whether working with a language or a package, the modeler needs to understand the software "world view" in terms of entities or transactions that flow through the model, resources that entities use (possibly after a delay), and operations, representing work done to or by an entity as it travels through the system. Also, both languages and packages drive the model forward in time via the use of a discrete clock. The discrete clock is "master" of the software; after the software completes all actions possible at the current time, the clock advances to the next time at which an action is scheduled to occur (Schriber and Brunner 1996). Extensive descriptions and comparisons of many simulation languages and packages appear in (Banks 1996). All languages and packages provide pseudo random number generators to permit modeling of stochastic processes.

Aside from the availability of general-purpose statistical packages for analyses of simulation input data and output results, more specialized computer software tools address data analyses highly specific to simulation. For example, tools such as BestFit (Jankauskas and McLafferty 1996) and ExpertFit (Law and McComas 1996) are available to choose the probability density function most appropriate for characterization of an empirical input data set.

6 GLIMPSES OF SEVERAL CASE STUDIES

Several case studies, briefly described next, illustrate the power of and benefits from simulation in improvement of manufacturing operations. Simulation can profitably be applied to manufacturing system design during any or all stages of the production system life cycle - the conceptual design phase, the detailed design phase, the launching phase, or the fully operational phase (Ülgen and Upendram 1997).

6.1 Analysis of Foundry Operations

The casting system in an automotive foundry required modification to accommodate longer mold cooling times to meet revised metallurgical and geometric casting properties required by product changes. Two promising alternatives, a straightforward lengthening of the current line or addition of an auxiliary set of cooling lanes, were proposed to meet these requirements. Both alternatives sought to reduce system entropy, introduce a parallel pull operation mode, and reduce in-process inventory. Simulation analyses proved that the first alternative provided the greater increase in overall system capacity while avoiding capital investment in a multi-million dollar piece of equipment (Hardy and Hardy 1997).

6.2 Increasing Utilization and Reducing Work-in-Process

A semi-automated production line manufacturing home appliances was studied to increase machine utilization and decrease work-in-process. Two simulation models were built. The first model reflected the current production control process among ten machines, six of which were dedicated to production of particular items (the remaining four were assigned to items by plant-floor supervision according to market demand). The second model reflected a proposed system dedicating each of the ten machines to the production of a particular item or set of items. Simulation analyses proved that the proposed system would achieve dramatic improvements in both machine utilization and work-in-process inventory; both of these improvements then being achieved in practice (Parker and Chengalvarayan 1992).

6.3 Improving Engine Upper Manifold Assembly

Automobile engines being assembled travel along a main line toward a spur line responsible for fabricating an upper manifold to be attached to the engine. Simulation was used to address the issues of determining the optimum operating pattern, the best number of pallets to be deployed on the recirculating spur line, and the best broadcast location along the main line. From this broadcast location, the approaching engine must electronically signal the spur line to specify a suitable manifold for itself. Simulation was used to study sixteen alternatives for number of pallets and broadcast point location. The three most promising alternatives achieved throughput quotas while reducing the number of pallets required and balancing lengths of the three queues within the spur loop. After implementation of the chosen alternative, actual system performance matched the simulation predictions within 5% (Williams and Orlando 1996).

7 SUMMARY

This paper has described discrete-event process simulation and contrasted it with continuous simulation, and described the necessary steps on the path to simulation project success. Discrete-event process simulation typically makes heavy use of statistical analysis methods and a computer software tool, either a language or a package. Examples and references to typical successful simulation projects in the manufacturing industry serve as additional evidence of the ability of discrete-event process simulation to achieve significant process improvements.

ACKNOWLEDGMENTS

Dr. Onur M. Ülgen, president, Production Modeling Corporation, and professor, University of Michigan - Dearborn, and John M. Dennis, simulation analyst, Ford Motor Company, have made valuable suggestions toward the improvement of this paper.

APPENDIX: TRADEMARKS

BestFit is a trademark of Palisade Corporation.
ExpertFit is a trademark of Averill M. Law and Associates.

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AUTHOR BIOGRAPHY

EDWARD J. WILLIAMS holds bachelor's and master's degrees in mathematics (Michigan State University, 1967; University of Wisconsin, 1968). From 1969 to 1971, he did statistical programming and analysis of biomedical data at Walter Reed Army Hospital, Washington, D.C. He joined Ford in 1972, where he works as a computer software analyst supporting statistical and simulation software. Since 1980, he has taught evening classes at the University of Michigan, including undergraduate and graduate statistics classes and undergraduate and graduate simulation classes using GPSS/H, SLAM II, or SIMAN. He is a member of the Association for Computing Machinery [ACM] and its Special Interest Group in Simulation [SIGSIM], the Institute of Electrical and Electronics Engineers [IEEE], the Institute of Industrial Engineers [IIE], the Society for Computer Simulation [SCS], the Society of Manufacturing Engineers [SME], and the American Statistical Association [ASA]. He serves on the editorial board of the International Journal of Industrial Engineering - Applications and Practice.