Computer simulation and its management applications

Computers in Industry 20 G-%;2) 229-238 Elsevier

229

Short Note

Computer simulation and its management applications

T.C.E. Cheng Department of Actuarial and Management Sciences, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Received September 17, 1991 Accepted December 28, 1991

In this paper, the historical basics of computer simulation are presented, the elementary simulation process is discussed, and several application areas of simulation in the field of business and management are highlighted. It is not the aim of the author to make the business manager an expert, but to provide him a soft introduction to consider the potentials of computer simulation as an effective and efficient decision- support tool to deal with a wide variety of complex management decision problems.

Keywords: Management science, Simulation analysis, Busi- ness, History of simulation

1. Introduction

"Simulation is a method used to study the dynamics of systems" [1]. Computer simulation is a decision-support tool used by decision-makers to imitate the behaviour and predict the performance of a complex real system functioning under different operating conditions over time. Sim- ulation of a system allows the problem-solver to better understand the real world situation by improving his ability to visualize the system and, therefore, enhance the overall comprehension of the problem.

The general purpose of simulation has been suggested by Maisel [2]: "to attain the essence

Correspondence to: Prof. T.C.E. Cheng, Department of Man- agement, Hong Kong Polytechnic, Hung Hom, Kowloon, Hong Kong. Fax: (852) 774 3679.

without the reality". Naylor et al. [3] have given an operational definition of simulation: "a nu- merical technique for conducting experiments on a digital computer, which involves certain types of mathematical and logical models that describe the behaviour of a business or an economical system (or some component thereof) over ex- tended periods of time". While it is true that simulation, usually computer-based, is performed by conducting sampling experiments on a mathematical or logical model of a particular system over a specific time frame, the types of system that can be simulated are much broader than just business or economical systems. Also, the dura- tion of the simulation experiment and the type of computer used for a simulation study depend on the type of system being simulated and on the kind of applications to be made.

A successful simulation study requires the identification of all important factors and aspects, and their inter-relationships, of the whole system under study, together with a thorough understanding of how the system interacts with its environment. As a result, the bias towards at- tempting to solve only one particular aspect of the problem is minimized as the focus of the decision-maker is directed towards the entire problem and its situational context. Thus, simu!a- tion adopts a systemic view of model building and places a great emphasis on a holistic approach to problem solving.

Simulation is a trial and error method that is used to gain an understanding of the problem but

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230 Short Note Computers in Industry

the results obtained by its use cannot be deemed optimal as these results are merely sample statistics that may contain sampling errors. Also, more often than not, the outcome provided by the simulation is not definitive enough to persuade the decision-maker to make a decision solely based on its generated data. In these cases, decisions are made on what the management team feels are the best actions from the list of alterna- tives generated by the simulation process. Thus, the emphasis of a simulation model tends to be one of "what if" rather than "what's best" as emphasized by other optimizing operations research techniques such as mathematical programming.

2. Advantages and disadvantages of simulation

While simulation is a versatile tool for the analysis of a variety of complex real-world systems, the decision-maker should consider its advantages and disadvantages before applying it to study a particular problem. As discussed by Schmidt and Taylor [4], Adkins and Pooch [5], Law and Kelton [6] and others, the primary advantages of simulation are:

(1) A simulation model is flexible in its use and, once constructed, may be used to analyze various proposed designs or policies under a pro- jected set of operating conditions with a long time frame, either in compressed or expanded time.

T,,C. Edwin Cheng is Professor of Op- erations Management in the Faculty of Management and Adjunct Profes- sor of Industrial Engineering in the Faculty of Engineering, University of Manitoba, Canada. He obtained a BSc (Eng.) with first class honours in In- dustrial Engineering from the Univer- sity of Hong Kong, an MSc in Indus- trial Management from the University of Birmingham and a PhD in Opera- tions Rest.arch from the University of Cambridge in 1979, 1980 and 1984,

respectively. He was previously on the staff of various univer- sities in England, Hong Kong, and Singapore. His research interests are in production scheduling, inventory control, and quality management. He has published numerous papers in a variety of academic and professional journals and two books. Dr. Cheng presently serves on the editorial board of eight international academic journals. A registered professional engineer in Manitoba and a Chartered Engineer in UK, he is active in consulting with business and industry.

(2) Simulation is well suited for the analysis of proposed strategies, where the available information and data pertaining to these strategies are minimal.

(3) Lower expenses are incurred by building and experimenting with a model of the system than would be if experimentation of the real system were to occur.

(4) Simulation models, if kept simple, are easy to operate and, therefore, they can be made available to various interested parties to study particular aspects of the system. If analytical models are used to study the system, the analysis would have to be performed by trained prol~es- sionals.

(5) A simulation model is far less restrictive than an analytical model in generating data to estimate any relevant performance measure of the system.

(6) For certain systems, particularly highly complex and analytically intractable ones, simulation is the only viable method available for system analysis and evaluation.

Some disadvantages the decision-maker should be aware of before using simulation are:

(1) It is often costly and time-consuming to develop and validate programs for computer simulation. Thus, the problem solver should attempt to maximize the use of pre-programmed modules in building a large-scale simulation model.

(2) Extensive running of a simulation model on a computer is usually required to obtain reli- able results and this can result in high computa- tional costs.

(3) Decision-makers have a tendency to apply the simulation method to a problem for which other more appropriate analytical methods of solution are available. Simulation should only be used as a last resort. Only after all other mathematical and analytical methods have been found inadequate for the particular problem in question, should the simulation model be implemented.

3. Objectives of the simulation process

The process of simulating a system, the simulation process, involves three types of objectives, which are:

Computers in Industry T.C.E. Cheng / Computer simulation 231

(1) The objective of the system being studied. This objective is usually to maximize the utility of the available system resources so as to optimize the goals of the system.

(2) The objective of the simulation model. This objective is to efficiently and effectively generate output statistics which are necessary ingredients for the application of the model to study a system.

(3) The objective of the simulation analyst. This objective encompasses the attempt of the analyst to maximize the derived benefits through the efficient allocation of the resources allocated to the budget of the simulation study.

Of these three objectives, the objective of the system is perceived to be the most important because the primary reason for pursuing a simulation study is to identify a most appropriate course of action for a decision problem, which usually involves some kind of resource allocation issues, arising from operating a real system. The remaining two objectives are of equal importance since the simulation study must be conducted within the budget constraints and it must produce adequate and accurate results to enable the decision-maker to make valid decisions.

4. Stages in the simulation process

The simulation process comprises several dis- tinct but somewhat overlapping stages, as discussed by Shannon [7] and Gordon [8]. A critical factor in a successful simulation study is the control of these overlapping activities to obtain a unified result. A brief discussion of each of the stages of simulation development follows. The system analyst should follow these stages closely in order to develop a sound and thorough simulation study.

4.1. Problem definition In this stage of the simulation process, the

decision-maker has to specify what questions have to be answered and then rank these questions in order of importance and cost feasibility. The proper and most effective way of presenting the information once it is generated is also a major concern for the decision-maker encompassed in this stage of the process. The cost and benefits of the model must also be analyzed and then a

decision made as to whether the project should be reoriented, continued, or abandoned. This cost/benefit analysis is most likely to contain some uncertainty and, therefore, should be made not only for the expected benefit but also for the optimistic and pessimistic limits as well. Due to the high uncertainty and the consequent risks, the project has to be fairly beneficial before management should agree to undertake it.

Another consideration that must be taken in this stage is the decision of what type of model should be used for the particular problem. There are generally two main categories of models: (a) "Trial and error" models, where questions

are asked and results observed. (b) Optimizing models, where the results are ei-

ther calculated directly or are found by using a built-in search procedure.

The decision as to which model to use should be dependent upon the nature of the problem, the analyst's understanding of the problem, his technical competence, and the resources made available for the simulation project.

This stage of the process has to be clearly defined and understood by everyone involved, i.e. the management (decision-maker), the project team (model builder and system analyst) and all others affected by the project, so that the project is completed efficiently and the results will be meaningful.

4.2. Project team selection and training This stage involves the selection of the model

builders of the system. This task cannot be viewed lightly as the success of the project depends upon the motivation and skills of the people involved. Model builders should fully comprehend every aspect of the situation involved. They should have the knowledge and capability to decide how and where to collect the data, as well as a scientific questioning approach and a good working rela- tionship with management. Above all, members of the project team should have the motivation and eagerness to complete the project quickly and efficiently.

In many cases, however, the team members do not possess all the necessary skills and expertise needed to work on the project, and training has to be provided to remove the deficiencies. This training can be accomplished through the use of one of two training methods available. The first


method, a formalized training course, is best suited for the training of analysts who will be working with a complex and costly system. With this method the participants in the course are taken through a series of linked exercises to show them, step-by-step and in sufficient detail, the modelling discipline. The second method, on-the- job training, is more appropriate for problems for which a quick solution has to be found. With on-the-job training the analysts are first familiar- ized with the project by setting up a simplified version of the model with a portrayal of only the main features and important aspects of the system. Then, as their confidence and skill level increase, necessary extensions of the model could be implemented. A benefit of on-the-job training is that team members are more motivated to learn and are more attentive due to the urgency of the situation than they would be with a formal training program.

4.3. Model building and testing There are three main objectives in this stage

that must be met: (a) Accuracy. This measures how well the

model resembles the real system. In order to maximize accuracy, the model should be kept simple with only necessary and important details included and all trivial details excluded.

(b) Acceptability. To improve the chances o~ management accepting the project rezults, the model builder should build the model as close to the real system as possible by seeking the opin- ions of those who have direct contact and are familiar with the system. The analyst should use vocabulary that will be easily understood by management and should prepare informative reports in a useful and recognizable form. The builder should be willing to compromise on certain aspects of the project in order to appease management and, consequently, increase the chance of the project being accepted.

(c) Speed. In order to meet this objective, strict deadlines should be set and closely adhered to. Deadlines should be made fairly optimistically by setting th~ proposed completion time at a date that will be hard but not impossible to meet so that the actual completion time will be shorter than if a generous completion date had been set.

The main steps involved in the building and testing of a simulation model include:

(i) identifying all relevant entities and available resources,

(ii) designing data flow diagrams to trace the flow of entities and recording the resource utilization patterns,

(iii) setting up time limits for each process, (iv) simplifying the model and adding other de-

tails as they become necessary, (v) performing a check of the system by hand

simulating the model, and (vi) performing tests to show tha; the results ~f

the model replicate the situation and answer all the related questions.

4. 4. Experimentation and modification In the experimentation stage, the model

builder has to attempt to develop a program that will accurately test the robustness of the model in any situation, that will use the computer in an efficient manner and will provide insight into the behaviour of the system for different circumstances.

After experimenting with the model, one finds that necessary changes become apparent and, therefore, must be implemented into the model. Only one variable should be changed at a time so that the effect of the change can be traced back to the particular variable responsible for it. Any modifications should be thoroughly investigated before being implemented to make sure that these modifications will improve the model and produce the results that the builder expects them to produce.

With regard to testing the robustness of the model, sensitMty analysis need be performed to determine how much the model is allowed to change before the generated solution becomes invalid. This is simply done by performing planned changes to the assumptions of the model in question and then analyzing these changes to observe their impact on the solutions.

4.5. Preparation and presentation of recommenda.. tions

It is very discouraging and frustrating to produce an efficient and effective model only to have it rejected by management due to poor presentation of the facts concerning the simulation project. The model builder must know what he wants to say and how he is to say it in order to maximize the chances of obtaining approval from


management of the recommendations for implementation.

The presentation should be designed in a way that would maximize making use of the presenter's strengths in his presentation style while concealing his weaknesses. Constructive criticisms should be sought from team members in order to improve on the material covered and on the way it is presented. Visually presenting the ideas and recommendations concerning the project is perhaps the most effective method, as well as ~he simplest and easiest to understand. Writ- ten and oral presentation should be kept to a minimum level and be made as simple and straight-forward as possible. Management usually appreciate efforts made to ease their understanding of a problem, hence facilitating their consequent absorption of the major results.

When making the presentation, the presenter should know the material well enough to be able to make the presentation as professional as possible. He should only present the major points of the model and use words and symbols that the audience is familiar with instead of trying to impress them with a heavy dose of technical jargon, and he should include sufficient technical details at a level congruent with the background and experience of the people on the receiving end of the presentation. Finally, he should leave ample time at the end of the prese~tation for questions. When answering questions he should make sure to answer the specific question asked and not trail off to a different subject.

4.6. Implementation "his stage makes use of the data flow diagrams

prepared in the model buildiiig stage. The logical flow of data and entities can be traced and performance measures can be set for each process in the model. As the project proceeds, comparisons of the actual performance with the expected performance should be made regularly. If deviations in performance exist, adaptations of the model can be implemented at the earliest opportunity.

4. Z Review of project The purpose of this stage is to evaluate the

~uccess of the model and how the model can be implemented into future management projects. Each stage in the simulation process is reviewed and, with the benefit of hindsight, any mistakes

made in the process can be analyzed and documented so that these same mistakes will not be repeated in the future. The review of the project can encompass the following areas:

(a) Feasibility and achievement. A comparison of what was promised and what actually was achieved is performed and any discrepancies can then be further investigated. Expected benefits and costs can be compared with actual results and a decision can be made as to what benefits were attributable to the modelling exercise.

(b) Technique. The model builder must decide whether the modelling approach was the most suitable for the problem in question or should an alternative type of model have been used instead. Also, a discussion as to what changes would be beneficial to implement into the technique before it is used again may prove to be advantageous.

(c) Work content. This area compares the orig- inal time estimates with the actual completion times and gives an explanation on why these two times were different. Some possible explanations for completion time variances are that, as the model is developed, new problem areas are un- covered which require solutions, delays caused by unforeseen circumstances may arise and, when meetings with management are scheduled, these discussions may be considerably longer than expected due to unforeseen conflicts of interest. An investigation of how these discrepancies came about should be made, considering such factors as naivety, carelessness, poor work rate, and equipment failure. As the model builder becomes more experienced, his estimation skills improve and a smaller deviation between expected and actual completion times will result.

(d) Equipment. An evaluation of computer ef- ficiency, adequacy, and speed of output should be made. If upon analysis of these aspects the model builder feels that improvements could have been made, then this should be documented so that these improvements will be implemented into the next project.

(e) People. This factor is probably the most crucial in the determination of whether the project will be successful or not. Motivated and highly skilled people tend to achieve better performance and will complete the job faster and more efficiently than people who are not as motivated or who do not possess the same level of skills. An analysis of the human resources and the working


environment can be compiled to determine the strengths and weaknesses of both the managers and the model builders, to assess their working relationships and to understand the working environment under which they cooperate on the project. This will provide suggestions as to what improvements can be made in this area for future endeavors.

$. Functions of the simulation model

The simulation model must perform several functions in order to produce meaningful results for the purposes of system analysis and design. Lee et al. [9] have identified the following essential functions in a typical stochastic simulation model, which is characterized by a continual probabilistic change in system states over time. The majority of real world management decision problems with their inherent random nature are formulated as stochastic models.

5.1. Random variable generation This is one of the most important functions in

stochastic simulation as the reliability and validity of the data generated is directly related to the effectiveness with which this function is performed by the simulation model. However, certain characteristics must be present in the generated random numbers in order for the model to perform effectively. These characteristics include:

(a) Uniform distribution. This ensures that each number has an equal chance of being selected. If this characteristic is not present the simulation model will become biased and it will not produce valid observations.

(b) Efficient generation. An efficient method must be used to generate streams of (pseudo)random numbers which will result in an inexpensive and fast model with non-degenerative data.

(c) Data b~dependence. Ideally the streams of random numbers generated should be totally in- dependent, thus, from a practical viewpoint, to be useful they should at least be serially uncorre- lated.

Common methods for random number generation incorporated by simulation models include the Monte Carlo approach and the inverse trans- formation technique. Due to its capability of gen~ erating random numbers, the simulation model

tends to be more versatile and accommodating than most analytical models.

5.2. Event control The sequence of events is controlled by the

logic of the simulation program. The flow diagrams designed in the model building stage picto- rially represent how the various events are related and in what order they are performed.

5.3. System state initialization The status of the system at the outset of the

modelling procedure is defined in this step to provide the initial setting for the ensuing simulation experiments.

5.4. System performance data collection This is an essential function, which collects

sample statistics and compiles information on the various system descriptors that are present in the model.

5.5. Statistical computations and report generation At the end of the simulation run, operating

and other statistics can be generated by the program and printed out for documentation of the results. This capability to produce a wide variety of statistics is a major advantage of simulation.

5.6. Model validation The model builder will want to test the model

to make sure that the program is logically sound and correct. A test should also be performed to measure how well the model resembles the real system. Although the validation procedure is a major difficulty for system modelling, several testing procedures have been developed which may help overcome this difficulty. These include:

(a) The model can be run a number of times for short periods of time and the validity of the results obtained can be checked with detailed hand simulation.

(b) The model can be broken down into smaller parts and then run separately. This re- duces the complexity of detecting programming and modelling errors and of testing the correct modelling of the relationships between specific variables.

A major difficulty in perforrning a simtr!at,.'on run is determining the starting conditions and how long the model should be run in order to


reach a steady-state condition. In most cases, a compromise has to be made between the dura- tion of the simulation periods and the statistical reliability of the simulation results.

6. Management applications of simulation

Being such a general, versatile and powerful method for dealing with large-scale complex systems and solving real world problems, simulation has been widely applied in a great variety of contexts, involving biological, chemical, physical, business, economical, political, social, and many other systems. A number of studies have reported that simulation is one of the most effective tools for management decision-making (see, for example, Refs. [10,11]). Surveys of the practical application of simulation in industry have been conducted by Watson [12], and Christy and Watson [12]. Millichamp [14], Lee et al. [9], and Hillier and Lieberman [15], among others, have discussed various real world examples of application of simulation in the field of business and management, which we summarize in the following.

6.1. Analysis of queueing systems Simulation is the only viable method available

to study complex queueing systems. A queueing situation arises when the amount of resources available is not sufficient tO meet all the demands at the same time. This, being a special case of the general resource allocation problem, is a funda- mental problem in production and operations management.

6.2. Inventory management For the inventory management system operat-

ing under conditions of stochastic demand and lead time, simulation is about the only method the analyst can use to study the system performance and to evaluate new inventory control policies.

6.3. Networks The PEP.T network, when solved analytically,

produces slightly biased results; these results are valid onl~ when the activity times follow a beta distribution. So, if the activity times follow some other distribution, the network could be more accurately analyzed by simulation.

6.4. Production Many operational problems arising in produc-

tion management can be analyzed with simulation. Such problems include, but are not limited to, scheduling, sequencing, line balancing, plant layout, Ideational analysis, vehicle routing, quality control, demand forecasting, production plan- ning, job design, and many others.

6.5. Maintenance Simulation is usually used in this area to sup-

plement analyses performed by analytical methods. The two main areas of maintenance generally analyzed by simulation are machine break- downs and facility failures due to the random nature of these two problems.

6.6. Finance For capital budgeting problems, estimates of

cash flows are needed and to be able to produce these estimates, it is necessary to generate numerous random variables. Simulation is an effective method for dealing with such stochastic problems.

6.Z Marketing This aspect of business is particularly suited to

simulation because marketing is noted for its encompassment of large amounts of uncertainty. By using simulation, the analyst is able to experiment with various courses of action, whether they are related to the product, price, consumer behaviour, distribution channels, or to other marketing variables.

6.8. Public service operations The operations of such public systems as pub-

lic transport, police department, fire department, ambulances, hospitals, court systems, airports, post offices and others are generally so complex that simulation is the only technique flexible and broad enough to effectively address all the relevant issues and to analyze the systems.

6.9. Environmental and resource conservation Simulation models of air, water and noise pol-

lution have been developed and tested in order to determine what the effect of these various forms of pollution have on the environment and to ascertain their detrimental effects on the ecologi- cal system. These models are becoming increas-


ingly popular as pollution and other environmental impacts are fast becoming a major issue in the management of new technologies.

7. Selection of simulation software

An increase in the use of simulation to study complex man-machine systems arising in business and industry has led to the proliferati6n of simulation software products developed to cater for a wide variety of simulation requirements. A system modeller will find it increasingly hard to select a simulation package for his company or for a particular application because of the diver- sity of choice with respect to cost, capabilities, user-friendliness, and technical support. There are essentially three major categories of software package for computer simulation of business and management systems, namely, high-level programming languages, general-purpose simulation languages and simulators. A comprehensive study of some twenty simulation packages have been conducted by Arthur et al. [16].

While it is possible to construct simulation models using such high-level programming languages as BASIC, FORTRAN, PASCAL and the like, it will be a very time-consuming and costly exercise, and it requires extensive programming skills on the part of the system modeller. This is so because high-level programming languages are not equipped with the desirable features to model complex stochastic systems. The features include modelling flexibility, generating random numbers with special statistical distributions, convenient data structures for event processing, and so on. They also lack the data handling and statistical analysis capabilities, such as data tallying, his- togram construction, graphic display and animation, necessary for efficient collection, analysis, and communication of simulation outputs.

It is inevitable that the modelling of complex systems requires a general-purpose simulation language. Examples of common general-purpose simulation languages are ECSL, GPSS, SIMAN, SIM-

SCRIPT and SLAM, to name a few. All of these simulation languages have flexible modelling capability and are able to perform a variety of desirable simulation functions. While a general- purpose simulation language has the highly ac- claimed ability to model almost any system, re-

gardless of its complexity and structure, to any level of detail demanded by the modeller, its efficient use generally requires a fairly high level of programming expertise and debugging skills. As a result, the time involved in the modelling process will be lengthy and the associated model building cost will be high.

For specific applications, such as financial modelling and manufacturing system design, the use of a simulator is highly recommended. Simu- lators designed for a particular application purpose will have special constructs that greatly sim- plify the process of modelling problems in the designated application area. They also possess the ability to handle data efficiently, to analyze results in a meaningful manner, and to display the simulation outputs in a form most convenient for decision-making under the perceived application environment. For example, ~FPS is a financial simulator which provides management with useful information to evaluate the impact of its decisions on the company's financial statement. S~M- FACTORY is a manufacturing simulator capable of simulating material flow in a factory and presenting an animated picture of the factory at work. The use of a relevant simulator for a particular application will greatly shorten the time needed to build valid models that are easy to use and that conveniently provide useful information to assist managers in making decisions.

The selection of the "right" simulation software depends on a number of factors with regard to the modelling philosophy, modelling approach, and general features of the software, along with a host of practical considerations. A representative group of factors that need to be considered are: (1) Acquisition and operating costs

(a) Software-purchase price and licensing fee for the software, supporting modules and other third-party products.

(b) Hardware-costs of the required computer system to run the software and the associated peripherals for data input and output display.

(c) Training-expenses incurred for personnel to attend training sessions.

(d) Maintenance-expenses incurred for maintaining the software and hardware.

(e) Operating-expenses incurred for operating the software and hardware.

(2) User-friendliness

Computers in Industry T C.E. Cheng / Computer simulation 237

(3)

(4)

(a) Ease of learning. (b) Ease of model development. (c) Ease of model debugging. (d) Ease of explanation to end-users. (e) Ease of use. Technical capabilities (a) Flexibility of modelling. (b) Maximum allowable model size. (c) Random number generation capabilities. (d) Data handling capabilities. (e) Experimental design capabilities. (f) Mathematical and statistical capabilities. (g) Animation, graphic, and other reporting

capabilities. (h) Application-specific capabilities. (i) Interchangeability with other software. (j) Speed of execution. (k) Compatibility across computer classes. Customer support (a) Documentation-user manuals, technical

references, text rJoks, training literature. (b) Training progra,.:Is-training methods and

personnel, on site training sessions, training centres and faciliues, training videos.

(c) Technical support-expert consultation and advice, toll-free numbers, bulletin boards, user groups, professional journals, trade magazines.

(d) Product upgrade-new product awareness, upgrading kits.

(e) Warranty-money-back guarantee, warranty period, product liabilities.

8. Conclusions

In order to accurately measure the performance of a simulation study, management must find answers to the following four questions: (1) Is the model a close depiction of the real

system under study? (2) Are the results obtained from the model valid

answers to the questions that are being asked? (3) Have enough simulation runs been performed

in order that the averag~ value of the performance measure will provide a reasonable estimate of the true expected value?

(4) Has enough consideration been taken for a particular situation so that the model builder can be reasonably confident that the simulation model has generated the best solution?

After this assessment is completed, management is able to produce, in a fair amount of detail, a report listing all the benefits and costs that were accrued over the simulation project, how the simulation model could have been improved and any suggestions or comments that may help remove the obstacles standing in the way of undertaking future simulation projects.

Simulation analysis helps managers to gain insight into proposed projects and the feasibility of implementing these projects. The flexibility and versatility of the simulation method allows the analyst the ability to perform numerous experiments under tightly controlled conditions to study different aspects of the problem. This provides him with a greater understanding and comprehension of the problem and points to potential sources of solution. However, the model that is to be used for analysis must follow a certain con- formity. Starting and ending conditions and any other extraneous effects must be eliminated, a steady-state condition must be present and the complexity of the model must be minimized. Complex systems result in high implementation and operating costs and, usually, generate large amounts of data, making it a difficult task to obtain a meaningful interpretation of the results. If the model conforms to these criteria, the results that will be obtained from the model will be as close to reality as is possible with simulation. In addition, it is important to acknowledge that the simulation results are as valid and useful as the data used as input into the model. Thus, it is worth making extra efforts to ensure the integrity of the input data.

Management is just starting to realize the great potential of computer simulation as an effective tool to assist them in dealing with a wide variety of complex management decision problems. As computer technology becomes more advanced, computer simulation applications will become more and powerful: the outlook for computer simulation as a decision-support tool is extremely promising.

Acknowledgement

This research was supported in part by a grant from the Faculty of Management Associates Fund of the University of Manitoba.


References

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Computer simulation and its management applications