SIMULATION

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Simulation is used to model efficiently a wide variety of systems that are important to managers. A simulation is basically an imitation, a model that imitates a real-world process or system. In business and management, decision makers are often concerned with the operating characteristics of a system. One way to measure or assess the operating characteristics of a system is to observe that system in actual operation. However, in many types of situations the cost of direct observation can be very high. Furthermore, changing some of the relationships or parameters within a system on an experimental basis may mean waiting a considerable amount of time to collect results on all the combinations that are of concern to the decision maker.

In business and management, a simulation is a mathematical imitation of a real-world system. The use of computers to conduct simulations is not essential from a theoretical standpoint. However, most simulations are sufficiently complex from a practical standpoint to require the use of computers in running them. A simulation can also be considered to be an experimental process. In a set of experimental runs, the decision maker actively varies some of the parameters or relationships in the system. If the mathematical model behind the simulation is valid, the results of the simulation runs will imitate the results of the real system if it were to operate over some period of time.

In order to better understand the fundamental issues of simulation, an example is useful. Suppose a regional medical center seeks to provide air ambulance service to trauma and burn victims over a wide geographic area. Issues such as how many helicopters would be best and where to place them would be in question. Other issues such as scheduling of flight crews and the speed and payload of various types of helicopters could also be important. These represent decision variables that are to a large degree under the control of the medical center. There are uncontrollable variables in this situation as well. Examples are the weather and the prevailing accident and injury rates throughout the medical center's service region.

Given the random effects of accident frequencies and locations, the analysts for the medical center would want to decide how many helicopters to acquire and where to place them. Adding helicopters and flight crews until the budget is spent is not necessarily the best course of action. Perhaps two strategically placed helicopters would serve the region as efficiently as four helicopters of some other type scattered haphazardly about. Analysts would be interested in such things as operating costs, response times, and expected numbers of patients who would be served. All of these operating characteristics would be impacted by injury rates, weather, and any other uncontrollable factors as well as by the variables they are able to control.

The medical center could run their air ambulance system on a trial-and-error basis for many years before they had any reasonable idea what combinations of resources would work well. Not only might they fail to find the best or near-best combination of controllable variables, but also they might very possibly incur an excessive loss of life as a result of poor resource allocation. For these reasons, this decision-making situation would be an excellent candidate for a simulation approach. Analysts could simulate having any number of helicopters available. To the extent that their model is valid, they could identify the optimal number to have to maximize service, and where they could best be stationed in order to serve the population of seriously injured people who would be distributed about the service region. The fact that accidents can be predicted only statistically means that there would be a strong random component to the service system and that simulation would therefore be an attractive analytical tool in measuring the system's operating characteristics.

BUILDING THE MODEL

When analysts wish to study a system, the first general step is to build a model. For most simulation purposes, this would be a statistically based model that relies on empirical evidence where possible. Such a model would be a mathematical abstraction that approximates the reality of the situation under study. Balancing the need for detail with the need to have a model that will be amenable to reasonable solution techniques isa constant problem. Unfortunately, there is no guarantee that a model can be successfully built so as to reflect accurately the real-world relationships that are at play. If a valid model can be constructed, and if the system has some element that is random, yet is defined by a specific probability relationship, it is a good candidate to be cast as a simulation model.

Consider the air-ambulance example. Random processes affecting the operation of such a system include the occurrence of accidents, the locations of such accidents, and whether or not the weather is flyable. Certainly other random factors may be at play, but the analysts may have determined that these are all the significant ones. Ordinarily, the analysts would develop a program that would simulate operation of the system for some appropriate time period, say a month. Then, they would go back and simulate many more months of activity while they collect, through an appropriate computer program, observations on average flight times, average response times, number of patients served, and other variables they deem of interest. They might very well simulate hundreds or even thousands of months in order to obtain distributions of the values of important variables. They would thus acquire distributions of these variables for each service configuration, say the number of helicopters and their locations, which would allow the various configurations to be compared and perhaps the best one identified using whatever criterion is appropriate.

MONTE CARLO SIMULATION

There are several different strategies for developing a working simulation, but two are probably most common. The first is the Monte Carlo simulation approach. The second is the event-scheduling approach. Monte Carlo simulation is applied where the passage of time is not incorporated into the simulation model. Consider again the air ambulance example. If the simulation is set up to imitate an entire month's worth of operations all at once, it would be considered a Monte Carlo simulation. A random number of accidents and injuries would generate a random number of flights with some sort of average distance incorporated into the model. Operating costs and possibly other operating values sought by the analysts would be computed.

The advantage of Monte Carlo simulation is that it can be done very quickly and simply. Thus, many months of operations could be simulated in the ambulance example. From the many months of operational figures, averages and distributions of costs could readily be acquired. Unfortunately, there is also a potentially serious disadvantage to the Monte Carlo simulation approach. If analysts ignore the passage of time in designing the simulation, the system itself may be oversimplified. In the air ambulance example, it is possible to have a second call come in while a flight is in progress which could force a victim to wait for a flight if no other helicopter is available. A Monte Carlo simulation would not account for this possibility and hence could contribute to inaccurate results. This is not to say that Monte Carlo simulations are generally flawed. Rather, in situations where the passage of time is not a critical part of the system being modeled, this approach can perform very well.

EVENT-SCHEDULING METHOD

The event-scheduling method explicitly takes into account time as a variable. In the air ambulance example, the hypothetical month-long simulation of the service system would emerge over time. First, an incident or accident would occur at some random location, at some random time interval from the beginning point. Then, a helicopter would respond, weather permitting, the weather being another random component of the model. The simulated mission would require some random time to complete with the helicopter eventually returning to its base. While on that service mission, another call might come in, but the helicopter would probably need to finish its first mission before undertaking another. In other words, a waiting line or queue, a term often used in simulation analysis to indicate there are "customers" awaiting service, could develop. The event scheduling approach can account for complexities like this where a Monte Carlo simulation may not.

With a computer program set up that would imitate the service system, hundreds of months would be simulated and operating characteristics collected and analyzed through averages and distributions. This would be done for all the relevant decision-variable combinations the analysts wish to consider. In the air ambulance example, these would include various numbers of helicopters and various base location combinations. Once the analysts have collected enough simulated information about each of the various combinations, it is very likely that certain combinations will emerge as being better than others. If one particular design does not rise to the top, at least many of them can usually be eliminated, and those that appear more promising can be subjected to further study.

PROGRAMMING LANGUAGES

It was noted that while there is no theoretical need to computerize a simulation, practicality dictates that need. In the air ambulance example, analysts would require thousands of calculations to simulate just one month of operation for one set of decision-variable values. Multiply this by hundreds of monthly simulations, and the prospect of doing it somehow by hand becomes absolutely daunting. Because of this problem, programming languages have been developed that explicitly support computer-based simulation. Using such programs, analysts can develop either of the types of simulations mentioned here, a Monte Carlo simulation or an event-scheduling method simulation, or other types as well.

A particularly widely used language is called SIMSCRIPT. It is particularly well-suited to the event-scheduling method. The language itself has undergone several incarnations, so different versions, identified by Roman numeral, can be found on different computer systems. To apply this language, analysts would develop a logical flow diagram, or model, of the system they seek to study. SIMSCRIPT is a stand-alone language that can be used to program a wide variety of models. Thus, someone who uses simulation regularly on a variety of problem types might be well-served by having this type of language available.

Another widely used language is called GASP IV. It operates more as an add-in set of routines to other high-level programming languages such as FORTRAN or PL/1. With the rapid proliferation of personal computers in recent years, specific simulation software packages, simulation add-ins to other packages, and other capabilities have become widely available. For instance, a simple Monte Carlo simulation can be performed using a spreadsheet program such as Microsoft's Excel. This is possible because Excel has a built-in random number function. However, one must be aware that the validity of such random number functions is sometimes questionable.

One of the basic building blocks within any simulation language or other tool is the random number generator. Ordinarily, such a generator consists of a short set of programming instructions that produce a number that "looks" uniformly random over some numeric interval, usually a decimal fraction between zero and one. Of course, since the number comes from programming code, it is not really random; it only looks random. Any fraction between zero and one is theoretically as likely as any other. Such numbers can then be combined or transformed into apparently-random numbers that follow some other probability function, such as a normal probability distribution or a Poisson probability distribution.

This capability facilitates building simulations that have different types of random components within them. However, if the basic generator is invalid or not very effective, the simulation results may very well be invalid even though the analysts have developed a perfectly valid model of the system being studied. Thus, there is a need for analysts to be sure that the underlying random number generating routines produce output that at least 'looks' random. There is a need for external validity in a simulation model, a need for the model to accurately imitate reality. There is just as critical a need for the building blocks within the model to be valid, for internal validity which can be a problem when an untested random number generator is employed.

EXPERIENTIAL GAMES

One particularly fast-growing area of simulation applications lies in experiential games. Board games that we played as youngsters were basically simulations. Usually, some kind of race was involved. The winner was the player who could maneuver their playing pieces around the board, in the face of various obstacles and opponents' moves, the fastest. The basic random number generator was usually a pair of dice. Computer-based simulations have expanded the complexity and potential of such gaming a great deal.

Management and business simulations have been developed that are sufficiently sophisticated to use in the college classroom setting. Almost all of these consist of specialized computer programs that accept decision sets from the game's players. With their decision sets entered into the computer program, some particular period of time is simulated, usually a year. The program outputs the competitive results with financial and operating measures that would include such variables as dollar and unit sales, profitability, market shares, operating costs, and so forth. Some competitors fare better than others because their decisions proved to be more effective than others in the face of competition in the computer-simulated marketplace. An important difference between board games and business simulations lies in the complexity of outcomes. The board game traditionally has only one winner. A well-developed business simulation can have several winners with different players achieving success in different aspects of the simulated market that is the game's playing field. Hence, business simulations have become very useful and effective learning tools in classroom settings. A fundamental reason for this lies in the fact that simulation permits an otherwise complex system to be imitated at very low costs, both dollar and human.

Simulation will continue to prove useful in situations where timely decision making is important and when experimenting with multiple methods and variables are not fiscally possible or sound. Simulation allows for informative testing of viable solutions prior to implementation.

SEE ALSO: Models and Modeling

James H. Macomber

Revised by Monica C. Turner

FURTHER READING:

Laguna, M., and J. Marklund. Business Process Modeling, Simulation, and Design. Upper Saddle River, NJ: Pearson/Prentice Hall, 2005.

McLeish, D.L. Monte Carlo Simulation and Finance. Hoboken, NJ: Wiley, 2005.

Robert, C.P., and G. Casella. Monte Carlo Stastical Methods. 2nd ed. New York, NY: Springer, 2004.

Santos, M. "Making Monte Carlo Work." Wall Street & Technology 23, no. 3 (March 2005): 22–23.

Savage, S. "Rolling the Dice." Financial Planning 33, no. 3 (March 2003): 59–62.

Scheeres, J. "Making Simulation a Reality." Industrial Engineer 35, no. 2 (February 2003): 46–48.



Also read article about Simulation from Wikipedia

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Aug 31, 2011 @ 5:05 am
Hello
Please I want your help for provide me mathematical model of cpu and another of Hard DIsk ,i need understand thermal behavior

I am not working in Modeling to use Software ,The Idea that I want Ready Mathematical Model for Processor Whatever And Another for HardDisk Whatever ,I want to understand these Models and Thinking for strategy for cooling

Demonstration:as The Processor has exponential equations expressed of its thermal behavior example(Temperature Rise Equations and Temperature Fall Equations and so on)
I find Equations for Hard Disk Like as Processor???

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