Bartın İİBF Dergi Sayı 12

 

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Bartın İİBF Dergi Sayı 12

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Comparison of the Monte Carlo Method and the Method of System Simulation Asisst. Prof. Dr. Süleyman ŞAHİN Abant İzzet Baysal University Faculty of Economics And Administrative Sciences suleymansahin@ibu.edu.tr Abstract: The purpose of this study is to show some differences between the Monte Carlo method and the method of System Simulation. For this purpose, firstly, some general information has been given about simulation. Then, described briefly the Monte Carlo method and the method of System Simulation. Moreover, an application for each method has been given. Thirdly, made comparison of the two methods. Finally, talked about which method is useful and superior and in which cases these two methods can be used. Key words: Simulation, Monte Carlo method, System Simulation. Monte Carlo Metodu ve Sistem Similasyonu Methodunun Karşılaştırılması Özet: Bu çalışmanın amacı, Monte Carlo yöntemi ve Sistem Simülasyonu yöntemi arasındaki bazı farklılıkları göstermektir. İlk olarak, simülasyon hakkında bazı genel bilgiler verilmiştir. Ardından, kısaca Monte Carlo yöntemi ve Sistem Simülasyonu yöntemi hakkında temel bilgiler verilmiştir. Daha sonra, her bir yöntem için birer uygulama örneği verilmiştir. Üçüncü olarak da, iki yöntemin karşılaştırılması yapılmıştır. Son olarak, bu iki yöntemin uygulamada kullanılması durumunda hangi yöntemin daha yararlı ve üstün özelliklere sahip olduğu incelenmiştir. Anahtar kelimeler: Simülasyon, Monte Carlo yöntemi, Sistem Simülasyonu. Introduction There are many problems in the social sciences, physical sciences, engineering, and business fields that can be stated in mathematical terms, but for which there are no analytical methods of solution. It is, as a rule, difficult to analyze complex dynamic behavior by means of mathematics, as an alternative to mathematical analysis we can turn to numerical methods to solve these problems, proceed as follows, assume some initial state or condition for the 1

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Bartın Üniversitesi İ.İ.B.F. Dergisi Yıl: 2015 Cilt: 6 Sayı: 12 system being studied, and use whatever laws or rules of change we have in order to evaluate the states or positions some stipulated period. Increasingly, simulation is being used to study such problems. Because this type of calculation proceeds in true time-sequence, we can regard it as “simulating” or copying the behavior of the system under study. This becomes more obvious if the calculation is programmed for a computer (John Smith, 1968: 3). 1. Literature Review 1.1. What Is Simulation? Simulation generally can be described as an approach to the numerical solution of interactive problems which are based upon a mathematical model. On the other hand, scientifically, it can be described as creating artificial random process repeating correct physical process by means of using random numbers or computer (Elbistanlıoğlu, 1988: 31). Simulation shall used to mean the process of conducting experiments on a model of system in lieu of either direct analytical solution of some problem associated with the system (Mize et al., 1968: 1). Many problems must be viewed in a larger context, leading to a degree of complexity beyond the ability of analytical solutions to handle. The limitations of analytical solutions were one of the factors leading to the development of simulation as a means of dealing with complex problem situations. Another motivation for the development of simulation was the desire to be able to examine the details of the dynamics of a complex operating system (Turner et al., 1993: 396). 2.1. Where Is Simulation Used? The process of simulation involves the design and study of a model of some physical, economic, or sociological system. For example, customer service, job shop scheduling, transport problems, mechanical handling problems, maintenance problems, production buffer stocks, etc. Simulation, which can be practiced in all areas, previously was used by Neumann and Ulam as an operational research method in solving a complex problem about the nuclear activities (Elbistanlıoğlu, 1988: 31). Computer simulation methods have developed since the early 1960s and may well be the most commonly used of all the analytical tools of management science. For example, manufacturing, health care, business process reengineering, transport systems, defense, etc (Pidd, 2004: 1-11). 2

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Süleyman ŞAHİN Comparison of the Monte Carlo Method and the Method of System Simulation System simulation has become the most widely used tool among industrial and system engineers (Turner et al., 1993: 396). 1.3. What Advantages Does Simulation Provide? For the purposes of the present chapter, simulation may be taken to mean constructing a mathematical model of a physical system. The advantages of having such a mathematical model will now be made clear. Suppose it is proposed to change an existing production line by installing new machinery or employing extra staff at various stages. Such changes will involve considerable expenditure and it would be very useful to estimate in advance the effect these changes will have on the production line. Simulation enables us to do this (Thomas, 1979: 1). As the cost of computation continues to fall, it is becoming economical for more and more system to be studied by simulation rather than by direct mathematical analysis (Forrest, 1970: 1). To be sure, simulation methods are used more broadly than in “deriving a solution” from a mathematical model of a process. The expressed purpose of certain simulation studies is to provide a means of observing the behavior of the components of a system under varying conditions . No “solution”, in the mathematical sense, is sought; rather, the objective is to gain an understanding of the relationships among components of the system (Mize et al., 1968: 2-3). Simulation has an expanding role in many aspects of industrial production, including research, design, operations, maintenance, and regulatory compliance (Liptak, 2006: 235). 2. The Simulation Methods 2.1. Monte Carlo Method The class of variance – reducing techniques that known as “Monte Carlo” techniques, which rely not on statistical analysis of the input and output variables of a simulation but on reorganization of the simulation itself. Numerous techniques have been proposed for increasing the sampling efficiency of the Monte Carlo simulations above that obtainable with simple random sampling (Thomas, 1969: 252-263). The Monte Carlo method is a way of performing numerical integrations of functions that are impossible with direct analytical approaches. The Monte Carlo method uses these approaches with random numbers (Pidd, 2004: 45-48). 3

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Bartın Üniversitesi İ.İ.B.F. Dergisi Yıl: 2015 Cilt: 6 Sayı: 12 Monte Carlo methods are sampling methods; therefore, the estimates that result from Monte Carlo procedures have associated sampling errors. The fact that the estimate is not equal to its expected value (assuming that the estimator is unbiased) is not an error or a mistake; its just a result of the variance of the random (or pseudorandom) data. Monte Carlo methods are experiments using random data. The variability of the random data results in experimental error, just as in other scientific experiments in which randomness values of the estimator of interest (Gentle, 2003: 235). 2.1.1 The Principles 2.1.1.1 Random Sampling The “random numbers” used in simulation have been “random” in e very respect which in practice means passing all the tests usually applied to a random number generator. A random number variable is a numerically valued variable defined on a sample space. For each point of the sample space the random variable would be assigned a value. The random variable may be positive or negative, it may have the same value at different points of the sample space, it made discrete or continuous, and so forth. Theoretically, the set of values that such a random variable would have consists of zero and the natural numbers (Mize et al., 1968: 22). Simulations that use sequences of random numbers and which are independent time, such as use of random numbers to evaluate definite integrals, are called Monte Carlo simulations (Stewart, 2009: 680). 2.1.2 Kinds Of problem Dating from the 1940s, Monte Carlo methods were used to evaluate definite multiple in mathematical physics. There is now a resurgence of interest in such methods, particularly in finance and statistical inference (Daspunar, 2007: 1). Some have been applied in particle – physics applications with outstanding success. Some have been applied to simple examples of operational problems. Monte Carlo method is usually used for problems whose distributions are not known. For example, to determine the optimal number of repair. 4

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