Simulation theory


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Simulation theory

  1. 1. Simulation Theory ABU BASHAR
  3. 3. What is Simulation? Simulation means imitation of reality. The purpose of simulation in the business world is to understand the behavior of a system. Before making many important decisions, we simulate the result to insure that we are doing the right thing.
  4. 4. When to use Simulation?? First, when experimentation is not possible. Note that if we can do a real experiment, the results would obviously be better than simulation.• Second condition for using simulation is when the analytical solution procedure is not known. If analytical formulas are known then we can find the actual expected value of the results quickly by using the formulas. In simulation we can hope to get the same results after simulating thousands of times.
  5. 5.  Simulation is basically a data generation technique. Sometimes it is time consuming to conduct real study to know about a situation or problem. An example is the simulation of the flow of customers into and out of a bank, to help determine service requirements. The use of simulation frees the programmer and user from having to observe a bank and keep track of exactly when each customer arrives and leaves. Thus, simulation is used when actual experimentation is not feasible.
  6. 6. Example We read and hear about Air force pilots being trained under simulated conditions. Since it would be impossible to train a person when an actual war is going on, all the conditions that would prevail during a war are reconstructed and enacted so that the trainee could develop the skills and instincts that would be required of him during combat conditions. Thus, war conditions are simulated to impart training.
  7. 7. Example Cont’d All automobile manufacturing companies have a test- track on which the vehicles would be initially driven. The test-track would ideally have all the bends, slopes, potholes etc., that can be found on the roadways on which the vehicles would be subsequently driven. The test-track is therefore, a simulated version of the actual conditions of the various roadways. Simulation, in general, means the creation of conditions that prevail in reality, in order to draw certain conclusions from the trials that are conducted in the artificial conditions. A vehicle manufacturer, by driving the vehicle on the test-track, is conducting a trial in artificial conditions in order to draw conclusions regarding the road-
  8. 8. Types of simulation Deterministic and probabilistic SimulationThe deterministic simulation is used when process is very complex or consists multiple stages with complicated (but known) procedural interactions between them.In probabilistic simulation, one or more of the independent variables is probabilistic i.e. it follows a certain probability distribution. Time dependent and Time independent simulationIn time independent simulation it is not important to known exactly when the event is likely to occur. E.g. we know demand of 3 units per day but don’t know when during the day the item was demanded.In time dependent it is important to know the precise time when the event is likely to occur. In a queeing situation the precise time of arrival of customer must be known (to know
  9. 9. Types of simulation Cont’d…. Visual Interactive SimulationIt uses computer graphic displays to present the consequences of change in the value of input variation in the model. The decisions are implemented interactively while the simulation is running. The decision maker keep track of development of model on a graphic interface and can alter the simulation as it progress. Business GamesIt involves several participants who need to play a role in a game that simulates a realistic competitive situation. Individual or teams compete to achieve their goals in competition with the other individual or team. Corporate and Financial SimulationIt is used in corporate planning, especially the financial aspects. The model integrate production, finance, marketing, and possibly other functions, into one
  10. 10. Application of SimulationTechnique Simulation is widely used for the following Simulation of Inventory Problem Simulation of Queuing Problem Simulation of investment problem Simulation of Maintenance Problem Simulation of PERT Problem
  11. 11. Advantages of Simulation Solves problems that are difficult or impossible to solve mathematically Allows experimentation without risk to actual system Compresses time to show long-term effects Serves as training tool for decision makers
  12. 12. Limitations of Simulation Does not produce optimum solution Model development may be difficult Computer run time may be substantial Monte Carlo simulation only applicable to random systems
  13. 13. Monte Carlo Method of Simulation The principle behind this method of simulation is representative of the given system under analysis by a system described by some known probability distribution and then drawing random samples for probability distribution by means of random number. In case it is not possible to describe a system in terms of standard probability distribution such as normal, Poisson, exponential, etc., an empirical probability distribution can be constructed.
  14. 14.  It can be usefully applied in cases where the system to be simulated has a large number of elements that exhibit chance (probability) in their behaviour. Simulation is normally undertaken only with the help of a very high-speed data processing machine such as computer. The user of simulation technique must always bear in mind that the actual frequency or probability would approximate the theoretical value of probability only when the number of trials are very large i.e. when the simulation is repeated a large no. of times. This can easily be achieved with the help of a computer by generating random numbers.
  15. 15. steps involved in Monte-Carlo simulation  Step I.  Obtain the frequency or probability of all the important variables from the historical sources.  Step II.  Convert the respective probabilities of the various variables into cumulative probabilities.  Step III.  Generate random numbers for each such variable.  Step IV.  Based on the cumulative probability distribution table obtained in Step II, obtain the interval (i.e.; the range) of the assigned random numbers.  Step V.  Simulate a series of experiments or trails.
  16. 16. Example New Delhi Bakery House keeps stock of a popular brand of cake. Previous experience indicates the daily demand as given below
  17. 17. Preparing Cumulative probabilityand assigning random numbers
  18. 18. Calculation of next demand
  19. 19.  Next demand is calculated on the basis of cumulative probability (e.g., random number 21 lies in the third item of cumulative probability, i.e., 0.36. Therefore, the next demand is 25. ) Similarly, we can calculate the next demand for others. Total demand = 320 Average demand = Total demand / no. of days The daily average demand for the cakes = 320 / 10 = 32 cakes.