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# Simulation & Modelling

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### Simulation & Modelling

1. 1. Presentation by, Mohammed Riza, Saneem Nazim,
2. 2. What is Simulation  A simulation model is a mathematical model that calculates the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, etc.  A simulation model will include:  Model inputs that are uncertain numbers/ uncertain variables  Intermediate calculations as required  Model outputs that depend on the inputs -- These are uncertain functions
3. 3.  Simulation is imitation of some real thing, or a process.  The act of simulating something generally involves representation of certain  key characteristics or  behaviors of a selected physical or abstract system.  Simulation involves the use of models to represent real life situation.
4. 4. Definition Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose of understanding the behavior for the operation of the system. -Shannon
5. 5. Simulation techniques  Simulation techniques can be used to assist management decision-making, where analytical methods are either not available or inappropriate.  Typical business problems where simulation could be used to aid management decision-making are  Inventory control.  Queuing problems.  Production planning.
6. 6. Advantages of Simulation  It is useful for sensitivity analysis of complex systems.  It is suitable to analyze large and complex real life problems that cannot be solved by the usual quantitative methods.  It is the remaining tool when all other techniques become intractable or fail.  It can be used as a pre-service test to try out new policies and decision rules for operating a system.
7. 7. Disadvantages of Simulation  Sometimes simulation models are expensive and take a long time to develop.  Each application of simulation is ad hoc to a great extent.  The simulation model does not produce answers by itself.  It is the trial and error approach that produces different solutions in repeated runs .It does not generate optimal solutions to the problems.
8. 8. Types of Simulation  Time dependent and time independent simulation : In time dependent simulation know the precise time when the event is likely to occur, but incase of time independent simulation it is not important to know the time when the event is occur.  Corporate and financial simulations : The corporate and financial simulation is used in corporate planning, especially the financial aspects. The models integrate production, finance, marketing, and other functions.  Visual interactive simulation : It uses computer graphic displays to present the consequences of change in the value of input variations in the model.
9. 9. Steps of Simulation Process  Identify the problem : The simulation process is used to solve a problem only when the assumptions required for analytical models are not satisfied.  Identify the decision variables and decide the performance: The inventory control situation, the demand, lead time and safety stock are identified as decision variables and measure the performance.  Construct a simulation model : For developing a simulation model, an intimate understanding of the relationships among the elements of the system being required.
10. 10.  Testing and validating the model : Any simulation model must represent the system under study. This requires comparing a model with actual system validation process.  Designing of the experiment : It refers to controlling the conditions of the study, such as the variables to include. In this situations where observations are taken but the conditions of the study are not controlled.  Run the simulation model : The computer to get the results in the form of operating characteristics.  Evaluating the result : The simulation process is complete, then select the best course of action, otherwise make desired changes in model decisions variables.
11. 11. Simulation and Queuing problems.  A major application of simulation has been in the analysis of waiting line, or queuing systems.  Since the time spent by people and things waiting in line is a valuable resource, the reduction of waiting time is an important aspect of operations management.  Waiting time has also become more important because of the increased emphasis on quality. Customers equate quality service with quick service and providing quick service has become an important aspect of quality service
12. 12. Queuing problems.  For queuing systems, it is usually not possible to develop analytical formulas, and simulation is often the only means of analysis.  Simulation can hence be used to investigate problems that are common in any situation involving customers, items or orders arriving at a given point, and being processed in a specified order.  For ex:  Customers arrive in a bank and form a single queue, which feeds a number of service desks. The arrival rate of the customers will determine the number of service desks to have open at any specific point in time
13. 13. Components of queuing systems  A queue system can be divided into four components  Arrivals: Concerned with how items (people, cars etc) arrive in the system.  Queue or waiting line: Concerned with what happens between the arrival of an item requiring service and the time when service is carried out.  Service: Concerned with the time taken to serve a customer.  Outlet or departure: The exit from the system.  A queuing problem involves striking a balance between the cost of making reductions in service time and the benefits gained from such a reduction
14. 14. Structures of queuing system  There are a number of structures of queuing systems in practice.  We will study only one i.e. single queue – single service point.  Single queue – single service point  Queue discipline is first come – first served.  Arrivals* are random and for simulation this randomness must be taken into account.  Service times** are random and for simulation this randomness must be taken into account *Inter-arrival time: Is the time between the arrival of successive customers in a queuing situation. **Service time: Is the length of time taken to serve customers
15. 15. Monte Carlo simulation The principle behind the Monte Carlo technique is representative of the given system under analysis by a system  Setting up a probability distribution to be analysed.  Building a cumulative probability distribution for a random variable.  Generate random numbers . Assign an appropriate set of random numbers to represents value or range(interval) of values each random variable.
16. 16. Waiting time should be as less as possible!!