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WOOD 492 MODELLING FOR DECISION SUPPORT

WOOD 492 MODELLING FOR DECISION SUPPORT. Lecture 24 Simulation. Why simulation?. A technique involving using a computer to imitate the events of a real world system Used when: No optimization method available Optimization algorithm takes too long System too big or complicated

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WOOD 492 MODELLING FOR DECISION SUPPORT

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  1. WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 24 Simulation

  2. Why simulation? • A technique involving using a computer to imitate the events of a real world system • Used when: • No optimization method available • Optimization algorithm takes too long • System too big or complicated • We have many stochastic (uncertain) factors Wood 492 - Saba Vahid

  3. simulation • An extremely popular technique in operations research • Typical steps in a simulation study of a model: • First, the real world system is modelled mathematically • The rough model is tested using simulation techniques under a variety of scenarios • A detailed and modified final model emerges as the result of the simulations • The final model is then tested and modified in the real world context Simulation is an experiment while optimization is a calculation Wood 492 - Saba Vahid

  4. Some applications of simulation • Forest growth and yield, harvest schedules • Sawing pattern simulations • Designing queuing system (e.g. design customer service call centers where number of calls is random) • Managing inventory systems (taking into account the stochastic demand changes and supply fluctuations) • Estimating the probability of a project completion by the deadline (possible delays) • Health care systems (simulating the use of hospital resources for different diseases, simulation ambulance service calls) Wood 492 - Saba Vahid

  5. Some useful definition • State of the system: a measure of the current condition of a system (e.g. number of people in the queue at a coffee shop, the number of outgoing patients in a hospital, the volume of lumber produced in a mill) • Events: actions that are happening in a system that change the state of the system, usually random and following a probability distribution (e.g. arrival of new customers, release of a patient, producing lumber) • System transition formula: how do the events change the state of the system • Simulation clock: an internal clock that keeps the time during the simulation run (e.g. number of days or months passed since the start of the run) Wood 492 - Saba Vahid

  6. Two types of simulation • Continuous simulation: a simulation where the state of the system changes continuously (e.g. location of a truck at any moment in a transportation simulation) • Discrete even simulation: when the state of the system changes at random points according to occurrence of some event (e.g. a customer arrives at the coffee shop) • Discrete event simulation is more common and can also be used to approximate the changes in a continuous system Wood 492 - Saba Vahid

  7. Distributions • Various probability distributions are used for different random events • Poisson : distribution of number of arrivals per unit of time • Exponential : distribution of time between successive events (arrivals, serving customers,…) • Uniform: for random number generation • Normal : for some physical phenomenon's, normally used to represent the distributions of the means of observations from other distributions • Binomial: coin flip • … Wood 492 - Saba Vahid

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