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 –We have many stochastic (uncertain) factors Nov 2, 2012Wood Saba Vahid2

simulation An extremely popular technique in operations research Typical steps in a simulation study of a model: 1.First, the real world system is modelled mathematically 2.The rough model is tested using simulation techniques under a variety of scenarios 3.A detailed and modified final model emerges as the result of the simulations 4.The final model is then tested and modified in the real world context Simulation is an experiment while optimization is a calculation Nov 2, 2012Wood Saba Vahid3

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) Nov 2, 2012Wood Saba Vahid4

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) Nov 2, 2012Wood Saba Vahid5

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 Nov 2, 2012Wood Saba Vahid6

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 … Nov 2, 2012Wood Saba Vahid7