SimulationModel-CalPolyPomona仿真模型-加州波莫纳

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1、,,Click to edit Master title style,,Click to edit Master text styles,,Second level,,Third level,,Fourth level,,Fifth level,,*,Computer Simulation,,Henry C. Co,,Technology and Operations Management,,,California Polytechnic and State University,,,1,2,Simulation Model,,Simulation: a descriptive techniq

2、ue that enables a decision maker to evaluate the behavior of a model under various conditions.,,Simulation models complex situations,,Models are simple to use and understand,,Models can play “what if〞 experiments,,Extensive software packages available,3,Analytic models: values of decision variables

3、are the outputs.,,Simulation models: values of decision variables are the inputs. Investigate the impacts on certain parameters when these values change.,4,Why Simulation?,,,5,Analytic models,,May be difficult or impossible to obtain.,,Typically predict only average or steady-state behavior.,,Simula

4、tion models,,Wide availability of software and more powerful PCs make implementation much easier than before.,,More realistic random factors can be incorporated.,,Easier to understand.,6,Simulation Process,,,7,Identify the problem,,Develop the simulation model,,Test the model,,Develop the experiment

5、s,,Run the simulation and evaluate results,,Repeat until results are satisfactory,8,Implementation,,Identify the boundaries of the system of interest.,,Identify the random variables, decision variables, parameters, and the performance measure(s).,,Develop an objective function for the performance me

6、asure(s) in terms of random variables, decision variables, and parameters.,,Use computer to generate the simulated values of these random variables.,,Compute the values of the objective function using these simulated values of random variables and values of decision variables.,,Statistical analysis.

7、,9,Monte Carlo Simulation,,,10,Monte Carlo method: Probabilistic simulation technique used when a process has a random component,,Identify a probability distribution,,Setup intervals of random numbers to match probability distribution,,Obtain the random numbers,,Interpret the results,11,Major Comp

8、onents of Models,,,12,Random input factors: sales, demand, stock prices, interest rates, the length of time required to perform a task.,,Random performance measures:,,Business profit within a time interval.,,Average waiting time of a customer in a queuing system.,,Random input factors,,random perfo

9、rmance measures.,13,An “Analog〞 Approach,,,14,“Game Spinner〞 for uniform random variable on the interval 0 to 1.,,,,Every point on the circumference corresponds to a number between 0 and 1.,,For example, when the pointer is in the 3 O’clock position, it is pointing to the number 0.25.,15,Simulating

10、a Discrete Distribution,,,16,10% of the interval (0.0 to 0.09999) is mapped (assigned) to a demand d= 8.,,20% of the interval (0.1 to 0.29999) is mapped to d =9.,,30% of the interval (0.3 to 0.59999) is mapped to d =10.,,etc., etc.,17,Excel Functions Useful in Simulation,,RAND(): a,volatile,Excel Fu

11、nction,,Function =RAND() generates a uniformly-distributed random number between 0 -1.,,VLOOKUP,18,Use function =RAND() to generate a uniformly-distributed random number between 0 and 1.,19,20,F4=RAND() ; copy and paste F5:F13,,G4=VLOOKUP(F4,$B$4:$C$10,2,1); copy and paste G5:G13,21,A Machine Breakd

12、own Example,,,22,F4=RAND() ; copy and paste F5:F13,,G4=VLOOKUP(F4,$B$4:$C$10,2,1); copy and paste G5:G13,23,Simulating a Continuous Distribution,,,24,The,inverse transformation method,,,To transform this random number into a sample value of the random variable.,F(w) is the CDF F(x)=Prob. {W,,x}.,25

13、,Inverse Transformation Method,,Define F(x)=Prob. {W,,x} = the probability that random variable W is less than or equal to a specific value w.,,Denote the 0-1 random number by u and let u = F(x).,,Use =RAND() to generate a value for u, substitute it into x= F-1(u) which in turn gives a value of x.,

14、26,EXCEL Implementation,,Exponential Distribution,,u = RAND(),,For example, if arrival rate,,= 0.05, and RAND()=.75, the observation from the exponential distribution is (-1/0.05)ln(1-.75) = 23.73.,,Normal Dist’n: Function NORMINV,,For example, NORMINV(RAND(),1000,100) returns a normally distribute

15、d random number with mean 1000 and standard deviation 100.,27,Using an EXCEL Simulation Model,,Information obtained from a Simulation model:,,Summary statistics about the performance measures,,Downside Risk and Upside Risk,,Distribution of outcomes,,Based on the simulation results (Output), several

16、alternatives (decisions) can be evaluated.,28,How Reliable is the Simulation?,,,29,The more trials we run, the higher the confidence we have in our results (just like any statistical analysis with real data sample).,,The confidence intervals about the parameters (or any other estimated parameters) c

17、an be computed.,,Given sample size and significant level,,confidence intervals can be computed, or given the half width of the confidence interval and significance level,,compute the minimum number of replications we have to run.,30,Advantages,,31,Solves problems that are difficult or impossible t

18、o solve mathematically,,Allows experimentation without risk to actual system,,Compresses time to show long-term effects,,Serves as training tool for decision makers,32,Limitations,,33,Does not produce optimum solution,,Model development may be difficult,,Computer run time may be substantial,,Monte Carlo simulation only applicable to random systems,34,