Computer Simulation,Henry C. Co Technology and Operations Management, California Polytechnic and State University,Simulation Models (Henry C. Co),2,Simulation Models (Henry C. Co),3,Simulation Model,Simulation: a descriptive technique 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,Simulation Models (Henry C. Co),4,Analytic models: values of decision variables are the outputs. Simulation models: values of decision variables are the inputs. Investigate the impacts on certain parameters when these values change.,Why Simulation?,Simulation Models (Henry C. Co),6,Analytic models May be difficult or impossible to obtain. Typically predict only average or steady-state behavior. Simulation 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.,Simulation Process,Simulation Models (Henry C. Co),8,Identify the problem Develop the simulation model Test the model Develop the experiments Run the simulation and evaluate results Repeat until results are satisfactory,Simulation Models (Henry C. Co),9,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 measure(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.,Monte Carlo Simulation,Simulation Models (Henry C. Co),11,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,Major Components of Models,Simulation Models (Henry C. Co),13,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 performance measures.,An “Analog” Approach,Simulation Models (Henry C. Co),15,“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 Oclock position, it is pointing to the number 0.25.,Simulating a Discrete Distribution,Simulation Models (Henry C. Co),17,10% 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.,Simulation Models (Henry C. Co),18,Excel Functions Useful in Simulation,RAND(): a volatile Excel Function Function =RAND() generates a uniformly-distributed random number between 0 -1. VLOOKUP,Simulation Models (Henry C. Co),19,Use function =RAND() to generate a uniformly-distributed random number between 0 and 1.,Simulation Models (Henry C. Co),20,Simulation Models (Henry C. Co),21,F4=RAND() ; copy and paste F5:F13 G4=VLOOKUP(F4,$B$4:$C$10,2,1); copy and paste G5:G13,A Machine Breakdown Example,Simulation Models (Henry C. Co),23,F4=RAND() ; copy and paste F5:F13 G4=VLOOKUP(F4,$B$4:$C$10,2,1); copy and paste G5:G13,Simulating a Continuous Distribution,Simulation Models (Henry C. Co),25,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.,Simulation Models (Henry C. Co),26,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.,Simulation Models (Henry C. Co),27,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 Distn: Function NORMINV For example, NORMINV(RAND(),1000,100) returns a normally distributed random number with mean 1000 and standard deviation 100.,Simulation Models (Henry C. Co),28,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 alternatives (decisions) can be evaluated.,How Reliable is the Simulation?,Simulation Models (Henry C. Co),30,The more tria