supplement to chapter nineteen irwin/mcgraw-hill © the mcgraw-hill companies, inc., 1999 simulation...
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SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-1
Chapter 19 Supplement
Simulation
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-2
SimulationSimulation: 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
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-3
Simulation Process
• Identify the problem• Develop the simulation model• Test the model• Develop the experiments• Run the simulation and evaluate results• Repeat until results are satisfactory
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-4
Monte Carlo SimulationMonte 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
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-5
Simulating Distributions• Poisson
– Mean of distribution is required
• Normal– Need to know the mean and standard
deviation
Simulatedvalue
Mean Randomnumber
Standarddeviation
+ X=
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-6
Uniform Distribution
a b0 x
F(x)
Simulatedvalue
a + (b - a)(Random number as a percentage)=
Figure 19S-1
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-7
Negative Exponential Distribution
F(t)
0 T t
P t T RN( ) .
Figure 19S-2
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-8
Advantages of Simulation
• Solves problems that are difficult or impossible to solve mathematically
• Allows experimentation without risk to actual system
• Compresses time to show long-term effects
• Serves as training tool for decision makers
SUPPLEMENT TO CHAPTER NINETEEN
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1999
SIMULATION
19S-9
Limitations of Simulation
• Does not produce optimum solution
• Model development may be difficult
• Computer run time may be substantial
• Monte Carlo simulation only applicable to random systems