1. McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Simulation

2. 18S-2 Learning Objectives  Explain what is meant by the term simulation  List some of the reasons for simulation’s popularity as a tool for decision making  Explain how and why random numbers are used are used in simulation  Outline the advantages and limitations of simulation  Describe the alternatives that a manager would reject before choosing simulation as a decision making tool  Solve typical problems that require simulation

3. 18S-3 Simulation 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

4. 18S-4 Simulation Process 1.Identify the problem 2.Develop the simulation model 3.Test the model 4.Develop the experiments 5.Run the simulation and evaluate results 6.Repeat 4 and 5 until results are satisfactory

5. 18S-5 Monte Carlo Simulation 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

6. 18S-6 Example S-1

7. 18S-7 Example S-1

8. 18S-8 Simulating Distributions  Poisson  Mean of distribution is required  Normal  Need to know the mean and standard deviation Simulated value Mean Random number Standard deviation + X=

9. 18S-9 Uniform Distribution ab0x F(x) Simulated value a + (b - a)(Random number as a percentage) = Figure 18S.1

10. 18S-10 Negative Exponential Distribution Figure 18S.2 F(t) 0Tt

11. 18S-11 Computer Simulation  Simulation languages  SIMSCRIPT II.5  GPSS/H  GPSS/PC  RESQ

12. 18S-12 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

13. 18S-13 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