1. SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-1 Chapter 19 Supplement Simulation

2. SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-2 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

3. 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

4. SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-4 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

5. 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 Simulated value Mean Random number Standard deviation + X=

6. SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-6 Uniform Distribution ab0x F(x) Simulated value a + (b - a)(Random number as a percentage) = Figure 19S-1

7. SUPPLEMENT TO CHAPTER NINETEEN Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999 SIMULATION 19S-7 Negative Exponential Distribution F(t) 0Tt Figure 19S-2

8. 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

9. 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