19s-1

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Chapter 19 Supplement

Simulation

19s-2

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

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

19s-3

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

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

19s-4

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

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

19s-5

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Example S-1

19s-6

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Example S-1

19s-7

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Simulating Distributions

• Poisson– Mean of distribution is required

• Normal– Need to know the mean and standard

deviation

Simulatedvalue

Mean Randomnumber

Standarddeviation

+ X=

19s-8

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Uniform Distribution

a b0 x

F(x)

Simulatedvalue

a + (b - a)(Random number as a percentage)=

Figure 19S-1

19s-9

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

Negative Exponential Distribution

F(t)

0 T t

P t T RN( ) .

Figure 19S-2

19s-10

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

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

19s-11

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Simulation

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