Prepared by Lee Revere and John Large

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna

15-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Prepared by Lee Revere and John LargePrepared by Lee Revere and John Large

Chapter 15Chapter 15

Simulation Simulation ModelingModeling



Learning ObjectivesLearning Objectives

Students will be able to:1. Tackle a wide variety of problems

by simulation.

2. Understand the seven steps of conducting a simulation.

3. Explain the advantages and disadvantages of simulation.

4. Develop random number intervals and use them to generate outcomes.

5. Understand the alternative simulation packages available commercially.



Chapter OutlineChapter Outline

15.1 Introduction

15.2 Advantages and Disadvantages of Simulation

15.3 Monte Carlo Simulation

15.4 Simulation and Inventory Analysis

15.5 Simulation of a Queuing Problem

15.6 Fixed Time Increment and Next Event Increment Simulation Models



Chapter OutlineChapter Outline

15.7 Simulation Model for Maintenance Policy

15.8 Two Other Types of Simulation

15.9 Verification and Validation

15.9 Role of Computers in Simulation



IntroductionIntroduction

imitate a real-world situation mathematically.

study its properties and operating characteristics.

draw conclusions and make action decisions.

Simulation is one of the most widely used quantitative analysis tools. It is used to:



Introduction: Seven Introduction: Seven Steps of Simulation Steps of Simulation

Define a Problem

Conduct the Simulation

Introduce Important Variables

Construct Simulation Model

Specify Values to be Variables

Examine the Results

Select Best Course of Action



Advantages of SimulationAdvantages of Simulation

Straightforward and flexible Computer software make simulation

models easy to develop Enables analysis of large, complex,

real-world situations Allows “what-if?” questions Does not interfere with real-world

system Enables study of interactions Enables time compression Enables the inclusion of real-world

complications



Disadvantages of Disadvantages of SimulationSimulation

Often requires long, expensive development process.

Does not generate optimal solutions; it is a trial-and-error approach.

Requires managers to generate all conditions and constraints of real-world problem.

Each model is unique and not typically transferable to other problems.



Simulation ModelsSimulation ModelsCategoriesCategories

Monte Carloconsumer demandinventory analysisqueuing problemsmaintenance policy

Operational Gaming Systems Simulation



Monte Carlo Monte Carlo SimulationSimulation

The Monte Carlo simulation is

applicable to business problems

that exhibit chance, or uncertainty.

For example:

1. Inventory demand2. Lead time for inventory3. Times between machine breakdowns4. Times between arrivals5. Service times6. Times to complete project activities7. Number of employees absent



Monte Carlo Monte Carlo Simulation Simulation (continued)(continued)

Five steps:

1. Set up probability distributions

2. Build cumulative probability distributions

3. Establish interval of random numbers for each variable

4. Generate random numbers

5. Simulate trials

The basis of the Monte Carlo simulation is experimentation on the probabilistic elements through random sampling. It is used with probabilistic variables.



Harry’s Auto Tires: Harry’s Auto Tires: Monte Carlo ExampleMonte Carlo Example

A popular radial tire accounts for a large portion of the sales at Harry’s Auto Tire. Harry wishes to determine a policy for managing his inventory of radial tires.

Let’s use Monte Carlo simulation to analyze Harry’s inventory…

0 10 0.051 20 0.102 40 0.203 60 0.304 40

0.205 30 0.15

Demand Frequency Probability for Tires

200 1.00

= 10/200



Demand Probability

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5

X

p(X)


(continued)(continued)Step 1: Set up the probability distribution for radial tire.

Using historical data, Harry determined that 5% of the time 0 tires were demanded, 10% of the time 1 tire was demand, etc…

P(1) = 10%




(continued)(continued)

Demand Cumulative Probability

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5

X

P(X)

Step 2: Build a cumulative probability distribution.

15% of the time the demand was 0 or 1 tire: P(0) = 5% + P(1) = 10%



Harry’s Auto Tires: Monte Harry’s Auto Tires: Monte Carlo Example (Carlo Example (continued)continued)

Dem

and

Fre

q ue n

c y

Pro

babi

lity

Cum

ulat

ive

Pro

babi

lity

Ran

dom

N

umbe

r In

terv

al

0 10 0.05 0.05 01 - 05

1 20 0.10 0.15 06 - 15

2 40 0.20 0.35 16 - 35

3 60 0.30 0.65 36 - 65

4 40 0.20 0.85 66 - 85

5 30 0.15 1.00 86 - 00

Step 3: Establish an interval of random numbers.

Mu

st b

e in

cor

rect

pro

por

tion

Note: 5% of the time 0 tires are demanded, so the random number interval contains 5% of the numbers between 1 and 100



5237826998963350889050274581667430

0663570294526933323048881402830534

5028683690622750183661214601148287

8802284936872195502418623278748201

5374057106491113626985691382279374

3035949978566044578223644974760911

1024033223599534345108486697039646

4703111067238962567454316237333382

9929277589786864623017127445115259

3760792185714839313512734131977894

6674909529721755153680028694591325

9185879021908929408569689899810634

3590929425573430900124009242722832

3273413873010964345584169849003023

0059099769989349519292168427649417

8455257134575044956416465464612301

5717367285314430260949133389133758

0760774976955116148559854042523973

Harry’s Auto Tires: Monte Harry’s Auto Tires: Monte Carlo ExampleCarlo Example (continued)(continued)

Step 4: Generate random numbers.



Harry’s Auto Tires: Monte Harry’s Auto Tires: Monte Carlo ExampleCarlo Example (continued)(continued)

Step 5: Simulate a series of trials.

Using random number table on previous slide, simulated demand for 10 days is:

Random number: 52 06 50 88 53 30 10 47 99 37Simulated demand: 3 1 3 5 3 2 1 3 5 3

Tires Interval ofDemanded Random Numbers

0 01 - 051 06 - 152 16 - 353 36 - 654 66 - 855 86 - 1001

2

3



Three Hills Power Three Hills Power Company: Monte Company: Monte

Carlo ExampleCarlo Example

Three Hills provides power to a large city. The company is concerned about generator failures because a breakdown costs about $75 per hour versus a $30 per hour salary for repairpersons who work 24 hours a day, seven days a week. Management wants to evaluate the service maintenance cost, simulated breakdown cost, and total cost.

Let’s use Monte Carlo simulation to analyze Three Hills system costs.



Three Hills PowerThree Hills PowerGenerator Breakdown Times: Generator Breakdown Times:

Monte Carlo Monte Carlo (continued)(continued)

½ 5 0.05 0.05 01 - 05

1 6 0.06 0.11 06 - 11

1 ½ 16 0.16 0.27 12 - 27

2 33 0.33 0.60 28 - 60

2 ½ 21 0.21 0.81 81 - 81

3 19 0.19 1.00 82 - 00

Tim

e B

e tw

een

Bre

a kdo

wn s

(H

r s)

Num

ber

of

Tim

es O

bser

ved

Pro

babi

lity

Cum

ulat

ive

Pro

babi

lity

Ran

dom

Num

ber

Inte

rval

Steps 1-3: Determine probability, cumulative probability, and random number interval - BREAKDOWNS.

Total 100 1.00



Three Hills PowerThree Hills PowerGenerator Repair Generator Repair

TimesTimes

1 28 0.28 0.28 01 - 28

2 52 0.52 0.80 29 - 80

3 20 0.20 1.00 81 - 00

Rep

air

Tim

e R

equi

red

(Hou

rs)

Num

ber

of

Tim

es O

bser

ved

Pro

babi

lity

Cum

ulat

ive

Pro

babi

lity

Ran

dom

N

umbe

r In

terv

al

Steps 1-3: Determine probability, cumulative probability, and random number interval - REPAIRS.





1 57 2 2:00 2:00 7 1 3:00 1

2 17 1.5 3:30 3:30 60 2 5:30 2

3 36 2 5:30 5:30 77 2 7:30 2

4 72 2.5 8:00 8:00 49 2 10:00 2

5 85 3 11:00 11:00 76 2 13:00 2

: : : : : : : : :

14 89 3 4:00 6:00 42 2 8:00 4

15 13 1.5 5:30 8:00 52 2 10:00 4.5

Sim

ula

tion

Tri

al

Ran

dom

N

um

ber

Tim

e R

epai

rC

an B

egin

Ran

dom

N

um

ber

Tim

e R

epai

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nd

s

Rep

air

Tim

e

No.

of

hrs

.M

ach

ine

is d

own

Tim

e b

/tB

reak

dow

ns

Tim

e of

Bre

akd

own

Steps 4 & 5: Generate random numbers and simulate.





Cost Analysis:

Service maintenance: = 34 hrs of worker service X $30 per hr

= $1,020

Simulate machine breakdown costs: = 44 total hrs of breakdown X $75 lost per hr of downtime = $3,300

Total simulated maintenance cost of the current system: = service cost + breakdown costs

= $1,020 + $3,300 = $4,320



Operational Gaming Operational Gaming Simulation ModelSimulation Model

Operational gaming refers to

simulation involving competing

players.

Examples:

Military games

Business games



Systems Simulation Systems Simulation ModelModel

Systems simulation is similar to

business gaming because it allows

users to test various managerial

policies and decision. It models the

dynamics of large systems.

Examples: Corporate operating system Urban government Economic systems



Econometric Econometric Simulation ModelsSimulation Models

Inco

me

Tax

Lev

els

C

orpo

rate

Tax

Rat

es

I

nter

est R

ates

Gov

ernm

ent S

pend

ing

F

orei

gn T

rade

Pol

icy

Economic

Model

GN

P

In

flat

ion

Rat

es

Une

mpl

oym

ent R

ates

Mon

etar

y S

uppl

ies

Pop

ulat

ion

Gro

wth

Rat

es



Verification and Verification and Validation Validation

Verification of simulation models involves determining that the computer model is internally consistent and follows the logic of the conceptual model.

Validation is the process of comparing a simulation model to a real system to assure accuracy.



The Role of Computers The Role of Computers in Simulationin Simulation

General-purpose languages Visual Basic, C++, Java

Special-purpose simulation languages GPSS/H, SLAM II, SIMSCRIPT II.5

1. require less programming2. more efficient and easier to check for errors3. have random number generators built in

Pre-written simulation programs Extend, AutoMod, ALPHA/Sim, SIMUL8,STELLA, Arena, AweSim!, SLX, etc.



Harry’s Auto Tires: Harry’s Auto Tires: Excel DemonstrationExcel Demonstration

Create lookup table using cumulative probability

Generate a random number and look it up in

the table



Harry’s Auto Tires: Harry’s Auto Tires: Excel DemonstrationExcel Demonstration

ResultsResults

Documents

Prepared by Lee Revere and John Large