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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 Large Simulation Modeling
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Page 1: Simulation

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 Large

Simulation Modeling

Page 2: Simulation

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

15-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Introduction

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:

Page 3: Simulation

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

15-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Introduction: Seven 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

Page 4: Simulation

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

15-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Advantages 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

Page 5: Simulation

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

15-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Disadvantages of Simulation

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.

Page 6: Simulation

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

15-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Simulation ModelsCategories

Monte Carloconsumer demandinventory analysisqueuing problemsmaintenance policy

Operational Gaming Systems Simulation

Page 7: Simulation

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

15-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Monte Carlo Simulation

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

Page 8: Simulation

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

15-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Monte Carlo Simulation (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.

Page 9: Simulation

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

15-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Harry’s Auto Tires: Monte 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

Page 10: Simulation

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

15-10 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Demand Probability

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5

X

p(X)

Harry’s Auto Tires: Monte Carlo Example

(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%

Page 11: Simulation

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

15-11 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Harry’s Auto Tires: Monte Carlo Example

(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%

Page 12: Simulation

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

15-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Harry’s Auto Tires: Monte Carlo Example (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

Page 13: Simulation

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

15-13 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

5237826998963350889050274581667430

0663570294526933323048881402830534

5028683690622750183661214601148287

8802284936872195502418623278748201

5374057106491113626985691382279374

3035949978566044578223644974760911

1024033223599534345108486697039646

4703111067238962567454316237333382

9929277589786864623017127445115259

3760792185714839313512734131977894

6674909529721755153680028694591325

9185879021908929408569689899810634

3590929425573430900124009242722832

3273413873010964345584169849003023

0059099769989349519292168427649417

8455257134575044956416465464612301

5717367285314430260949133389133758

0760774976955116148559854042523973

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

Step 4: Generate random numbers.

Page 14: Simulation

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

15-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Harry’s Auto Tires: Monte Carlo Example (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

Page 15: Simulation

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

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

Three Hills Power Company: Monte

Carlo 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.

Page 16: Simulation

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

15-16 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Three Hills PowerGenerator Breakdown Times:

Monte Carlo (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 T

imes

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

Page 17: Simulation

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

15-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Three Hills PowerGenerator Repair

Times

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 T

imes

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.

Page 18: Simulation

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

15-18 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Three Hills PowerGenerator Breakdown Times:

Monte Carlo (continued)

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

rE

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.

Page 19: Simulation

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

15-19 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Three Hills PowerGenerator Breakdown Times:

Monte Carlo (continued)

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

Page 20: Simulation

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

15-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Operational Gaming Simulation Model

Operational gaming refers to

simulation involving competing

players.

Examples:

Military games

Business games

Page 21: Simulation

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

15-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Systems Simulation Model

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

Page 22: Simulation

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

15-22 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458

Verification and 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.