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
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
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:
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
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
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.
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
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
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.
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
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%
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%
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
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.
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
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.
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
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.
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.
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
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
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
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.