Chapter 13
Operational Decision-Making Tools:
Simulation
Lecture Outline
• Monte Carlo Simulation
• Computer Simulation with Excel
• Areas of Simulation Application
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-2
Simulation
• Mathematical and computer modeling technique for
replicating real-world problem situations
• Modeling approach primarily used to analyze
probabilistic problems
• It does not normally provide a solution; instead it provides
information that is used to make a decision
• Physical simulation
• Space flights, wind tunnels, treadmills for tires
• Mathematical-computerized simulation
• Computer-based replicated models
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Supplement 13-3
Monte Carlo Simulation
• Select numbers randomly from a probability
distribution
• Use these values to observe how a model
performs over time
• Random numbers each have an equal likelihood
of being selected at random
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Supplement 13-4
Probability Distribution of Demand
LAPTOPS DEMANDED
PER WEEK, x
0
1
2
3
4
Copyright 2011 John Wiley & Sons, Inc
FREQUENCY OF
DEMAND
PROBABILITY OF
DEMAND, P(x)
20
40
20
10
10
0.20
0.40
0.20
0.10
0.10
100
1.00
Supplement 13-5
Roulette Wheel of Demand
0
90
x=4
80
x=0
20
x=3
x=2
x=1
60
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Supplement 13-6
Generating Demand from
Random Numbers
DEMAND,
x
RANGES OF RANDOM NUMBERS,
r
0
1
2
3
4
0-19
20-59
60-79
80-89
90-99
Copyright 2011 John Wiley & Sons, Inc
r = 39
Supplement 13-7
Random Number Table
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-8
15 Weeks of Demand
WEEK
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Copyright 2011 John Wiley & Sons, Inc
r
39
73
72
75
37
02
87
98
10
47
93
21
95
97
69
DEMAND (x)
REVENUE (S)
1
2
2
2
1
0
3
4
0
1
4
1
4
4
2
4,300
8,600
8,600
8,600
4,300
0
12,900
17,200
0
4,300
17,200
4,300
17,200
17,200
8,600
 = 31
$133,300
Supplement 13-9
Computing Expected Demand
Estimated average demand = 31/15 = 2.07 laptops/week
E(x)
= (0.20)(0) + (0.40)(1) + (0.20)(2)
+ (0.10)(3) + (0.10)(4)
= 1.5 laptops per week
•Difference between 1.5 and 2.07 is due to small number
of periods analyzed (only 15 weeks)
•Steady-state result
•average result which stays constant after enough trials
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-10
Random Numbers in Excel
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-11
Simulation in Excel
Enter this formula
in G6 and copy to
G7:G20
Enter “=4300*G6”
in H6 can copy to
H7:H20
=AVERAGE(G6:G20)
Copyright 2011 John Wiley & Sons, Inc
Generate random
number for cells
F6:F20 with the
formula “=RAND()”
in F6 and copying
to F7:F20
Supplement 13-12
Simulation in Excel
Spreadsheet “frozen”
at row 16 to show
first 10 weeks
and last 6
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-13
Decision Making with Simulation
This formula entered in
G7 and copied to
G8:G105
=G6*50 entered into
cell L6 and copied
to L7:L105
=VLOOKUP
(F6,LOOKUP,2)
in H6 and copied
to H7:H105
Shortages computed
by entering
=MIN(G6-H6,0)
in I6 and copying
to I7:I105
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-14
Decision Making with Simulation
New formula for two
laptops ordered
per week.
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-15
Areas of Simulation Application
• Waiting Lines/Service
• Complex systems for which it is difficult to develop
analytical formulas
• Determine how many registers and servers are needed
to meet customer demand
• Inventory Management
• Traditional models make the assumption that customer
demand is certain
• Simulation is widely used to analyze JIT without having
to implement it physically
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Supplement 13-16
Areas of Simulation Application
• Production and Manufacturing Systems
• Production scheduling, production sequencing,
assembly line balancing, plant layout, and plant location
analysis
• Machine breakdowns typically occur according to some
probability distributions
• Capital Investment and Budgeting
• Capital budgeting problems require estimates of cash
flows, often resulting from many random variables
• Simulation has been used to generate values of cash
flows, market size, selling price, growth rate, and
market share
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-17
Areas of Simulation Application
• Logistics
• Random variables include, distance, transport modes,
shipping rates, and schedules
• Allows analysis of different distribution channels
• Service Operations
• Police departments, fire departments, post offices,
hospitals, court systems, airports
• Complex operations where only simulation can be
employed
• Environmental and Resource Analysis
• Impact of manufacturing plants, waste-disposal
facilities, nuclear power plants, waste and population
conditions, feasibility of alternative energy sources
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-18
Copyright 2011 John Wiley & Sons, Inc.
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information herein.
Copyright 2011 John Wiley & Sons, Inc
Supplement 13-19