2. Lecture Outline
• Monte Carlo Simulation
• Computer Simulation with Excel
• Areas of Simulation Application
Copyright 2011 John Wiley & Sons, Inc Supplement 13-2
3. 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
Copyright 2011 John Wiley & Sons, Inc Supplement 13-3
4. 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
Copyright 2011 John Wiley & Sons, Inc Supplement 13-4
5. Probability Distribution of Demand
LAPTOPS DEMANDED FREQUENCY OF PROBABILITY OF
PER WEEK, x DEMAND DEMAND, P(x)
0 20 0.20
1 40 0.40
2 20 0.20
3 10 0.10
4 10 0.10
100 1.00
Copyright 2011 John Wiley & Sons, Inc Supplement 13-5
7. Generating Demand from
Random Numbers
DEMAND, RANGES OF RANDOM NUMBERS,
x r
0 0-19
1 20-59 r = 39
2 60-79
3 80-89
4 90-99
Copyright 2011 John Wiley & Sons, Inc Supplement 13-7
10. 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
11. Random Numbers in Excel
Copyright 2011 John Wiley & Sons, Inc Supplement 13-11
12. Simulation in Excel
Enter this formula
in G6 and copy to
G7:G20
Enter “=4300*G6”
in H6 can copy to
H7:H20
Generate random
number for cells
=AVERAGE(G6:G20) F6:F20 with the
formula “=RAND()”
in F6 and copying
to F7:F20
Copyright 2011 John Wiley & Sons, Inc Supplement 13-12
13. 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
14. 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
15. Decision Making with Simulation
New formula for two
laptops ordered
per week.
Copyright 2011 John Wiley & Sons, Inc Supplement 13-15
16. 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
Copyright 2011 John Wiley & Sons, Inc Supplement 13-16
17. 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
18. 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
19. Copyright 2011 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of this
work beyond that permitted in section 117 of the 1976
United States Copyright Act without express permission
of the copyright owner is unlawful. Request for further
information should be addressed to the Permission
Department, John Wiley & Sons, Inc. The purchaser
may make back-up copies for his/her own use only and
not for distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages caused
by the use of these programs or from the use of the
information herein.
Copyright 2011 John Wiley & Sons, Inc Supplement 13-19
