Chapter 13
Operational Decision-Making Tools:
Simulation
Copyright 2011 John Wiley & Sons, Inc
Lecture Outline
• Monte Carlo Simulation• Computer Simulation with Excel• Areas of Simulation Application
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Copyright 2011 John Wiley & Sons, Inc
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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Copyright 2011 John Wiley & Sons, Inc
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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Copyright 2011 John Wiley & Sons, Inc
Probability Distribution of Demand
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LAPTOPS DEMANDED FREQUENCY OF PROBABILITY OFPER WEEK, x DEMAND DEMAND, P(x)
0 20 0.201 40 0.402 20 0.203 10 0.104 10 0.10
100 1.00
Copyright 2011 John Wiley & Sons, Inc
Roulette Wheel of Demand
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90
80
60
20
0
x = 2
x = 0x = 4
x = 3
x = 1
Copyright 2011 John Wiley & Sons, Inc
Generating Demand from Random Numbers
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DEMAND, RANGES OF RANDOM NUMBERS,x r
0 0-19
1 20-59 r = 39
2 60-79
3 80-89
4 90-99
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Random Number Table
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Copyright 2011 John Wiley & Sons, Inc
15 Weeks of Demand
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WEEK r DEMAND (x) REVENUE (S)
1 39 1 4,3002 73 2 8,6003 72 2 8,6004 75 2 8,6005 37 1 4,3006 02 0 07 87 3 12,9008 98 4 17,2009 10 0 0
10 47 1 4,30011 93 4 17,20012 21 1 4,30013 95 4 17,20014 97 4 17,20015 69 2 8,600
= 31 $133,300
Copyright 2011 John Wiley & Sons, Inc
Computing Expected Demand
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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
Estimated average demand = 31/15 = 2.07 laptops/week
Copyright 2011 John Wiley & Sons, Inc
Random Numbers in Excel
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Copyright 2011 John Wiley & Sons, Inc
Simulation in Excel
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Enter this formulain G6 and copy to
G7:G20
Enter “=4300*G6”in H6 can copy to
H7:H20
Generate randomnumber for cellsF6:F20 with the
formula “=RAND()”in F6 and copying
to F7:F20
=AVERAGE(G6:G20)
Copyright 2011 John Wiley & Sons, Inc
Simulation in Excel
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Spreadsheet “frozen”at row 16 to show
first 10 weeksand last 6
Copyright 2011 John Wiley & Sons, Inc
Decision Making with Simulation
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=G6*50 entered intocell L6 and copied
to L7:L105
This formula entered inG7 and copied to
G8:G105
=VLOOKUP(F6,LOOKUP,2)in H6 and copied
to H7:H105
Shortages computedby entering
=MIN(G6-H6,0)in I6 and copying
to I7:I105
Copyright 2011 John Wiley & Sons, Inc
Decision Making with Simulation
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New formula for twolaptops ordered
per week.
Copyright 2011 John Wiley & Sons, Inc
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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Copyright 2011 John Wiley & Sons, Inc
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
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Copyright 2011 John Wiley & Sons, Inc
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
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Copyright 2011 John Wiley & Sons, Inc Supplement 13-19
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.