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Operational Decision-Making Tools:Simulation
Lecture Outline
Monte Carlo Simulation Computer Simulation with Excel Areas of Simulation Application
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
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
Supplement 13-4
Probability Distribution of Demand
Supplement 13-5
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
Roulette Wheel of Demand
Copyright 2011 John Wiley & Sons, Inc Supplement 13-6
90
80
60
20
0
x = 2
x = 0x = 4
x = 3
x = 1
Generating Demand from Random Numbers
Supplement 13-7
DEMAND, RANGES OF RANDOM NUMBERS,x r
0 0-19
1 20-59 r = 39
2 60-79
3 80-89
4 90-99
Random Number Table
Supplement 13-8
15 Weeks of Demand
Supplement 13-9
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
Computing Expected Demand
Supplement 13-10
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
Random Numbers in Excel
Supplement 13-11
Simulation in Excel
Supplement 13-12
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)
Simulation in Excel
Supplement 13-13
Spreadsheet “frozen”at row 16 to show
first 10 weeksand last 6
Decision Making with Simulation
Supplement 13-14
=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
Decision Making with Simulation
Supplement 13-15
New formula for twolaptops ordered
per week.
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
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
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
Supplement 13-18