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

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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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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

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

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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

Random Number Table

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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

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

Random Numbers in Excel

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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)

Simulation in Excel

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Spreadsheet “frozen”at row 16 to show

first 10 weeksand last 6

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

Decision Making with Simulation

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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

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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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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