DSC 3120 - Business Analysis
Georgia State University - Spring, 2004
Simulation
Models
1
Outline
n
n
n
n
n
n
n
Simulation Models
Random Variables
Probability Distributions
Simulation with Excel
Simulation with Crystal Ball
Basic Queuing Model
Queuing Terminology
2
Simulation Models
n
Simulator is a device that acts like
(simulates) certain important aspects of
a system
n
n
n
Airplane performance testing in a wind
tunnel simulator
Computer simulations (manufacturing,
military, transportation, etc..)
Simulation model – a symbolic model
where uncertainty in parameters is
modeled with statistical distributions
n
n
Profit model
Capital budgeting model
3
Sec# 50442, 50447, 50449
1
DSC 3120 - Business Analysis
Georgia State University - Spring, 2004
When to Use Simulation?
n
n
n
When it is impossible to obtain an
analytical model
When analytical model exists, but is too
complex to solve for a ‘closed-form’
solution or simply too expensive to
implement
Because simulation models can be
implemented with a variety of readily
available software
n
n
n
Spreadsheets (Excel)
Spreadsheet add-ins (Crystal Ball)
Simulation languages (Extend)
4
Random Variables
n
n
Random variable – a variable whose
outcome is not know with certainty
Probability distribution – describes
the behavior of a random variable by
defining its central tendency, variability,
limits, and nature
n
n
n
n
Mean (or Expected Value)
Standard Deviation
Upper and Lower Limits
Discrete and Continuous
5
Discrete, Cumulative and
Continuous Distributions
n
Discrete distributions
n
n
n
Cumulative distribution
n
n
Typically used when only a small number
of different values can occur
Also used as an approximation for the
continuous random variables
Describes the likelihood that a random
variable has a value which is less then or
equal to a given constant
Continuous distributions
n
Used when a large number of continuous
values (typically a range) can occur
Sec# 50442, 50447, 50449
6
2
DSC 3120 - Business Analysis
Georgia State University - Spring, 2004
Continuous Distributions
n
Uniform distribution
n
n
All values between minimum and maximum
occur with equal likelihood
Conditions
n
n
n
n
Minimum value is fixed
Maximum value is fixed
All values occur with equal likelihood
Normal distribution
n
n
Most widely used
Conditions
n
n
n
Some value of the random variable is most likely
(mean)
Random variable is symmetric around the mean
Random variable is more likely to be in vicinity of
the mean than far away
7
Simulating Data
n
Triangular Distribution
n
n
Used when we know where the min, max,
and the most likely value occur
Conditions
n
n
n
Min and max values are fixed
The most likely value is between min and max,
forming a triangle
Generating Simulation Data
n
Using Excel functions
n
Using Excel add-ins
n
n
RAND() in combination with other functions
Crystal Ball - wide variety of distributions
8
Airbus Industries Case
Step 1: Study Environment
n
Diagnose the problem and organize facts:
n
n
n
Airbus Industries competing with Boeing on longrange jumbo jets
Proposed new jumbo model A3XX characteristics:
number of seats (550), multiple decks, etc..
Frame management situation
n
n
Critical decision: determining the number of planes
to be produced in the next 4 years to make a profit
(or at least break-even)
Capital budgeting decision making
n
n
Aggregate future cash flows using Net Present Value and
compare with the initial startup costs
If NPV exceeds startup costs, project might be worth a
while, otherwise the project should be rejected
Sec# 50442, 50447, 50449
9
3
DSC 3120 - Business Analysis
Georgia State University - Spring, 2004
Airbus Industries Case
Step 2: Model Formulation
Create a selective representation of
reality, identify decisions, and objectives
n
Revenue based on the demand for A3XX
jumbo jet and its selling price
Costs based on initial startup cost, annual
fixed and variable costs, and depreciation
Other relevant parameters are discount &
tax rates
Decision variables: production levels for
each of the 4 years
Objective: maximize NPV
n
n
n
n
n
10
Airbus Industries Case
Step 3: Model Construction
n
Construct a symbolic model
n
n
n
n
Profit before tax = Revenue – Total Cost –
Depreciation
Profit after tax = Profit before tax – Tax
Net cash flow = Profit after tax +
Depreciation
Stream of cash flows
n
n
n
Cash outflow for the startup cost now
Cash inflows for each of the future years
Discount the future cash flows to present
11
Simulation with Excel
n
Simulating discrete distributions
n
n
n
Running simulation a lot of times to
get more accurate results
n
n
n
Cumulative distribution
RAND() and VLOOKUP() functions
Repeatedly press F9 function key
Use Data Table function
Summarizing simulation results
n
n
n
Descriptive statistics
Confidence interval
Frequency chart
Sec# 50442, 50447, 50449
12
4
DSC 3120 - Business Analysis
Georgia State University - Spring, 2004
Basic Queuing Model
n
A queuing model is one in which there
is a sequence of items (such as people)
arriving at a facility for service
People waiting in line to deposit paychecks
or to buy groceries
Orders lining up to be filled at the online
catalogue retailer
Telephone calls “waiting” in line at the
switchboard to be routed to their destination
Airplanes waiting on the runway to take off
n
n
n
n
13
Quantities of Interest
n
The number of people in the system
n
The number of people currently being
served, as well as those waiting for service
n
The number of people in the queue
n
The waiting time in the system
n
n
n
The number of people waiting for service
The interval between when an individual
enters the system and when he or she
leaves the system (includes service time)
The waiting time in the queue
n
The time between entering the system and
the beginning of service
14
Queuing Terminology
n
Arrival Process
n
n
n
n
Each arrival is called a “job”
Interarrival time (time between the arrivals) is
uncertain and modeled by an exponential
distribution (not symmetric)
λ is the mean arrival rate in number of jobs that
arrive per unit time (typically minutes)
Service Process
n
n
n
The service time is the time that it takes to
complete a job
Also uses the exponential distribution
µ is the mean service rate in number of jobs per
unit time (usually minutes)
15
Sec# 50442, 50447, 50449
5