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By: Jessica Gahtan 1 Omis Quiz 2 Notes
th
Hey! So, just a reminder th vote for UBC elections from Monday March 17 at 8:00AM until
Wednesday March 19 at 11:59PM at evote.yorku.ca
I know my shameless promotion is annoying but like… none of you guys will remember
otherwise since I’m pretty sure you are all studying your guts out for this quiz.
GOOOD LUCK ON THE QUIZZ!!!!!!!!!
- Jess
By: Jessica Gahtan 2 Omis Quiz 2 Notes
Chapter
11
–
Time
Series
Forecasting
-‐ A time series is a set/series of observations on a quantitative variable collected over time
▯ ▯ ▯▯
-‐ Focus on: 𝑀𝑆𝐸 = ▯( ▯ ▯) *Remember that you want the MSE to be SMALL
▯ ▯ ▯
-‐ A moving average calculates the average of the past ‘k’ observations – since we don’t know the best
value of k – we should try different ones to see which gives the best results
-‐ A weighted moving average is a variation of the moving average that assigns weights to the data
being average – Use solver to determine the value of k and w that mi nimize MSE
-‐ Exponential smoothing is for stationary data – allows weights to be assigned to past data – more
recent data = higher weight
-‐ Seasonality refers to the regular, repeating patterns in the data
-‐ Additive seasonal effects tend to be on the same order of magnitude each time a given season is
encountered
-‐ Multiplicative seasonal effects tend to have an increasing effect each time a given season is
encountered
-‐ Stationary data with Additive Seasonal Effects:
𝑌▯▯▯ = 𝐸 ▯ 𝑆 ▯▯▯▯▯ 𝐸 ▯ 𝛼 𝑌 − ▯ ▯▯▯ + (1 − 𝛼)𝐸 ▯▯▯ 𝑆▯= 𝛽 𝑌 − ▯ ▯ + (1 − 𝛽)𝑆 ▯▯▯
0 ≤ 𝛼 ≤ 1 𝑎𝑛𝑑 0 ≤ 𝛽 ≤ 1
E teps the expected level of the time series in period t S teps the seasonal factor for period t
The constant p reps the # of seasonal periods in the data
The forecast for time period t+n is simply the expected level of the time series at period t adjusted upward or downward
by the seasonal factor S
t+n-p
In order to use the eq’ns, it’s necessary to initialize the estimated levels & seasonal factors for the first p periods
▯ ▯▯
𝐸 ▯ ▯▯▯ ▯ ,𝑡 = 1,2,…,𝑝 𝑆▯= 𝑌 −▯𝐸 ,𝑡 ▯ 1,2,…,𝑝
-‐ Stationary data with Multiplicative Seasonal Effects:
𝑌▯▯▯ = 𝐸 ▯𝑆 ▯▯▯▯▯ 𝐸 ▯ 𝛼 𝑌 /𝑆▯ ▯▯▯ + (1 − 𝛼)𝐸 ▯▯▯
𝑆▯= 𝛽 𝑌 /𝐸▯ ▯ + (1 − 𝛽)𝑆 ▯▯▯ 0 ≤ 𝛼 ≤ 1 𝑎𝑛𝑑 0 ≤ 𝛽 ≤ 1
E tepresents the expected level of the time series in period t
Strepresents the seasonal factor for period t
The constant p represents the number of seasonal period in the data
The forecast for time period t+n is simply the expected level of the time series at period t multiplied by the seasonal factor
St+n-p
In order to use the equations, necessary to initialize the estimated levels and seasonal factors for the first p periods
▯ ▯▯ ▯▯
𝐸 ▯ ▯▯▯ ,𝑡 = 1,2,…,𝑝 𝑆▯= ,𝑡 = 1,2,…,𝑝
▯ ▯▯
-‐ Trend is a long-term sweep or general direction of movement in a time series – reflect net influence of
long-term factors that affect the time series in a fairly consistent and gradual way over time
-‐ Consistent underestimation of the actual values if there’s an upward trend (and vice versa)
-‐ Double exponential smoothing is often an effective forecasting tool for time series data that exhibits
a linear trend
After observing the value of the time series at period t (Y ), tompute an estimate of the base, or expected, level of the
time series (E t and the expected rate of increase or decrease (trend) per period (T ) t
𝑌▯▯▯ = 𝐸 ▯ 𝑛𝑇 ▯
𝐸 = 𝛼𝑌 + (1 − 𝛼)(𝐸 + 𝑇 )
▯ ▯ ▯▯▯ ▯▯▯
𝑇 = 𝛽 𝐸 − 𝐸 + (1 − 𝛽)𝑇
▯ ▯ ▯▯▯ ▯▯▯ By: Jessica Gahtan 3 Omis Quiz 2 Notes
Chapter
12
–
Intro
to
Simulation
using
Risk
Solver
Platform
-‐ Random variable is any variable whose value can’t be predicted w/certainty
-‐ Amount of risk involved in a given decision making situation – is a function of the uncertainty in the
outcome of the decision and the magnitude of the potential loss (Uncertainty -> risk -> potential for loss)
-‐ Different ways to analyze risk:
1. Best-Case / Worst-Case Analysis
-‐ Calculate values of the most pessimistic and optimistic scenarios
-‐ Doesn’t tell you about the distribution of the possible values w/i n the range or probability
2. What-If Analysis
-‐ Can change values of uncertain input variables to see what happens to the company’s bottom line –
shows sensitivity to changes to the input variable
-‐ 3 problems with it: (1) manager can manipulate the values selec ted for the independent variables; (2)
to get a good idea of underlying variability in the bottom -line you’d need to do hundreds or thousands
of what-if scenarios; (3) insight gained from playing out random scenarios isn’t very valuable when
recommending something to top management
3. Simulation
-‐ Measures and describes various characteristics of the bottom -line performance measure of a model
when one or more values for the independent variables are uncertain – Goal is to describe the
distribution and characteristics of the possible values of Y (the performance measure) given the
possible values/behaviors of the independent (X) variables
-‐ To perform simulation in a spreadsheet, first you need to place a random number generator (RNG)
formula in each cell that reps a
random, or uncertain,
independent variable – each
RNG provides a sample
observation from an appropriate
distribution that reps the range
and frequency of possible values
for the variable
-‐ It’s important to distinguish b/w
discrete and continuous variables
***
-‐ When preparing the model for
Simulation: either use the
available historic data on the
uncertain variables to determine
appropriate RNGs for the
variables OR use sample the
historic data itself
-‐ Risk Solver Platform also has the
ability to identity probability
distributions that fit with the
historical data pretty well
-‐ Running the simulation: Need
to recalculate the spreadsheet
100s/1000s times and record the
resulting values generated for the
output cells – Risk Solver
Platform will do this if you tell it
how many times you want it to
replicate the model. (1) Identify output cell, (2) indicate number of replications to perform (3) run
simulation
-‐ To analyze the data – you can look at the best/worst case scenarios, view the distribution of the output
cells, look at the cumulative distribution of the output cells, obtain other cumulative probabilities, analyze
sensitivity – which variables have the largest impact
-‐ Sampling is inherently the best you can do is take a random sample and hope for the best!
• Constructing a confidence interval for a population proportion By: Jessica Gahtan 4 Omis Quiz 2 Notes
o May want to construct a confidence interval for the true proportion of a population that fall
below (or above) some value
o Let p denote the proportion of observations in a sample of size n that falls below some value
Y p
o Assuming n is sufficiently large (n≥30)
o The Central Limit Theorem tell us that the lower and upper limits of a 95% confidence interval
for the true proportion of the population falling belop Y are represented by
95% 𝐿𝑜𝑤𝑒𝑟 𝐶𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒 𝐿𝑖𝑚𝑖𝑡 = 𝑝 − 1.96× ▯(▯▯▯)
▯
▯(▯▯▯)
95% 𝑈𝑝𝑝𝑒𝑟 𝐶𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒 𝐿𝑖𝑚𝑖𝑡 = 𝑝 + 1.96×
▯
• As the number of replications (n) increases, the width of the confidence in terval decreases
-‐ Interactive Simulation
• The Simulate icon on the Risk Solver Platform tab is on (or the light bulb is illuminated), Risk Solver
Platform is in interactive simulation mode
o Anytime you make a change to your workbook that requires the spreads heet to recalculate (or
manually recalculate by pressing F9), Risk Solver Platform performs a complete simulation of
your model
• PsiTarget (cell, target value) returns the cumulative probability of a specified distribution or output cell
being less than or equal to a given target value By: Jessica Gahtan 5 Omis Quiz 2 Notes
Chapter
13:
Queuing
Theory
-‐ Queuing theory is a mgmt. science term referring to the body of knowledge dealing with waiting times
-‐ Objective is usually to find the optimal service level that achieves an acceptable balance b /w the cost
of providing service and customer satisfaction
-‐ System configurations:
o Single-queue, single-server system: Customers enter system, wait in line, FIFO basis until
they receive service (@ which pt they exit the system)
o Single-queue, multi-server system: Customers enter the system and join a FIFO queue ->
Upon reaching the front of the line, a customer is serviced by the next available server
o Collection of single-queue, single-server systems: Customers arrive and choose one of the
queues, waits in the line to receive service -> Can often be analyzed as a independent, single-
queue, single-server systems
Characteristics of Queuing Systems:
-‐ Need to make some assumptions about the way customers arrive in the system, amt. of time it takes
them to receive the service
-‐ Arrival rate - # of arrivals that happen in a period of time reps a random variable
o Appropriate to model the arrival process in a qu

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