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Concise Summary Management Science Course for Written Exam
This document is a summary of all the material necessary for the written exam. It focuses on chapters 2, 3, 4, and 12 as these are part of the written exam.
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1WRITTEN EXAM MANAGEMENT SCIENCE
SESSION 1 INTRODUCTION.....................................................................................................................1
REVIEW QUESTIONS...........................................................................................................................1
SLIDES.................................................................................................................................................2
BOOK SLIDES.......................................................................................................................................3
SESSION 2 CLASSIFICATION & FORECASTING..........................................................................................5
REVIEW QUESTIONS...........................................................................................................................5
HOMEWORK.......................................................................................................................................7
PROBLEMS..........................................................................................................................................9
SLIDES.................................................................................................................................................9
PREPARATION QUIZ 2.1.....................................................................................................................18
PREPARATION QUIZ 2.2.....................................................................................................................18
BOOK SLIDES.....................................................................................................................................19
SESSION 5 NONLINEAR PROGRAMMING & DECISION ANALYSIS..........................................................25
REVIEW QUESTIONS.........................................................................................................................25
HOMEWORK.....................................................................................................................................26
PROBLEMS........................................................................................................................................27
SLIDES...............................................................................................................................................29
PREPARATION QUIZ 5........................................................................................................................31
BOOK SLIDES.....................................................................................................................................33
SESSION 1 INTRODUCTION
CHAPTER 2
REVIEW QUESTIONS
2.3.3: What is the difference between a numerical and categorical variable? Numerical variable= A
variable that takes on numerical values. The possible numerical values could be continuous (any
numerical or decimal value) or integer, usually within a given range. Categorical variable= A type of
variable that can take on only a small number of values that represent the few possible categories.
The values could be expressed either numerically (0 or 1) or with text. Categorical variables can be
further differentiated into either nominal variables (order of values have no meaning) or ordinal
variables (natural order in values).
2.4.4: What does the k-nearest-neighbours algorithm base its predictions upon? It uses the
observed behaviour of customers (for example) (the k nearest neighbours of this customer) to predict
what the prospective customer will do.
2.4.9: What does it mean to overfit to the data? A model that fits the historical data too precisely is
referred to as overfitting the data because it is overly accounting for the noise. Overfitting the data=
Making a predictive model less accurate when using new data sets by having the model align too
closely to the given data instead of taking into account the inherent idiosyncrasies in the given data
due to randomness.
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A model that overfits to the historical data will incorporate and account for too much of the noise,
potentially to the point of missing the main signal, and therefore may make poor predictions with
new data.
2.4.11: What is the difference between specificity and sensitivity? Specificity= The ability to
correctly predict a negative outcome. Sensitivity= The ability to correctly predict a positive outcome.
SLIDES
Linear Regression:
- Linear regression involves approximating the relationship between the dependent variable
and the independent variable by a straight trendline.
- The equation for the linear regression trendline has the form y= ax + b, where
o Y= Estimated value of the dependent variable
o A= Slope of the linear regression trendline
o X= Value of the independent variable
o B= Intercept of the linear regression trendline with the y-axis
Overfitting the Data:
- It may appear that the sixth-order polynomial equation does a nearly perfect job. The
trendline nearly ‘perfectly fits the data’.
- We don’t want a trendline that is so tied to the data that it shows a strange shape that
contradicts what we know about the effect on sales of increasing the advertising level (always
increasing but with diminishing returns from advertising).
- Overfitting the data: Making a predictive model less accurate when using new data sets by
having the model align too closely to the given data instead of taking into account the
inherent idiosyncrasies in the given data due to randomness.
The Square-Root Effect: The square-root effect would suggest using nonlinear regression to look for a
curving trendline of the form:
Confusion Matrix:
o Sensitivity: hit rate, power, recall, true positive rate
o Specificity: true negative rate
o Accuracy: classification rate, proportion (percentage) correct, simple matching
coefficient
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o Precision: absolute support, certainty factor, confidence, correct alarm ratio,
frequency of hits, positive predictive value, success ratio
BOOK SLIDES
Chapter 2
Defining the entire problem in a
decision model requires defining:
- The individual decisions to
be made.
- The overall objective for the
problem.
- The constraints on what can be done.
Descriptive analytics: focused on analysing data to create information descriptions of what has
happened so far. Four steps:
1. Gather and organise relevant data.
2. Clean the data.
a. ETL process:
i. The Extract step involves extracting the relevant data.
ii. The purpose of the Transform step is to ‘clean up’ the data.
iii. The Load step involves moving the transformed data into a target data store.
3. Explore the data.
4. Communicate performance information using data visualisation.
Predictive analytics (aka data mining): focused on using models to create predictions of what is likely
to happen in the future. Five steps:
1. Develop a model.
a. Prediction models: predicts a numeric outcome.
b. Classification models: attempts to predict a yes-or-no outcome.
2. Partition the data. Partitioning the data can be used to try to avoid overfitting. A quick
approach to validate (sometimes improve) the model is to split up (partition) the historical
data set into two parts:
a. Training partition: data is used to develop (‘train’) the model.
b. Validation partition: data is validated.
3. Test and refine the current model.
a. Confusion matrix: shows how the predicted outcomes compare to the actual
outcomes.
b. Error report: summarizes the data from the confusion matrix by reporting the
percentage of predictions that differed from the outcome (the error rate).
c. Various metrics:
i. Accuracy: the overall rate of correct predictions.
ii. Specificity: the ability to correctly predict a negative outcome.
iii. Sensitivity: the ability to correctly predict a positive outcome.
4. Repeat steps 1-3 for several models, and then choose the best.
a. KNN
b. Classification trees
c. Logistic regression
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d. Naïve Bayes
5. Implementation.
Numerical variables can be transformed to categorical variables by binning; creating categories
(‘bins’) such as low, medium, and high.
A lift chart graphically shows the improvement that an algorithm provides when compared against a
random guess that is represented by the straight diagonal line.
Prescriptive analytics: the stage of the analytics approach that involves using decision models,
including optimization models, to prescribe the best options for managerial decision making. Five
steps:
1. Formulate a decision model: describes a problem concisely and forms a bridge to the use of
mathematical techniques and computers to analyse the problem.
a. If there are n related quantifiable decisions to be made, they are represented as
decision variables (x1, x2, …xn) whose respective values are to be determined.
b. The appropriate measure of performance is then expressed as a mathematical
function of these decision variables. This function is the objective function.
c. Constraints: any restrictions on the values of the decision variables are also expressed
mathematically.
d. Parameters: the constants (namely, the coefficients and right-hand sides) in the
constraints and the objective function.
i. If there is uncertainty about the true value of a parameter, it is important to
analyse how the solution would change (if at all) if the value assigned to the
parameter were to be changed to other plausible values. This process is
referred to as what-if analysis (or sensitivity analysis).
2. Learn how to derive solutions from the model.
3. Test the model.
a. Retrospective test: involves using historical data to reconstruct the past and then
determining how well the model and the resulting solution would have performed if
they had been used. A disadvantage is that it uses the same data that guided the
formulation of the model.
4. Prepare to apply the model.
5. Implementation.
A crucial step in formulating a decision model is the construction of the objective function:
- If there are multiple objectives, their respective measures commonly are then transformed
and combined into a composite measure, called the overall measure of performance.
- This overall measure might be something tangible (e.g. profit) or it might be something that
attempts to combine multiple objectives.
Post-optimality analysis (analysis done after finding an optimal solution), sometimes referred to as
what-if analysis:
- Involves addressing some questions about what would happen to the optimal solution if
different assumptions are made about future conditions.
- These questions often are raised by the managers who will be making the ultimate decisions.
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