Chapter 1 Introduction to Quantitative Analysis
§1.1 What is Quantitative Analysis?
Quantitative Analysis = A scientific approach to managerial decision making, also known
as management science. The
approach starts with data, and leaves out whim, emotions and guesswork.
This data is manipulated
or processed into useful information and represents the hart of quantitative
analysis.
In addition to quantitative analysis, qualitative factors should be considered. Quantitative
analysis will be an aid to the decision-making process and will therefore be combined with
qualitative information.
§1.2 Business Analytics
Business Analytics = A data-driven approach to decision making that allows companies to
make better decisions. The
study involves large amounts of data, which means that information
technology related to the
management of the data is very important. Quantitative methods are used to
analyse the data and
provide useful information to the decision maker. There are three categories:
Descriptive analytics: involves the study and consolidation of historical
data for a business and an industry. It measures and compares the past
and present performance.
Predictive analytics: aimed at forecasting future outcomes based on
patterns in the past data. Uses statistical and mathematical models.
Prescriptive analytics: involves the use of optimisation methods to provide
new and better ways to operate based on specific business objectives.
§1.3 The Quantitative Analysis Approach
The quantitative analysis approach consists of multiple steps, that are the building blocks of any
successful use of quantitative analysis:
1. Defining the problem: develop a clear, concise statement of the problem. This can be the
most important and the most difficult step. It is important to analyse how the solution to one
problem affects other problems or the situation in general. Choose the most important
problems;
2. Developing a model: a model is a representation of a situation. In the quantitative analysis,
mathematical models, sets of mathematical relationships, are used. Relationships are
expressed in equations and inequalities, and contain one or more variables and parameters;
3. Acquiring input data: when a model has been developed, date must be obtained. Accurate
data for the model is essential. Improper data will result in misleading results: garbage in,
garbage out;
4. Developing a solution: developing a solution involves manipulating the model to arrive at
the best (optimal) solution to the problem. A solution can be found by means of an equation,
trial-and-error methods, or repetition (algorithm);
5. Testing the solution: both input data and the model require testing. This testing includes
determining the accuracy and completeness of the data used by the model;
6. Analysing the results and sensitivity analysis: it is determined how much the solution
will change if there are changes in the model or the input data;
7. Implementing the results: the process of incorporating the solution into the company’s
operations.
§1.4 How to Develop a Quantitative Analysis Model
f s = selling price per unit v = variable cost per unit
BEP= Profit=sX−f −vX f = fixed cost X = number of units sold
s−v
In addition to the profit model above, decision makers are often interested in the break-even
point. The advantages of mathematical models, like the profit model, is that they can accurately
represent reality; formulate problems; give insight and information; save time and money; solve
large and complex models; and can be used to communicate problems and solutions to others.
, Mathematical models can be categorised by risk. Deterministic models involve zero risk or
chance and assume they know all values used in the model with complete certainty. Other
models involve risk or chance and are therefore called probabilistic models.
§1.6 Possible Problems in the Quantitative Analysis Approach
The quantitative analysis approach has been presented as a logical, systematic means of
tackling decision-making problems. However, per step, there are many possible problems:
1. Defining the problem: conflicting viewpoints, impact on other departments, beginning
assumptions and outdated solutions;
2. Developing a model: fitting the textbook models and understanding the model;
3. Acquiring input data: using accounting data and validity of data;
4. Developing a solution: hard-to-understand mathematics and the limitation of only one
answer;
5. Testing the solution: solutions cannot be intuitively obvious and therefore be rejected;
6. Analysing the results and sensitivity analysis : not all changes in the organisation can be
accounted.
§1.7 Implementation – Not Just the Final Step
The ‘last’ step, implementation, is greatly affected by the changes of the steps above. Next to
that, managers often have a lack of commitment and resistance to change and therefore reject
the implementation, as it might prove other decisions wrong. Successful implementation
requires that the analyst not tell the users what to do but rather work with them and take their
feelings into account.
Chapter 3 Decision Analysis
§3.1 The Six Steps in Decision Making
Decision theory = An analytic and systematic approach to the study of decision making.
A good decision is based on
logic, considers all available data and possible alternatives, and applies the
quantitative approach.
There are six steps in decision making:
1. Clearly define the problem at hand;
2. List the possible alternatives: an alternative is a course of action or a strategy that the
decision maker can choose;
3. Identify the possible outcomes or states of nature: the outcomes over which the
decision maker has little or no control are called states of nature;
4. List the payoff (typically profit) of each combination of alternatives and outcomes:
payoffs are often called conditional values and can easily be presented in a so-called payoff
table;
5. Select one of the mathematical decision theory models: this depends on the
environment in which you’re operating, and the amount of risk and uncertainty involved;
6. Apply the model and make your decision.
§3.2 Types of Decision-Making Environments
In decision making under certainty, decision makers know with certainty the consequences of
every alternative or decision choice. In decision making under uncertainty, there are several
possible outcomes for each alternative, and the decision maker does not know the probabilities
of the various outcomes. In decision making under risk, there are several possible outcomes for
each alternative, and the decision maker knows the probability of occurrence of each outcome.
§3.3 Decision Making Under Uncertainty
There are several criteria that exist for making decisions under conditions of uncertainty.
The optimistic criterion considers and selects the best (maximum) payoff for each
alternative. Hence, this criterion is often called the maximax criterion.
The pessimistic criterion considers the worst (minimum) payoff for each alternative and
then selects the best (maximum) of these. Hence, this criterion is often called the maximin
criterion.
