BDM FROM TEXTBOOKS Flashcards
Business Decision Models
Quantitative analysis
uses a scientific approach to managerial decision making
- the approach starts with data
Qualitative factors in quantitative analysis
the weather, new technological breakthroughs, federal ligislation (in most cases, it will be an aid to decision making).
POM
production/operations management
Business analytics
is a data driven-approach to decision making, allows companies to make better decisions.
- involves the use of large amounts of data
3 categories of Business analytics
1) descriptive
2) predictive
3) prescriptive
Descriptive analytics
involves the study and consolidation of historical data for a business and an industry (measures how company has performed in the past and how it is performing now)
ex: statistical quality control
Predictive analytics
is aimed at forecasting future outcomes based on patterns in the past data
ex: decision trees, regression models, forecasting, etc
Prescriptive analytics
Involves the use of optimization methods to provide new and better ways to operate, based on specific business objectives
ex: economic order quantity, linear programming
The Quantitative Analysis Approach
defining a problem, developing a model, acquiring input data, developing a solution, testing the solution, analyzing the results, implementing the results
The Quantitative Analysis Approach: Defining the problem
develop a clear, concise statement of the problem.
- selecting the problem that creating the greatest increase in profits or reduction in costs
The Quantitative Analysis Approach: Developing a model
2nd step is to develop a model. physical, scale, schematic, and mathematical models
schematic model
a picture, drawing or chart of reality
A Mathematical model
is a set of mathematical relationships
Variable
a measurable quantity that may vary or is subject to change. can be either controllable (decision variable) or uncontrollable
parameter
a measurable quantity that is inherent in the problem. In most cases, theses are known
Acquiring Input Data
“garbage in, garbage out” -
Developing a solution
involves manipulating the model to arrive a the best optimal solution to the problem. The input data and model determine the accuracy of the solution
Testing the Solution
testing the data and model is done before the results are analyzed
Analyzing the results and sensitivity analysis
sensitivity analysis determines how the solution wills change with a different model or input data
Profit formula
revenue - expenses
sX - f - vX s = selling price per unit f = fixed cost v = variable costs per unit X = number of units sold
Expenses include…
fixed and variable costs
BEP
Break-even-point. the number of units sold that will result in $0 profits
BEP formula
= fixed costs
_____________
(SP per unit - VC per unit)
Advantages of Mathematical modeling
- accurately represent reality
- help decision makers formulate problems
- give us insight and information
Deterministic model
A model in which all values used in the model are known with complete certainty
Probabilistic model
means models that involve change or risk (often measured as a probability value
Possible problems in the Quantitative analysis approach
Defining the problem :
All viewpoints should be considered before formally defining the problem (conflicting viewpoints, impact on other departments, beginning assumptions)
Developing solution:
Hard to understand Mathematics
Assumptions should be reviewed
Implementation problems
- Lack of commitment and resistance to change
- Lack of commitment by quantitative analysts (technical)
Mathematical model
a model that uses mathematical equations and statements to represent the relationships within the model
A probability
is a numerical statement about the chance that an event will occur
Two basic rules of probability
Regardless of how probabilities are determined, they must adhere to these two rules:
1) the probability of any event or state of nature occurring is greater than or equal to 0 and less than or equal to 1 (probability of 0 indicates that an event is never expected to occur
2) the sum of simple probabilities for all possible outcomes of an activity must equal 1
2 different ways to determine probability
objective approach
subjective approach
the Relative frequency approach
an objective probability assessment in general: P(event) = number of occurrences of the e vent \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ total number of trails or outcomes
Determining objective probabilities
classical or logical method
Mutually exclusive
if only one of the events can occur on any one trail
Collectively exhaustive
if the list of outcomes includes every possible outcome
Intersection of two events
is the set of all outcomes that are common to both events (the word and is commonly associated with the intersection)
joint probability
implies that both events are occurring at the same time or jointly
The union of two events
the set of all outcomes that are contained in either of these two events. the word or is commonly associated with the union, as in the symbol
Probability of the union of two events (additive rule)
on formula sheet
P(A or B) = P(A) + P(B) - P(A and B)
Conditional Probability
is the probability of an event occurring given that another event has already happened
Equation on formula sheet
Two events are independent
Independent if the occurrence of one has no impact on the occurrence of the other
independent if :
P(A/B) = P(A)
probability of the intersection is:
P(A and B) = P(A)P(B)
Bayes Theorem
used to incorporate additional information as it is made available and help create revised or posterior probabilities from the original prior probabilities.
revised or posterior probabilities
two conditional probabilities
Thomas Bayes
did the work leading to the Bayes theorem
Random Variables
assigns a real number to every possible outcome or event in an experiment
Types of random variables
Discrete random variables
continuous random variable
discrete random variables
if it can assume only a finite or limited set of values. Probability value assigned to each event - must be between 0 and 1 and must sum to 1
continuous random variable
is a random variable that has a infinite or unlimited set of values
3 rules request of all probability distributions
1) events are mutually exclusive and collectively exhaustive
2) individual probability values are between 0 and 1 inclusive
3) the total of the probability values is 1
Expected value
the central tendency of the distribution
Variance
amount of variability or spread of the distribution
Expected value of a discrete probability distribution
the expected value of a discrete distribution is the weighted average of the values of the random variable.
Given on Formula sheet
Variance of a discrete probability distribution
is a number that reveals the overall spread or dispersion of the distribution. For a discrete probability distribution, it can be computed using the following equation.
Given on Forumla sheet
Standard deviation
a relative measure of dispersion or spread (square root of the variance)
Probability distribution of Continuous Random Variable
used the probability density function
Probability density function
f(X), is a mathematical way of describing the probability distribution. Shaded area under the graph represents probability.
The Binomial Distribution
a discrete distribution that describes the number of successes in independent trails of a Bernoulli process
Used to find the probability of a specific number of success out of n trials of a Bernoulli process.
Bernouli process, following characteristics
- each trail has only two possible outcomes - success and a failure
- probability stays the same from one trail to the next
- the trails are statistically independent
- the number of trails is a positive integer
!
symbol used in binomial distribution, means factorial (ex: 4! = (4) (3) (2) (1) = 24
The normal distribution
continuous bell-shaped distribution that is a function of two parameters, mean and standard deviation of the distribution
affects a large number of processes in our lives (e.g. filling boxes of cereal with 32 ounces of corn flakes). Each normal distribution depends on the mean and standard deviation
as standard deviation becomes smaller, normal distribution becomes steeper, vise versa
formula is on formula sheet
Area under the normal curve
normal distribution is symmetrical, the highest point is at the mean. Area under the curve (in a continuous distribution) describes the probability that a random variable has a value in a specified interval
The Empirical Rule
This rule states that for a normal distribution:
68% of all the values will be within +/- 1 standard deviation of the mean
95% of the values will be within +/- 2 standard deviations of the mean
about 99.7% of the values will be within +/- standard deviations of the mean
the F distribution
is a continuous probability distribution that is helpful in testing hypotheses about variances. Used when regression models are tested for significance.
Finding the F value
associated with a particular probability and degrees of freedom
The exponential Distribution
used in dealing with queuing problems. A continuous distribution, Function is given on sheet.
The Poisson distribution
this distribution is used in many queuing models to represent arrival patterns
formula is given
Bernouli Process
A process with two outcomes in each of a series of independent trials in which the probabilities of the outcomes do not change
objective approach
the method of determining probability vales based on historical data or logic
Decision Theory
is an analytic and systematic way to tackle problems. a good decision is based on logic
6 steps in decision making
- clearly define the problem at hand
- list the possible alternatives
- identity the possible outcomes or states of nature
- list the payoff (typically profit) of each combination of alternative and outcomes
- select one of the mathematical decision theory models
- apply the model and make your decision
Types of decision-making environments
there decision-making environments:
- decision making under certainty
- decision making under uncertainty
- decision making under risk
decision-making under certainty
decision makers know with certainty the consequence of every alternative or decision choice (maximize their well-being)
decision-making under uncertainty
the decision maker does not know the probabilities of the various outcomes. sometimes it is impossible to assess the probability of success of a new undertaking or product
Several criter for making decisions under conditions of uncertainty
- optimistic
- pessimist
- criterion of realism (HUrwicz)
- Equally Likely (Laplace
- Minimax regret
decision making under risk
there are several possible outcomes for each alternative, and the decision maker knows the probability of ocurence of each outcome .
selecting the altnerative with the highest expected monetary value (or simply expected value)
optimistic (maximax)
the best (maximum) payoff for each alternative is considered and the alternative with the best (maximum) of these is selected
Pessimistic
the worst (minimum) payoff for each altnerative I s considered, and the alternative with the best (maximum) of these is selected. (Maximin)
Criterion of Realism (Hurwicz Criterion)
comprised of an optimistic and a pessimistic decision. Uses the weighted average approach
weighted average formula
Weighted average = a(best in a row) - (1-a)(worst in row)
Equally Likely (Laplace)
Involves finding the average payoff for each altnerative and selecting the altnerative with the best or highest average
Minimax regret
Opportunity loss refers to the difference between the optimal profit or payoff for a given state of nature and the actual payoff received for a particular decision for that state of nature
Expected Monetary Value
is the weighted sum of possible payoffs for each altnerative
