Toma De Decisiones

QUANTITATIVE DECISION MAKING IN BUSINESS
Bertrand MARESCHAL bmaresc@ulb.ac.be http://homepages.ulb.ac.be/~bmaresc/

Contents
Decision analysis Probability
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Discrete probability Continuous probability distributions Sampling Confidence intervals Estimation

Statistics
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Simulation modeling Regressions models

Chapter 1 Decision Analysis
Decisions in an uncertainenvironment. A decision tree model. General method of decision analysis. Need for probability theory.

A simple example
Exercise 1.1

Nodes
Decision nodes:
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represented by a square each branch corresponds to a possible decision represented by a circle each branch corresponds to a possible outcome, with its probability of occurence

Event nodes:
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EMV
Expected Monetary Value:
!the EMV of an uncertain event is the weighted average of all possible numerical outcomes, with the probabilities of each of the possible outcomes used as the weights.

Folding back the decision tree (Backwards induction)
Start with the final branches of the tree
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for an event node, compute the EMV of the node as the weighted average of the EMV of each branch weighted by itsprobability, for a decision node, compute the EMV of the node by choosing that branch from the node with the best EMV value.

The EMV for the starting branch of the tree corresponds to the optimal decision strategy.

A simple example
Exercise 1.1 (cont.)

Case module 1

Kendall Crab & Lobster, Inc.
Decisions ? Uncertainties ? Revenues and costs ?

Case module 2

Buying a house

Chapter2

Fundamentals of discrete probability
Outcomes, probabilities and events. Laws of probability. Probability tables. Random variables. Discrete probability distributions. Summary measures. Covariance and correlation.

Outcomes, probabilities and events
Experiment:

Outcomes:
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heads or tails, 1, 2, 3, 4, 5 or 6, one of 52 cards.

Outcomes, probabilities and events
Outcomes:mutually exclusive and collectively exhaustive. Probability: likelihood that an outcome will occur. Event: collection of outcomes. Mutually exclusive events: contain no common outcome.

The Laws of Probability
1st Law:

0 ≤ P (E ) ≤ 1
2nd Law: if A and B are mutually exclusive events, then:

P ( A or B ) = P ( A ) + P ( B )

The Laws of Probability
3rd Law: if A and B are two events,then:

P( A | B) =

P ( A and B ) P (B)

Independent events: A and B such that:

P ( A | B ) = P ( A) → P ( A and B ) = P ( A ) × P ( B )

Conditional probability
Example:
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class of 100 students: 40 m – 60 n 70 French: 25 m – 45 n 30 international students: 15 m – 15 n one student is selected at random:

(F: French, I: international, M: man, W: woman)

P (F | M ) =

P (F and M ) P (M )

Probability table
Distribution of students in the class:
French Men Women Total 25 45 70 Internat. 15 15 30 Total 40 60 100

Probability table:
French Men Women Total 0.25 0.45 0.70 Internat. 0.15 0.15 0.30 Total 0.40 0.60 1.00

Random variables
When outcomes are numbers. Discrete random variable:
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distinct and separate values. any value within some interval.Continuous random variable:
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Discrete probability distributions
List of the possible values (Xi), along with the corresponding probabilities (Pi).
Orders Probability
Probability distibution
0.30 0.25 0.20 0.15 0.10 0.05 0.00 42 43 44 45 Orders 46 47 48

42 43 44 45 46 47 48

0.05 0.10 0.15 0.20 0.25 0.15 0.10

Probability

The binomial distribution
Experiment: n independenttrials. Each trial has 2 possible outcomes:
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success: failure:

P (success) = p P (failure) = 1 – p

Random variable: X = number of successes "binomial distribution

Binomial distribution: example in quality control
Units produced by a production process:
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P (good quality) = 0.92 P (bad quality) = 0.08

Production in shifts of 140 units. X = number of good quality units in...