Probability & Statistical ModellingDecision Making Techniques
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 2 (of 68)Topic & Structure of the lessonIntroductionDecision making Under UncertaintyExpected Value / Expected Opportunity LossExpected Value of perfect informationDecision TreesSequential TreesComputerised decision tree analysis
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 3 (of 68)Learning Outcomes At the end of this topic, You should be able to:
Understand how to calculate and use Expected ValueKnow how to value Perfect and Imperfect informationUse various decision rulesKnow what is meant by a Decision TreeBe able to describe Decision Trees and Outcomes Nodes
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 4 (of 68)Understand how to draw Decision Trees using the Forward PassKnow that the outcome values are calculated using the backward passBe able to incorporate Bayes Theorem into a Decision Tree.
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 5 (of 68)Key Terms you must be able to useIf you have mastered this topic, you should be able to use the following terms correctly in your assignments and exams:(Prepare your own list)
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 6 (of 68)IntroductionDecision making involves the following steps:Recognise and clearly define the problemCollect the information needed to analyse possible alternativesChoose and implement the most feasible alternative
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 7 (of 68)Problem formulationA decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.The decision alternatives are the different possible strategies the decision maker can employ.The states of nature refer to future events, not under the control of the decision maker, which may occur. States of nature should be defined so that they are mutually exclusive and collectively exhaustive.
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 8 (of 68)a general approach to decision making when the outcomes associated with alternatives are often in doubtList the feasible alternativesList the eventsCalculate the payoff Estimate the likelihood of each eventSelect a decision ruleDecision Theory
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 9 (of 68)When a decision has to be made, there will be a range of possible actionEach action will have a certain consequences or payoff
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 10 (of 68)Manager knows which event will occurpick the alternative with the best payoff
What is the best choice if future demand will be low?Decision Making Under Certainty
Possible Future Demand
Alternative
Low
High
Small facility
200
270
Large facility
160
800
Do nothing
0
0
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 11 (of 68) Decision making without probability (no probability of occurrence are assigned)
Decision making with probabilities (probabilities can be assigned)Decision Making Under Uncertainty
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 12 (of 68)Decision Making Without ProbabilitiesDecision Criteria Maximax criterionMaximin criterionMinimax regret criterionHurwicz criterion
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 13 (of 68)Maximax Criterion maximise the maximum profitoptimistic - looks at the best possible payoffsignores the possibility of a potential loss
N/B: maximax criterion deals with profit, if the payoff table consists of costs, then minimum criterion would be used ( i.e. minimise the minimum costs)
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 14 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
Determine the maximax criterion for our investment.
State of Nature
Decision
(purchase)
Good Economic conditions
Poor Economic conditions
Apartment building
$50,000
$30,000
Office building
100,000
-40,000
Warehouse
30,000
10,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 15 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
The maximax criterion for our investment is to purchase office building.
Decision
(purchase)
Apartment building
$50,000
Office building
100,000
Warehouse
30,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 16 (of 68)Maximin Criterion looks at the worst possible payoffspessimistic and conservativeresults in the maximum of the minimum profit
Its equivalent is minimax (i.e. minimise the maximum cost)
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 17 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
Determine the maximin criterion for our investment.
State of Nature
Decision
(purchase)
Good Economic conditions
Poor Economic conditions
Apartment building
$50,000
$30,000
Office building
100,000
-40,000
Warehouse
30,000
10,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 18 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
The maximin criterion for our investment is to purchase apartment building.
Decision
(purchase)
Apartment building
30,000
Office building
-40,000
Warehouse
10,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 19 (of 68)Minimax Regret CriterionRegret (opportunity loss) is the difference between the payoff from the best decision and all other decision payoffs in those circumstances
In this criterion decision maker attempts to avoid regret by selecting the decision alternative that minimises the maximum regret
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 20 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
State of Nature
Decision
(purchase)
Good Economic conditions
Poor Economic conditions
Apartment building
$50,000
$30,000
Office building
100,000
-40,000
Warehouse
30,000
10,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 21 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
Regret Table
State of Nature
Decision
(purchase)
Good Economic conditions
Poor Economic conditions
Apartment building
$50,000
0
Office building
0
70,000
Warehouse
70,000
20,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 22 (of 68)Quick Review Question Decision making without probability (no probability of occurrence are assigned)
Decision:
According to minimax regret criterion, the decision should be to purchase apartment building because this decision will result, at most, $50,000 in regret.
Decision (purchase)
Apartment building
$50,000
Office building
70,000
Warehouse
70,000
CT042-3-2 Probability and Statistical ModelingDecision Making Techniques
Slide 23 (of 68)Hurwicz Criterion a comprise between the maximax and maximin criteriaintroduce , the coefficient of optimism 0< 40, 0.4120,0002040, 0.2 40,000