decision making theory

48
Managerial Decision Modeling with Spreadsheets Chapter 8 Decision Theory

Upload: drpanu

Post on 27-Oct-2014

382 views

Category:

Documents


10 download

TRANSCRIPT

Page 1: Decision Making Theory

Managerial Decision Modeling with Spreadsheets

Chapter 8

Decision Theory

Page 2: Decision Making Theory

Learning Objectives

• List steps of decision making process.• Describe different types of decision making

environments.• Make decisions under uncertainty when probabilities are

not known.• Make decisions under risk when probabilities are known.• Use Excel for problems involving decision tables.• Develop accurate and useful decision trees.• Use TreePlan to set up and analyze decision tree

problems with Excel.• Revise probability estimates using Bayesian analysis.• Understand the importance and use of utility theory in

decision making.

Page 3: Decision Making Theory

8.1 Introduction • Decision theory is analytic and systematic approach to

study of decision-making. • What makes difference between good and bad

decisions? • Good decisions may be defined as:

– Based on logic, – Considered all possible decision alternatives,– Examined all available information about future, and– Applied decision modeling approach.

• Bad decision may be defined as: – Not based on logic, – Did not use all available information, – Did not consider all alternatives, and – Did not employ appropriate decision modeling techniques.

Page 4: Decision Making Theory

8.2 Five Steps of Decision Making

1. Clearly define problem at hand.

2. List all possible decision alternatives.

3. Identify possible future outcomes for each decision

alternative.

4. Identify payoff (usually, profit or cost) for each

combination of alternatives and outcomes.

5. Select one of decision theory modeling techniques,

apply decision model, and make decision.

Page 5: Decision Making Theory

Thompson Lumber Company Step 1. Identifies problem as: whether to expand product line by manufacturing and

marketing new product which is “backyard storage sheds.”

Step 2. Generate decision alternatives available. Decision alternative is defined as course of action or

strategy that may be chosen by decision maker. Alternatives are to construct:

(1) large plant to manufacture storage sheds, (2) small plant to manufacture storage sheds, or (3) build no plant at all.

Step 3. Identify possible future outcomes of various alternatives.

Page 6: Decision Making Theory

Thompson Lumber Company

Step 4. Express payoff resulting from each possible

combination of alternatives and outcomes.

Objective is to maximize profits.

Step 5. Select decision theory model and apply it to

data to help make decision.

Type of decision model available depends on

operating environment and amount of uncertainty and

risk involved.

Page 7: Decision Making Theory

Thompson Lumber Company

Page 8: Decision Making Theory

8.3 Types Of Decision Making Environments

 Type 1: Decision Making under Certainty. Decision maker knows with certainty consequence of every decision alternative.

Type 2: Decision Making under Uncertainty. Decision maker has no information about various outcomes.

Type 3: Decision Making under Risk. Decision maker has some knowledge regarding probability of occurrence of each outcome or state of nature.

Examples:

• Probability of being dealt club from deck of cards is 1/4.

• Probability of rolling 5 on die is 1/6.

Page 9: Decision Making Theory

8.4 Decision Making Under Uncertainty

• Criteria for making decisions under uncertainty.

1. Maximax.

2. Maximin.

3. Equally likely.

4. Criterion of realism.

5. Minimax regret.

• First four criteria calculated directly from decision payoff table.

• Fifth minimax regret criterion requires use of opportunity loss table.

Page 10: Decision Making Theory

Maximax Criterion• Maximax criterion selects alternative maximizes

maximum payoff over all alternatives. • First locate maximum payoff for each alternative.• Select alternative with maximum number. • Decision criterion locates alternative with highest

possible gain.• Called optimistic criterion. • Table shows maximax choice is first alternative:

"construct large plant." • $200,000 payoff is maximum of maximum payoffs

for each decision alternative.

Page 11: Decision Making Theory

Maximax Criterion

• Maximax criterion selects alternative that maximizes maximum payoff over all alternatives.

• First alternative, "construct a large plant”, $200,000 payoff is maximum of maximum payoffs for each decision alternative.

Thompson Lumber Company

Page 12: Decision Making Theory

Maximin Criterion• Maximin criterion finds alternative maximizes

minimum payoff over all alternatives.

• First locate minimum payoff for each alternative.

• Select alternative with maximum number.

• Decision criterion locates alternative that has least possible loss.

• Called pessimistic criterion.

• Maximin choice, "do nothing," is shown in table.

• $0 payoff is maximum of minimum payoffs for each alternative.

Page 13: Decision Making Theory

Maximin Criterion

• Maximin criterion finds alternative maximizes minimum payoff over all alternatives.

• First locate minimum payoff for each alternative, and select alternative with maximum number.

Thompson Lumber Company

Page 14: Decision Making Theory

Equally Likely (Laplace) Criterion

• Equally likely, also called Laplace, criterion finds decision alternative with highest average payoff.

• Calculate average payoff for every alternative.• Pick alternative with maximum average payoff.• Assumes all probabilities of occurrence for states of

nature are equal. • Equally likely choice is second alternative, "construct

a small plant." • Strategy shown in table has maximum average payoff

($40,000) over all alternatives.

Thompson Lumber Company:

Page 15: Decision Making Theory

Equally Likely (Laplace) Criterion

• Equally likely criterion finds decision alternative with highest average payoff.

• Calculate average payoff for every alternative.

• Pick alternative with maximum average payoff.

Thompson Lumber Company

Page 16: Decision Making Theory

Criterion of Realism (Hurwicz)

• Often called weighted average, the criterion of realism (or Hurwicz) decision criterion is compromise between optimistic and pessimistic decision.

• Select coefficient of realism, , with value between 0 and 1.

– When is close to 1, decision maker is optimistic about future.

– When is close to 0, decision maker is pessimistic about future.  

Page 17: Decision Making Theory

Criterion of Realism

Formula for criterion of realism =

x (maximum payoff for alternative) +

(1-) x (minimum payoff for alternative)

• Assume coefficient of realism 0.80.

• Best decision would be to construct a large plant.

• Alternative has highest weighted average payoff:

$124,000 = (0.80)($200,000) + (0.20)(- $180,000).

Page 18: Decision Making Theory

Criterion of Realism

Coefficient of realism 0.80.

$124,000 = (0.80)($200,000) + (0.20)(- $180,000).

Thompson Lumber Company

Page 19: Decision Making Theory

Minimax Regret Criterion• Final decision criterion is based on opportunity loss.

• Opportunity loss, also called regret, is difference

between optimal payoff and actual payoff received.

• Develop opportunity loss table.

• Determine opportunity loss of not choosing best

alternative for each state of nature.

• Opportunity loss for any state of nature, or any

column, calculated by subtracting each outcome in

column from best outcome in same column.

Page 20: Decision Making Theory

Minimax Regret Criterion

• Best outcome for favorable market is $200,000 as

result of first alternative, "construct a large plant."

• Subtract all payoffs in column from $200,000.

• Best outcome for unfavorable market is $0 as result

of third alternative, "do nothing."

• Subtract all payoffs in column from $0.

• Table illustrates computations and shows complete

opportunity loss table.

Thompson Lumber Company

Page 21: Decision Making Theory

Minimax Regret Criterion

• Table illustrates computations and shows complete opportunity loss table.

Thompson Lumber Company

Page 22: Decision Making Theory

Minimax Regret Criterion

• Once opportunity loss table has been constructed, locate maximum opportunity loss within each alternative.

• Pick alternative with minimum number.

• Minimax regret choice is second alternative, "construct a small plant." Regret of $100,000 is minimum of maximum regrets over all alternatives.

Thompson Lumber Company

Page 23: Decision Making Theory

Using Excel to Solve Decision Making Problems Under Uncertainty Formulas

Page 24: Decision Making Theory

Using Excel to Solve Decision Making Problems Under Uncertainty Solutions

Page 25: Decision Making Theory

8.5 Decision Making Under Risk

• Common for decision maker to have some idea about

probabilities of occurrence of different outcomes or

states of nature.

• Probabilities may be based on decision maker’s

personal opinions about future events, or on data

obtained from market surveys, expert opinions, etc.

• When probability of occurrence of each state of nature

can be assessed, problem environment is called

decision making under risk.

Page 26: Decision Making Theory

Expected Monetary Value• Given decision table with conditional values (payoffs) and

probability assessments, determine expected monetary value (EMV) for each alternative.

• Computed as weighted average of all possible payoffs for alternative, where weights are probabilities of different states of nature: 

EMV (alternative i) =

(payoff of first state of nature) x (probability of first

state of nature) +

(payoff of second state of nature) x (probability of second

state of nature) + . . . +

(payoff of last state of nature) x (probability of last

state of nature)

Page 27: Decision Making Theory

• Probability of favorable market is same as probability of unfavorable market.

• Each state of nature has a 0.50 probability.

Expected Monetary ValueThompson Lumber Company

Page 28: Decision Making Theory

Expected Opportunity Loss• Alternative approach in decision making under risk is to

minimize expected opportunity loss (EOL).

• Opportunity loss, also called regret, refers to difference between optimal profit or payoff and actual payoff received.

• EOL for an alternative is sum of all possible regrets of alternative, each weighted by probability of state of nature for that regret occurring.

  EOL (alternative i) = (regret of first state of nature)

x (probability of first state of nature)

+ (regret of second state of nature)

x (probability of second state of nature)

+ . . . + (regret of last state of nature)

x (probability of last state of nature)

Page 29: Decision Making Theory

EOL Decision

• EOL values are computed as shown.

• Using minimum EOL as decision criterion, best decision would be second alternative, "construct a small plant" with an EOL of $60,000.

• Minimum EOL will always result in same decision alternative as maximum EMV.

Thompson Lumber Company

Page 30: Decision Making Theory

Expected Value of Perfect Information• Expected value with perfect information is expected or

average return, if one has perfect information before decision has to be made.

• Choose best alternative for each state of nature and multiply its payoff times probability of occurrence of that state of nature:Expected value with perfect information (EV with PI) =(best payoff for first state of nature)x (probability of first state of nature)+ (best payoff for second state of nature)x (probability of second state of nature)+ . . . + (best payoff for last state of nature)x (probability of last state of nature)

EVPI = EV with PI - maximum EMV

Page 31: Decision Making Theory

EV with PI and EVPI• Best outcome for state of nature "favorable market" is

"build a large plant" with a payoff of $200,000. • Best outcome for state of nature "unfavorable market" is

"do nothing," with payoff of $0. • Expected value with perfect information (EV with PI) = ($200,000)(0.50) + ($0)(0.50) = $ 100,000. • If one had perfect information, an average payoff of

$100,000 if decision could be repeated many times.• Maximum EMV or expected value without perfect

information, is $40,000. • EVPI = EV with PI - maximum EMV = $100,000 - $40,000 = $60,000.

Page 32: Decision Making Theory

Using Excel to Solve Decision Making Problems Under Risk Formulas View

Page 33: Decision Making Theory

Using Excel to Solve Decision Making Problems Under Risk Formulas View

Page 34: Decision Making Theory

8.6 Decision Trees

• Any problem presented in decision table can be graphically illustrated in decision tree.

• All decision trees are similar in that they contain decision nodes (or points) and state of nature nodes (or points).

• These nodes are represented using following symbols: = A decision node.

Arcs (lines) originating from decision node denote all decision alternatives available at that node.

О = A state of nature (or chance) node. Arcs (lines) originating from a chance node denote all states of nature that could occur at that node.

Page 35: Decision Making Theory

Decision Tree

• Tree usually begins with decision node.

• Decision is determine whether to construct large plant, small plant, or no plant.

• Once decision is made, one of two possible states of nature (favorable or unfavorable market) will occur.

Thompson Lumber Company

Page 36: Decision Making Theory

Folding Back a Decision Tree

• In folding back decision tree, use following two rules:

– At each state of nature (or chance) node, compute expected value using probabilities of all possible outcomes at that node and payoffs associated with outcomes.

– At each decision node, select alternative that yields better expected value or payoff.

Thompson Lumber Company

Page 37: Decision Making Theory

Reduced Decision Tree

• Using rule for decision nodes, select alternative with highest EMV.

• Corresponds to alternative to build small plant. • Resulting EMV is $40,000.

Thompson Lumber Company

Page 38: Decision Making Theory

Decision Trees for Multi-stage Decision Making Problems

Page 39: Decision Making Theory

Decision Tree With EMVs Shown

Thompson Lumber Company

Page 40: Decision Making Theory

Expected Value of Sample Information

• One way of measuring value of market information is to compute the expected value of sample information (EVSI), as follows:

Page 41: Decision Making Theory

8.8 Estimating Probability Values Using Bayesian Analysis

• There are many ways of getting probability data for

problem.

• Numbers (e.g., 0.78, 0.22, 0.27, 0.73 ) can be

assessed by manager based on experience and

intuition.

• They can be derived from historical data or

computed from other available data using Bayes’

theorem.

Page 42: Decision Making Theory

Calculating Revised Probabilities• Assume following four conditional probabilities

were known.

Page 43: Decision Making Theory

Market Survey Reliability in Predicting Actual States of Nature

Page 44: Decision Making Theory

Market Survey Reliability in Predicting Actual States of Nature

Page 45: Decision Making Theory

Probability Revisions Given Positive Survey

Page 46: Decision Making Theory

Probability Revisions Given Negative Survey

Page 47: Decision Making Theory

Potential Problems in Using Survey Results

• Survey results or pilot studies are done before actual decision is made.

• Bayes’ analysis used to help determine correct conditional probabilities

• Need to have data about surveys and accuracy.

• Cannot get data about those situations in which decision was not to build a plant or not to take some course of action.

• Probabilities are based only on cases in which decision to build a plant or take some course of action is actually made.

• Conditional probability information is not quite as accurate as desired.

Page 48: Decision Making Theory

Summary• Introduced decision theory to study decision making. • Studied (1) decision making under certainty, (2) decision

making under uncertainty, and (3) decision making under risk.

• Identified best alternatives using criteria: maximax, maximin, equally likely, criterion of realism, and minimax regret.

• Discussed computation and use: expected monetary value (EMV), expected opportunity loss (EOL), and expected value of perfect information (EVPI).

• Decision trees were used for larger decision problems in which decisions had to be made in sequence.

• Computed expected value of sample information (EVSI).• Bayesian analysis used to revise or update probability values.• Discussed how decision trees can be set up and solved using

TreePlan, an Excel add-in.