How to calculate evpi from decision tree

Operations and Supply Chain Management

MGMT 3306

Lecture 08

Outline

Use Decision Tree to evaluate capacity alternatives

Fundamentals of decision making

Decision Tree

Decision making under risk

Expected Monetary Value (EMV)

Decision making with certainty

Expected Value with Perfect Information (EVPI)

Decision making under uncertainty

Decision Theory

Decision making when the outcomes associated with alternatives are in doubt.

A manager makes choices using the following process:

List a reasonable number of feasible alternatives;

List the events (States of nature);

Calculate the payoffs for each alternative in each state;

Estimate the probability of occurrence for each state;

Select the decision rule to evaluate the alternatives;

Pick the “best” alternative based on the decision rule.

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Fundamentals of decision making

Concepts

State of nature (Event): An occurrence or a situation over which the decision maker has little or no control (e.g. tomorrow’s weather.)

Alternative: A course of actions or strategy that may be chosen by a decision maker

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Note on Event

For an occurrence to be a state of nature (or event ), it has to satisfy three conditions:

The occurrence involves uncertainty.

The decision maker has little or no control over the uncertainty involved.

The uncertainty has impact on the outcomes of the actions to be taken.

A simple example: Fundamentals

You watch the weather forecast for the coming Saturday and there is a 30% of chance of raining. You have to decide whether to go out this Saturday and if so whether to bring an umbrella.

Question 1: What are the possible outcomes?

Question 2: What is the event and what are the possible states of event?

Question 3: What are the possible actions available?

A simple example: Answers

The possible outcomes in this case are that you get wet or stay dry.

In this case, the weather on Saturday is an event. It is uncertain, out of your control, and has an impact on the outcome. It has two states that affect the outcomes: rain and not rain.

And you have three alternatives in each possible state of the event: rain or not rain:

Go out and bring an umbrella.

Go out and do not bring an umbrella.

Do not go out.

Decision Tree

Decision tree: a schematic model of the sequence of steps in a problem and the conditions and consequences of each step.

Decision tree helps understand problem and helps find solution.

Symbols used in a decision tree:

Decision node for which one of several alternatives may be selected:

A state-of-nature/event node out of which one state of nature will occur:

Example: Decision Tree

Getz Products company is investigating the possibility of producing and marketing backyard storage sheds. Undertaking this project would require the construction of either a large or a small manufacturing plant. The market for the product produced could be either favorable or unfavorable. Getz, of course, has the option of not developing the new product line at all.

Please depict the problem using a decision tree.

Note that “Do nothing” is also a feasible option.

Example: Decision Tree

Build a big plant

Build a small plant

Do nothing

Favorable market

Unfavorable market

Favorable market

Unfavorable market

Outcome 1

Outcome 2

Outcome 3

Outcome 4

Outcome 5

Example: Now we add numbers

Now let’s add some numbers to the problem:

Suppose there is a 50% possibility for the market to be favorable and 50% unfavorable for the product.

A large plant in a favorable market yields a net profit of $ 200,000; A large plant in an unfavorable market yields a net profit of -$180,000.

A small plant in a favorable market yields a net profit of $ 100,000; A small plant in an unfavorable market yields a net profit of - $20,000.

Doing nothing yields $0 in either market.

Which alternative to choose to maximize the expected net profit?

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Example: Decision Tree

Decision tree with all the probabilities and monetary value:

Build a big plant

Build a small plant

Do nothing

50% Favorable market

50%Unfavorable market

50% Favorable market

50% Unfavorable market

$200,000

- $180,000

$100,000

-$20,000

$0

Decision making under risk

To select an alternative, we need to calculate the EMV (Expected Monetary value) of each alternative.

EMV is the sum of all the possible payoffs from the alternative, each weighted by the probability of that payoff occurring.

A simple example: Suppose you choose to bid and have a 30% of chance of winning $1000 and 70% of chance of losing $500. Then the EMV of your decision of bidding is 30% * $1000 + 70% * (-$500) = - $50

Example: EMVs

Decision tree with EMVs

Build a big plant

Build a small plant

Do nothing

50% Favorable market

50%Unfavorable market

50% Favorable market

50% Unfavorable market

$200,000

- $180,000

$100,000

-$20,000

$0

EMV (Big) = 50%*$200,000 + 50%* (-$180,000) = $10,000

EMV (Small) = 50%*$100,000+50%*(-$20,000) = $ 40,000 (Highest)

EMV (Do nothing) = $0

Decision making under certainty

Now suppose the operations manager of Getz Products has been approached by a marketing research firm. The firm claims that their technical analysis will tell Getz with certainty whether the market is favorable for the product.

In other words, the marketing research firm can change Getz’s environment from one of decision making under risk to one of decision making under certainty.

The value of the information that eliminates the risk in decision making is called Expected Value of Perfect Information (EVPI).

EVPI

EVPI is the difference between the payoff under certainty and the payoff under risk

EVPI = Expected value with perfect information – Maximum EMV

Expected value with perfect information (EVwPI) = (Best outcome or consequence for 1st state of nature) * (Probability of 1st state of nature)
+ Best outcome for 2nd state of nature) * (Probability of 2nd state of nature)
+ … + Best outcome for last state of nature) * (Probability of last state of nature)
Example: EVwPI

The best outcome for the state of nature “favorable market” is “build a large facility” with a payoff of $200,000.

The best outcome for “unfavorable” is “do nothing” with a payoff of $0.

Therefore, Expected value with perfect information = ($200,000)(.50) + ($0)(.50) = $100,000

Example: EVPI

The maximum EMV is $40,000, which is the expected outcome without perfect information. (We have already calculated it in the example for EMV.)

Thus, EVPI = EVwPI – Maximum EMV

= $100,000 – $40,000

= $60,000

Therefore, the perfect information is worth $60,000 at maximum.

Another Example:

Andrew Thomas, a sandwich vendor at Hard Rock Café’s annual Rock fest, created a table of conditional values for the various alternatives (stocking decisions) and states of nature (size of crowd):

States of nature (Demand)
Alternatives Big Average Small
Large Stock $22,000 $12,000 -$2,000
Average Stock $14,000 $10,000 $6,000
Small stock $9,000 $8,000 $4,000
Another Example:

The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand.

Question 1: Which is the alternative that provides Andrew the greatest expected monetary value (EMV)?

Question 2: Compute the EMPV.

Decision making under uncertainty

When we cannot assess probabilities for each possible outcome, we reply on three decision rules.

Maximax: Find the maximum outcome within every alternative, and then pick the alternative with the maximum number. Maximax is called an “optimistic” decision criterion.

Maximin: Find the min outcome within every alternative, and then pick the alternative with the maximum number. Called a “pessimistic” decision criterion.

Equally likely: Find the alternative with the highest average outcome

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Example: Maximax Criterion

Suppose there are two alternatives and an event with 2 possible states. Alternative 1 has a payoff of $500 in State 1 and a payoff of -$300 in State 2. Alternative 2 has a payoff of $1000 in State 1 and a payoff of -$1000 in State 2.

Based on the Maximax criterion, Alternative 2 would be chosen since the maximum outcome of Alternative 2, $1000, is higher than that of Alternative 1.

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Example: Maximin Criterion

Suppose there are two alternatives and an event with 2 possible states. Alternative 1 has a payoff of $500 in State 1 and a payoff of -$300 in State 2. Alternative 2 has a payoff of $1000 in State 1 and a payoff of -$1000 in State 2.

Based on the Maximin criterion, Alternative 1 would be chosen since the minimum outcome of Alternative 1, -$300, is higher than that of Alternative 2, -$1000.

Example: Equally Likely Criterion

Suppose there are two alternatives and an event with 2 possible states. Alternative 1 has a payoff of $500 in State 1 and a payoff of -$300 in State 2. Alternative 2 has a payoff of $1000 in State 1 and a payoff of -$1000 in State 2.

Based on the Equally Likely criterion,

EMV of Alternative 1 = 50%*$500 + 50%*(-$300) = $100

EMV of Alternative 2 = 50%*$1000 + 50%*(-$1000) = $0

Note that probabilities would be equalized under this criterion.