BUAD306

Chapter 5S – Decision Theory

Why DM is Important

The act of selecting a preferred course of action among alternatives

A KEY responsibility of Operations Managers

DM Applications

Some Decision Making techniques can be specific:Capacity planningLocation planningLease/Buy

But in general, we can improve Decision Making by using logical approaches

How do WE make decisions?

Alternatives? Likelihoods? Outcomes?

Reasons for Poor DM

There may be better choices that have not been considered

Information about options may be imperfect Knowledge of existing circumstances may

be imperfect Past experience may be irrelevant Prediction of the future may be wrong Chains of cause and effect are subject to

high probability of error Too much Information Peer Pressure

DM Steps

1. Identify possible future conditions (states of nature)

2. Develop a list of alternatives3. Determine the estimated payoff for each

alternative for every condition4. Estimate the likelihood of each possible

condition5. Evaluate alternatives according to some

criterion and select best alternative

States of Nature

Possible outcomes that your business may experience

Examples:Demand: High, Medium, LowContracts: Awarded, Not AwardedWeather: Rainy, Mixed, Dry

Alternatives

Choices the business can make, given the state of nature or other information

Examples: Demand: Purchase new machinery, Don’t

purchase machinery Contracts: Hire Additional Staff, Don’t Hire Weather: Invest in Irrigation System, Don’t

Invest Do Nothing

Payoff Table

*Present value in $ millions(Page 180 in text)

Alternatives

Possible Future Demand

Low Moderate High

Small 100 100 100

Medium 70 120 120

Large (40) 20 160

Likelihoods of Conditions

Estimates of likelihood Typically stated in percentages, must total

to 1.0 Based on historical data or subjective Examples:

Demand: High (50%), Medium (30%), Low (20%)

Weather: Rainy (30%), Mixed (40%), Dry (30%)

Decision Environments

Certainty - Environment in which future events will definitely occur

Uncertainty - Environment in which it is impossible to assess the likelihood of various future events

Risk - Environment in which certain future events have probable outcomes

Different environments require different analysis techniques!

DM Under Certainty

When you know for sure which of the future conditions will occur, choose the alternative with the highest payoff!

DM Under Certainty Example

*Present value in $ millions(Page 180 in text)

We know for sure demand will be a) low, b) moderate, c) high

Alternatives

Possible Future Demand

Low Moderate High

Small 100 100 100

Medium 70 120 120

Large (40) 20 160

DM Under Uncertainty

Maximin Maximax Laplace

You don’t need to know Minimax Regret or Opportunity Loss Tables.

Maximin “The best of the worst”

Determine the worst possible payoff for each alternative, then

Choose the alternative that is the “best worst”.

AltsPossible Future Demand

MaximinLow Moderate HighSmall 100 100 100

Medium 70 120 120Large (40) 20 160

Maximax “The best of the best”

Determine the best possible payoff for each alternative, then

Choose the alternative that is the “best of the best”.

AltsPossible Future Demand

MaximaxLow Moderate HighSmall 100 100 100

Medium 70 120 120Large (40) 20 160

Laplace “The best average”

Determine the average payoff for each alternative, then

Choose the alternative that is the “best average”.

AltsPossible Future Demand

LaplaceLow Moderate HighSmall 100 100 100

Medium 70 120 120Large (40) 20 160

Alt Low Mod High

Droid 200 400 600

iPhone 100 500 800

Both -200 100 1000

Decision Under Uncertainty Example:

A Product Manager for a handheld software company is trying to decide whether to create an application for the Droid, iPhone or both devices. The revenue associated with each alternative depends on the demand for the product as noted below.

•What is the Maximin choice?

•What is the Maximax choice?

•What is the LaPlace choice?

Decision Under Uncertainty Example:

A Product Manager for a handheld software company is trying to decide whether to create an application for the Droid, iPhone or both devices. The revenue associated with each alternative depends on the demand for the product as noted below.

Alt Low Mod HighMaximin Maximax Laplace

Droid 200 400 600

iPhone 100 500 800

Both -200 100 1000

X Y ZA 150 70 130B 50 200 110C 160 60 100

Example: COST

Part A: Maximin, Maximax, Laplace

DM Under Risk

Most typical in business Incorporates likelihoods into the

process Allows you to weight payoffs by the

probability that the state of nature will occur

Expected Monetary Value

The best expected value among the alternatives

Steps:For each cell in the Payoff Table,

multiple the value by the likelihood of that state of nature

Sum up weighted values and selects the best payoff

We have established likelihoods of future demand as follows: Low: .40, Medium, .50, High, .10

EMV Example:

Alternatives

Possible Future DemandLow Moderate High

Small 100 100 100

Medium 70 120 120

Large (40) 20 160

Going back to our handheld application example, we now have the following likelihoods of future demand:

Low: 30%, Moderate: 50% and High: 20%What are the EMVs for each alternative?

EMV Example:

EMVDroid

EMViPhone

EMVCombo

Alt Low Mod High

Droid 200 400 600

iPhone 100 500 800

Both -200 100 1000

X Y ZA 150 70 130B 50 200 110C 160 60 100

Example: COST

Part B: Assume the following likelihoods: X= .5, Y = .2, Z = .3

Expected Value of Perfect Information (EVPI) What if you could delay your decision

until you had more data? Would you??

How much would you be willing to pay for that extra time?

EVPI allows you to determine that figure

Calculating EVPI

Want to know if the cost of obtaining the perfect information will be less than the expected gain due to delaying your decision. Therefore:

EVPI = Expected Payoff Expected PayoffUnder Certainty Under Risk (EMV)

EMV Example:

EVPI = Expected Payoff __ Expected Payoff

Under Certainty Under Risk

Expected Payoff Under Certainty:Expected Payoff Under Risk:EVPI =

Alternatives

Possible Future DemandLow Moderate High

Small 100 100 100

Medium 70 120 120

Large (40) 20 160

Low: .40, Medium, .50, High, .10

Going back to our handheld application example, we now have the following likelihoods of future demand:

Low: 30%, Moderate: 50% and High: 20%What is the EVPI for this scenario?

EMV Example:

Expected Payoff Under Certainty =

Expected Payoff Under Risk =

Expected Value of Perfect Information =

Alt Low Mod High

Droid 200 400 600

iPhone 100 500 800

Both -200 100 1000

X Y ZA 150 70 130B 50 200 110C 160 60 100

Example: COST

Part C: EVPI

Decision Trees

Schematic representation Helpful in analyzing sequential

decisions Can see all the options in front of you

and compare easily

Decision Tree Lingo

Nodes – Square Nodes - Make a decision Round Nodes – Probabilities of events

Branches – contain information re: that decision or state of nature

Right to Left Analysis Tree Pruning

Should we run the light?

HW #9 Firm must decide to build: Small, Medium or

Large facility. Demand for all sizes could be low (.2) or high (.8). If build small and demand is low, NPV = $42. If

demand is high, can subcontract (NPV = $42) or expand greatly (NPV = $48)

If build medium and demand is low, NPV = $22. If demand is high, can do nothing (NPV = $46) or expand greatly (NPV = $50)

If build large and demand is low, NPV = -$20. If demand is high, NPV = $72.