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Decision Analysis

Chapter 15. Decision Analysis. Introduction to Decision Analysis. Models help managers gain insight and understanding, but they can’t make decisions. Decision making often remains a difficult task due to: Uncertainty regarding the future Conflicting values or objectives

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Decision Analysis

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  1. Chapter 15 Decision Analysis

  2. Introduction to Decision Analysis • Models help managers gain insight and understanding, but they can’t make decisions. • Decision making often remains a difficult task due to: • Uncertainty regarding the future • Conflicting values or objectives • Consider the following example...

  3. Deciding Between Job Offers • Company A • In a new industry that could grow or bankrupt. • Low starting salary, but could increase rapidly. • Located near friends, family and favorite sports team. • Company B • Established firm with financial strength and commitment to employees. • Higher starting salary but slower advancement opportunity. • Distant location, offering few cultural or sporting activities. • Which job would you take?

  4. Characteristics of Decision Problems • Alternatives - different courses of action intended to solve a problem. • Work for company A • Work for company B • Reject both offers and keep looking • Criteria - factors that are important to the decision maker and influenced by the alternatives. • Salary • Career potential • Location • States of Nature - future events not under the decision makers control. • Company A grows • Company A goes bankrupt • etc

  5. An Example: Magnolia Inns • Hartsfield International Airport in Atlanta, Georgia, is one of the busiest airports in the world. • It has expanded many times to handle increasing air traffic. • Commercial development around the airport prevents it from building more runways to handle future air traffic. • Plans are being made to build another airport outside the city limits. • Two possible locations for the new airport have been identified, but a final decision will not be made for a year. • The Magnolia Inns hotel chain intends to build a new facility near the new airport once its site is determined. • Land values around both possible sites for the new airport are increasing as investors speculate that property values will increase greatly in the vicinity of the new airport. • See data in file Fig15-1.xls

  6. The Decision Alternatives 1) Buy the parcel of land at location A. 2) Buy the parcel of land at location B. 3) Buy both parcels. 4) Buy nothing. The Possible States of Nature 1) The new airport is built at location A. 2) The new airport is built at location B.

  7. Decision Rules • If the future state of nature (airport location) were known, it would be easy to make a decision. • Failing this, a variety of nonprobabilistic decision rules can be applied to this problem: • Maximax • Maximin • Minimax regret • No decision rule is always best and each has its own weaknesses.

  8. State of Nature Decision 1 2 MAX A 30 -10000 30 <--maximum B 29 29 29 The Maximax Decision Rule • Identify the maximum payoff for each alternative. • Choose the alternative with the largest maximum payoff. • See file Fig15-1.xls • Weakness • Consider the following payoff matrix

  9. Weakness • Consider the following payoff matrix State of Nature Decision 1 2 MIN A 1000 28 28 B 29 29 29 <--maximum The Maximin Decision Rule • Identify the minimum payoff for each alternative. • Choose the alternative with the largest minimum payoff. • See file Fig15-1.xls

  10. The Minimax Regret Decision Rule • Compute the possible regret for each alternative under each state of nature. • Identify the maximum possible regret for each alternative. • Choose the alternative with the smallest maximum regret. • See file Fig15-1.xls

  11. Consider the following payoff matrix State of Nature Decision 1 2 A 9 2 B 4 6 • The regret matrix is: State of Nature Decision 1 2 MAX A 0 4 4 <--minimum B 5 0 5 Anomalies with the Minimax Regret Rule • Note that we prefer A to B. • Now let’s add an alternative...

  12. State of Nature Decision 1 2 A 9 2 B 4 6 C 3 9 State of Nature Decision 1 2 MAX A 0 7 7 B 5 3 5 <--minimum C 6 0 6 Adding an Alternative • Consider the following payoff matrix • The regret matrix is: • Now we prefer B to A???

  13. Probabilistic Methods • At times, states of nature can be assigned probabilities that represent their likelihood of occurrence. • For decision problems that occur more than once, we can often estimate these probabilities from historical data. • Other decision problems (such as the Magnolia Inns problem) represent one-time decisions where historical data for estimating probabilities don’t exist. • In these cases, subjective probabilities are often assigned based on interviews with one or more domain experts. • Interviewing techniques exist for soliciting probability estimates that are reasonably accurate and free of the unconscious biases that may impact an expert’s opinions. • We will focus on techniques that can be used once appropriate probability estimates have been obtained.

  14. Expected Monetary Value • Selects alternative with the largest expected monetary value (EMV) • EMVi is the average payoff we’d receive if we faced the same decision problem numerous times and always selected alternative i. • See file Fig15-1.xls

  15. Weakness • Consider the following payoff matrix State of Nature Decision 1 2 EMV A 15,000 -5,000 5,000 <--maximum B 5,000 4,000 4,500 Probability 0.5 0.5 EMV Caution • The EMV rule should be used with caution in one-time decision problems.

  16. Expected Regret or Opportunity Loss • Selects alternative with the smallest expected regret or opportunity loss (EOL) • The decision with the largest EMV will also have the smallest EOL. • See file Fig15-1.xls

  17. The Expected Value of Perfect Information • Suppose we could hire a consultant who could predict the future with 100% accuracy. • With such perfect information, Magnolia Inns’ average payoff would be: EV with PI = 0.4*$13 + 0.6*$11 = $11.8 (in millions) • Without perfect information, the EMV was $3.4 million. • The expected value of perfect information is therefore, EV of PI = $11.8 - $3.4 = $8.4 (in millions) • In general, EV of PI = EV with PI - maximum EMV • It will always be the the case that, EV of PI = minimum EOL

  18. Land Purchase Decision Airport Location Payoff 13 A 31 Buy A 1 -18 6 -12 B A -8 4 Buy B 2 -12 23 B 11 0 5 A 35 Buy A&B 3 -30 29 -1 B A 0 0 Buy nothing 4 0 0 B 0 A Decision Tree for Magnolia Inns

  19. Land Purchase Decision Airport Location Payoff 0.4 13 A 31 Buy A 1 EMV=-2 -18 6 -12 B 0.6 0.4 A -8 4 Buy B 2 -12 EMV=3.4 23 B 11 0.6 0 0.4 5 A 35 Buy A&B EMV=3.4 3 -30 EMV=1.4 29 -1 B 0.6 0.4 A 0 0 Buy nothing 4 EMV= 0 0 0 B 0 0.6 Rolling Back A Decision Tree

  20. Alternate Decision Tree Land Purchase Decision Airport Location Payoff 0.4 13 A 31 Buy A 1 EMV=-2 -18 6 -12 B 0.6 0.4 A -8 4 Buy B 2 -12 EMV=3.4 23 B 11 0.6 0 0.4 5 A 35 Buy A&B EMV=3.4 3 -30 EMV=1.4 29 -1 B 0.6 Buy nothing 0 0

  21. Multi-stage Decision Problems • Many problems involve a series of decisions • Example • Should you go out to dinner tonight? • If so, • How much will you spend? • Where will you go? • How will you get there? • Multistage decisions can be analyzed using decision trees

  22. Technology Equipment Cost Microwave $4,000 Cellular $5,000 Infrared $4,000 continued... Multi-Stage Decision Example: COM-TECH • Steve Hinton, owner of COM-TECH, is considering whether to apply for a $85,000 OSHA research grant for using wireless communications technology to enhance safety in the coal industry. • Steve would spend approximately $5,000 preparing the grant proposal and estimates a 50-50 chance of receiving the grant. • If awarded the grant, Steve would need to decide whether to use microwave, cellular, or infrared communications technology. • Steve would need to acquire some new equipment depending on which technology is used…

  23. Steve knows he will also spend money in R&D, but he doesn’t know exactly what the R&D costs will be. Steve estimates the following best case and worst case R&D costs and probabilities, based on his expertise in each area. Best Case Worst Case Cost Prob. Cost Prob. Microwave $30,000 0.4 $60,000 0.6 Cellular $40,000 0.8 $70,000 0.2 Infrared $40,000 0.9 $80,000 0.1 COM-TECH(continued) • Steve needs to synthesize all the factors in this problem to decide whether or not to submit a grant proposal to OSHA. • See file Fig15-26.xls

  24. The $13,500 EMV for COM-TECH was created as follows: Event Probability Payoff Receive grant, Low R&D costs 0.5*0.9=0.45 $36,000 Receive grant, High R&D costs 0.5*0.1=0.05 -$4,000 Don’t receive grant 0.5 -$5,000 EMV $13,500 Risk Profiles • A risk profile summarizes the make-up of an EMV • This can also be summarized in a decision tree. • See file Fig15-28.xls

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