Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Decision Analysis

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Introduction to Decision Analysis u Models help managers gain insight and understanding, but they can’t make decisions. u Decision making often remains a difficult task due to: –uncertainty regarding the future –conflicting values or objectives u Consider the following example...

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Deciding Between Job Offers u Company A –In a new industry that could boom or bust. –Low starting salary, but could increase rapidly. –Located near friends, family and favorite sports team. u 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. u Which job would you take?

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Good Decisions vs. Good Outcomes u A structured approach to decision making can help us make good decisions, but can’t guarantee good outcomes. u Good decisions sometimes result in bad outcomes.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Characteristics of Decision Problems u Alternatives - different courses of action intended to solve a problem. –Work for company A –Work for company B –Reject both offers and keep looking u Criteria - factors that are important to the decision maker and influenced by the alternatives. –Salary –Career potential –Location u States of Nature - future events not under the decision makers control. –Company A grows –Company A goes bust –etc

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning An Example: Magnolia Inns u Hartsfield International Airport in Atlanta, Georgia, is one of the busiest airports in the world. u It has expanded numerous times to accommodate increasing air traffic. u Commercial development around the airport prevents it from building additional runways to handle the future air traffic demands. u Plans are being developed to build another airport outside the city limits.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning An Example: Magnolia Inns (con’t) u Two possible locations for the new airport have been identified, but a final decision is not expected to be made for another year. u The Magnolia Inns hotel chain intends to build a new facility near the new airport once its site is determined. u Land values around the two possible sites for the new airport are increasing as investors speculate that property values will increase greatly in the vicinity of the new airport. u See data in file Fig15-1.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning 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.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Possible States of Nature 1) The new airport is built at location A. 2) The new airport is built at location B.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Constructing a Payoff Matrix See file Fig15-1.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Decision Rules u If the future state of nature (airport location) were known, it would be easy to make a decision. u Failing this, a variety of nonprobabilistic decision rules can be applied to this problem: –Maximax –Maximin –Minimax regret u No decision rule is always best and each has its own weaknesses.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Maximax Decision Rule u Identify the maximum payoff for each alternative. u Choose the alternative with the largest maximum payoff. u See file Fig15-1.xls u Weakness –Consider the following payoff matrix State of Nature Decision 1 2 MAX A <--maximum B292929

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Maximin Decision Rule u Identify the minimum payoff for each alternative. u Choose the alternative with the largest minimum payoff. u See file Fig15-1.xls u Weakness –Consider the following payoff matrix State of Nature Decision 1 2 MIN A B <--maximum

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Minimax Regret Decision Rule u Compute the possible regret for each alternative under each state of nature. u Identify the maximum possible regret for each alternative. u Choose the alternative with the smallest maximum regret. u See file Fig15-1.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Anomalies with the Minimax Regret Rule u Consider the following payoff matrix State of Nature Decision 1 2 A9 2 B46 State of Nature Decision 1 2 MAX A0 4 4 <--minimum B505 u The regret matrix is: u Note that we prefer A to B. u Now let’s add an alternative...

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Adding an Alternative u Consider the following payoff matrix State of Nature Decision 1 2 A9 2 B46 C39 State of Nature Decision 1 2 MAX A0 7 7 B535 <--minimum C606 u The regret matrix is: u Now we prefer B to A?

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Probabilistic Methods u Sometimes, the states of nature can be assigned probabilities that represent their likelihood of occurrence. u For decision problems that occur more than once, we can often estimate these probabilities from historical data. u Other decision problems (such as the Magnolia Inns problem) represent one-time decisions where historical data for estimating probabilities don’t exist. u In these cases, probabilities are often assigned subjectively based on interviews with one or more domain experts. u Highly structured interviewing techniques exist for soliciting probability estimates that are reasonably accurate and free of the unconscious biases that may impact an expert’s opinions. u We will focus on techniques that can be used once appropriate probability estimates have been obtained.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Expected Monetary Value u Selects alternative with the largest expected monetary value (EMV)  EMV i is the average payoff we’d receive if we faced the same decision problem numerous times and always selected alternative i. u See file Fig15-1.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning EMV Caution u The EMV rule should be used with caution in one-time decision problems. u Weakness –Consider the following payoff matrix State of Nature Decision 1 2 EMV A15,000 -5,000 5,000 <--maximum B5,0004,0004,500 Probability0.50.5

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Expected Regret or Opportunity Loss u Selects alternative with the smallest expected regret or opportunity loss (EOL) u The decision with the largest EMV will also have the smallest EOL. u See file Fig15-1.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Expected Value of Perfect Information u Suppose we could hire a consultant who could predict the future with 100% accuracy. u With such perfect information, Magnolia Inns’ average payoff would be: EV with PI = 0.4*$ *$11 = $11.8 (in millions) u Without perfect information, the EMV was $3.4 million. u The expected value of perfect information is therefore, EV of PI = $ $3.4 = $8.4 (in millions) u In general, EV of PI = EV with PI - maximum EMV u It will always be the case that, EV of PI = minimum EOL

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning A Decision Tree for Magnolia Inns Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B B A A Payoff

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Rolling Back A Decision Tree Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B B A A Payoff EMV=-2 EMV=3.4 EMV=1.4 EMV= 0 EMV=3.4

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Alternate Decision Tree Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B A Payoff EMV=-2 EMV=3.4 EMV=1.4 EMV=3.4 0

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Using TreePlan u TreePlan is an Excel add-in for decision trees. u See file Fig15-14.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning About TreePlan u TreePlan is a shareware product developed by Dr. Mike Middleton at the University of San Francisco and distributed with this textbook at no charge to you. u If you like this software package and plan to use for more than 30 days, you are expected to pay a nominal registration fee. Details on registration are available near the end of the TreePlan help file.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Multi-stage Decision Problems u Many problems involve a series of decisions u Example –Should you go out to dinner tonight? –If so, v How much will you spend? v Where will you go? v How will you get there? u Multi-stage decisions can be analyzed using decision trees

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Multi-Stage Decision Example: COM-TECH u Steve Hinton, owner of COM-TECH, is considering whether or not to apply for a $85,000 OSHA research grant for using wireless communications technology to enhance safety in the coal industry. u Steve would spend approximately $5,000 preparing the grant proposal and estimates a chance of actually receiving the grant. u If awarded the grant, Steve would then need to decide whether to use microwave, cellular, or infrared communications technology.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning COM-TECH (continued) u Steve would need to acquire some new equipment depending on which technology is used. The cost of the equipment is summarized as: TechnologyEquipment Cost Microwave$4,000 Cellular$5,000 Infrared$4,000 u Steve knows he will also spend money in R&D, but he doesn’t know exactly what the R&D costs will be.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning COM-TECH (continued) u Steve needs to synthesize all the factors in this problem to decide whether or not to submit a grant proposal to OSHA. u See file Fig15-26.xls Cost Prob.Cost Prob. Microwave$30, $60, Cellular$40, $70, Infrared$40, $80, Best Case Worst Case u Steve estimates the following best case and worst case R&D costs and probabilities, based on his expertise in each area.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Analyzing Risk in a Decision Tree u How sensitive is the decision in the COM-TECH problem to changes in the probability estimates? u We can use Solver to determine the smallest probability of receiving the grant for which Steve should still be willing to submit the proposal. u Let’s go back to file Fig15-26.xls...

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Risk Profiles u A risk profile summarizes the make-up of an EMV. u The $13,500 EMV for COM-TECH was created as follows: Event Probability Payoff Receive grant, Low R&D costs0.5*0.9=0.45$36,000 Receive grant, High R&D costs0.5*0.1=0.05-$4,000 Don’t receive grant0.5-$5,000 EMV$13,500 u This can also be summarized in a decision tree. u See file Fig15-29.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Using Sample Information in Decision Making u We can often obtain information about the possible outcomes of decisions before the decisions are made. u This sample information allows us to refine probability estimates associated with various outcomes.

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Example: Colonial Motors u Colonial Motors (CM) needs to determine whether to build a large or small plant for a new car it is developing. u The cost of constructing a large plant is $25 million and the cost of constructing a small plant is $15 million. u CM believes a 70% chance exists that demand for the new car will be high and a 30% chance that it will be low. u The payoffs (in millions of dollars) are summarized below. Demand Factory SizeHighLow Large$175 $95 Small$125$105 u See decision tree in file Fig15-32.xls

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Including Sample Information u Before making a decision, suppose CM conducts a consumer attitude survey. If the survey response is unfavorable, this should increase CM’s belief that demand will be low. u Past performance of survey company is shown below: –The company predicts high demand with 86% probability P(F|H) –The company predicts low demand with 78% probability P(U|L) u How much should CM be willing to pay to conduct the consumer attitude survey? u We will combine prior probabilities with performane of company (conditional probabilities) using Bayes’ Theorem

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning Bayes’s Theorem u Bayes’s Theorem provides another definition of conditional probability that is sometimes helpful. u For example,

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning u Prior Probabilities P(H)=0.7, P(L)=0.3 u Conditional Probabilities u P(F|H)=0.86, P(U|L)=0.78, P(F|U)=0.14, P(U|H)=0.22 u The joint probabilities indicate: u The marginal probabilities indicate: u Posterior Probabilities,

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning The Expected Value of Sample Information u How much should CM be willing to pay to conduct the consumer attitude survey? Expected Value of Sample Information Expected Value with Sample Information Expected Value without Sample Information = - u In the CM example, E.V. of Sample Info. = $ $126 = $0.82 million

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. BILL GALLEN DEVELOPMENT COMPANY – B. G. D. plans to do a commercial development on a property. – Relevant data v Asking price for the property is $300,000 v Construction cost is $500,000 v Selling price is approximated at $950,000 v Variance application costs $30,000 in fees and expenses –There is only 40% chance that the variance will be approved. –If B. G. D. purchases the property and the variance is denied, the property can be sold for a net return of $260,000 –A three month option on the property costs $20,000 which will allow B.G.D. to apply for the variance. v A consultant can be hired for $5000 –P (Consultant predicts approval | approval granted) = 0.70 –P (Consultant predicts denial | approval denied) = 0.90

Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. What should BGD do? u Construction of the Decision Tree –Initially the company faces a decision about hiring the consultant. –After this decision is made more decisions follow regarding v Application for the variance. v Purchasing the option. v Purchasing the property.