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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-1 Decision Analysis

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-2 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...

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-3 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?

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-4 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-5 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-6 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-7 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-8 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-9 The Possible States of Nature 1) The new airport is built at location A. 2) The new airport is built at location B.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-10 Constructing a Payoff Matrix See file Fig15-1.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-11 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-12 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 A30 -10000 30 <--maximum B292929

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-13 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 A1000 28 28 B292929 <--maximum

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-14 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-15 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...

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-16 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?

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-17 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-18 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-19 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-20 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-21 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*$13 + 0.6*$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 = $11.8 - $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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-22 A Decision Tree for Magnolia Inns 0 1 2 3 4 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 13 -12 -8 11 5 0 0 31 6 4 23 35 29 0 0

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-23 Rolling Back A Decision Tree 0 1 2 3 4 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 13 -12 -8 11 5 0 0 31 6 4 23 35 29 0 0 0.4 0.6 0.4 0.6 0.4 0.6 0.4 0.6 EMV=-2 EMV=3.4 EMV=1.4 EMV= 0 EMV=3.4

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-24 Alternate Decision Tree 0 1 2 3 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 13 -12 -8 11 5 31 6 4 23 35 29 0.4 0.6 0.4 0.6 0.4 0.6 EMV=-2 EMV=3.4 EMV=1.4 EMV=3.4 0

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-25 Using TreePlan u TreePlan is an Excel add-in for decision trees. u See file Fig15-14.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-26 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-27 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-28 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 50-50 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-29 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-30 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$30,000 0.4$60,000 0.6 Cellular$40,000 0.8$70,000 0.2 Infrared$40,000 0.9$80,000 0.1 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-31 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...

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-32 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-33 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-34 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-35 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

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-36 Bayes’s Theorem u Bayes’s Theorem provides another definition of conditional probability that is sometimes helpful. u For example,

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-37 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,

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-38

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 15-39 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. = $126.82 - $126 = $0.82 million

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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

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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.

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Part 3 Probabilistic Decision Models

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