Ch15 Decision Analysis PDF

Decision Analysis Chapter 15 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distribu...

Decision Analysis Chapter 15 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Introduction Business analytics is about making better decisions Decision analysis can be used to develop an optimal strategy: When a decision maker is faced with several decision alternatives and an uncertain or risk-filled pattern of future events For example: The State of North Carolina used decision analysis in evaluating whether to implement a medical screening test to detect metabolic disorders in newborns A good decision analysis includes careful consideration of risk Risk analysis helps to provide the probability information about the favorable as well as the unfavorable outcomes that may occur Decision analysis considers problems that involve reasonably few decision alternatives and reasonably few possible future events © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 2 Problem Formulation The first step in the decision analysis process is problem formulation: Create verbal statement of the problem Identify the decision alternatives: The uncertain future events, referred to as chance events The outcomes associated with each combination of decision alternative and chance event outcome © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 3 Problem Formulation Example: Construction project of Pittsburgh Development Corporation PDC commissioned preliminary architectural drawings for three different projects: One with 30 condominiums One with 60 condominiums One with 90 condominiums The financial success of the project depends on: The size of the condominium complex The chance event concerning the demand for the condominiums © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 4 Problem Formulation The statement of the PDC decision problem is to select the size of the new luxury condominium project that will lead to the largest profit given the uncertainty concerning the demand for the condominiums PDC has the following three decision alternatives: d1 = a small complex with 30 condominiums d2 = a medium complex with 60 condominiums d3 = a large complex with 90 condominiums In decision analysis, the possible outcomes for a chance event are the states of nature: The chance event concerning the demand for the condominiums has two states of nature: s1 = strong demand for the condominiums s2 = weak demand for the condominiums © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 5 Problem Formulation Payoff Tables Table 15.1: Payoff Table for the PDC Condominium Project ($ Millions) Payoff is the outcome resulting from a specific combination of a decision alternative and a state of nature Payoff table is a table We will use the notation Vij to denote the payoff associated with decision alternative i showing payoffs for all and state of nature j combinations of Using Table 15.1, V31 = 20 indicates that a decision alternatives payoff of $20 million occurs if the decision is and states of nature to build a large complex (d3) and the strong demand state of nature (s1) occurs © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 6 Problem Formulation Decision Tree A decision tree provides a graphical representation of the decision-making process Shows the natural or logical progression that will occur over time Example: The topmost payoff of 8 indicates that an $8 million profit is anticipated if PDC constructs a small condominium complex (d1) and demand turns out to be strong (s1) © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 7 Figure 15.1: Decision Tree For The PDC Condominium Project ($ Millions) Nodes are used to represent decisions and chance events Squares are used to depict decision nodes, circles are used to depict chance nodes The branches connect the nodes; those leaving the decision node correspond to the decision alternatives The branches leaving each chance node correspond to the states of nature The outcomes (payoffs) are shown at the end of the states-of-nature branches © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 8 Decision Analysis Without Probabilities Decision analysis without probabilities is appropriate in situations: In which a simple best-case and worst-case analysis is sufficient Where the decision maker has little confidence in his or her ability to assess the probabilities 1. Optimistic Approach 2. Conservative Approach 3. Minimax Regret Approach © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 9 Decision Analysis Without Probabilities 1. Optimistic Approach—best best The optimistic approach evaluates each decision alternative in terms of the best payoff that can occur The decision alternative that is recommended is the one that provides the best possible payoff For minimization problems, this approach leads to choosing the alternative with the smallest payoff In the PDC problem, the optimistic approach would lead the decision maker to choose the alternative corresponding to the largest profit © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 10 Decision Analysis Without Probabilities 2. Conservative Approach—best worst The conservative approach evaluates each decision alternative in terms of the worst payoff that can occur The decision alternative recommended is the one that provides the best of the worst possible payoffs For problems involving minimization (for example, when the output measure is cost), this approach identifies the alternative that will minimize the maximum payoff In the PDC problem, the conservative approach would lead the decision maker to choose the alternative that maximizes the minimum possible profit that could be obtained © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 11 Decision Analysis Without Probabilities 3. Minimax Regret Approach Regret is the difference between the payoff associated with a particular decision alternative and the payoff associated with the decision that would yield the most desirable payoff for a given state of nature Regret is often referred to as opportunity loss Under the minimax regret approach, one would choose the decision alternative that minimizes the maximum state of regret that could occur over all possible states of nature © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 12 Decision Analysis Without Probabilities The regret associated with each combination of decision alternative di and state of nature sj is computed Payoff table Regret table © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 13  Decision Analysis Without Probabilities The next step in applying the minimax regret approach is to list the maximum regret for each decision alternative Table 15.5: Maximum Regret for Each PDC Decision Alternative For the PDC problem, the alternative to construct the medium condominium complex, with a corresponding maximum regret of $6 million, is the recommended minimax regret decision © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Decision Analysis with Probabilities Expected Value Approach Sensitivity Analysis © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Decision Analysis With Probabilities Expected Value Approach The expected value (EV) of a decision alternative is the sum of weighted payoffs for the decision alternative The weight for a payoff is the probability of the associated state of nature and therefore the probability that the payoff will occur © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 16 Applying the Expected Value Approach Using a Decision Tree for the PDC Condominium Project © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 17 Decision Analysis With Probabilities Select the decision branch leading to the chance node with the best expected value The decision alternative associated with this branch is the recommended decision In practice, obtaining precise estimates of the probabilities for each state of nature is often impossible, so historical data is preferred to use for estimating the probabilities for the different states of nature © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 18 Decision Analysis With Probabilities Sensitivity Analysis Sensitivity analysis determines how changes in the probabilities for the states of nature or changes in the payoffs affect the recommended decision alternative In many cases, the probabilities for the states of nature and the payoffs are based on subjective assessments Sensitivity analysis helps the decision maker understand which of these inputs are critical to the choice of the best decision alternative If a small change in the value of one of the inputs causes a change in the recommended decision alternative, the solution to the decision analysis problem is sensitive to that particular input © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 19 Decision Analysis With Probabilities Example: Suppose that, in the PDC problem, the probability for a strong demand is revised to 0.2 and the probability for a weak demand is revised to 0.8 EV(d1 ) = 0.2 (8) + 0.8 (7) = 7.2 EV(d2 ) = 0.2 (14) + 0.8 (5) = 6.8 EV(d3 ) = 0.2 (20) + 0.8 (-9) = -3.2 With these probability assessments, the recommended decision alternative is to construct a small condominium complex (d 1), with an expected value of $7.2 million When the probability of strong demand is large, PDC should build the large complex; when the probability of strong demand is small, PDC should build the small complex © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 20 Decision Analysis with Sample Information Expected Value of Perfect Information A special case of gaining additional information related to a decision problem is when the sample information provides perfect information on the states of nature © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 21 Decision Analysis with Sample Information Table 15.6: Payoff Table for the PDC Condominium Project ($ Millions) We can state PDC’s optimal decision strategy when the perfect information becomes available as follows: If s1, select d3 and receive a payoff of $20 million If s2, select d1 and receive a payoff of $7 22 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected million website for classroom use. Decision Analysis with Sample Information The original probabilities for the states of nature: P(s1) = 0.8 and P(s2) = 0.2 From equation (12.2) the expected value of the decision strategy that uses perfect information is 0.8(20) + 0.2(7) = 17.4 (i.e., expected value with perfect information (EVwPI)) Earlier, we found the expected value approach is decision alternative d3 $14.2 million; this is referred to as the expected value without perfect information (EVwoPI) © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 23 Decision Analysis with Sample Information Example for PDF: Expected value of the perfect information (EVPI) is $17.4 – $14.2 = $3.2 million In general, expected value for perfect information (EVPI) is computed as: © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.