Decision Making Under Uncertainty PDF

BUSINESS ANALYTICS Decision Making Under Uncertainty SHEEMA NOORAIN  6-1 Introduction  A formal framework for analyzing decision problems that involve uncertainty includes:  Criteria for choosing among alternative decisions  How probabilities are used in the decisi...

BUSINESS ANALYTICS Decision Making Under Uncertainty SHEEMA NOORAIN  6-1 Introduction  A formal framework for analyzing decision problems that involve uncertainty includes:  Criteria for choosing among alternative decisions  How probabilities are used in the decision-making process  How early decisions affect decisions made at a later stage  How a decision maker can quantify the value of information  How attitudes toward risk can affect the analysis  A powerful graphical tool—a decision tree—guides the analysis.  A decision tree enables a decision maker to view all important aspects of the problem at once: the decision alternatives, the uncertain outcomes and their probabilities, the economic consequences, and the chronological order of events. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-2 Elements of Decision Analysis (slide 1 of 3)  Decision analysis problems have common elements: 1. A problem has been identified that requires a solution. 2. A number of possible decisions have been identified. 3. Each decision leads to a number of possible outcomes. 4. There is uncertainty about which outcome will occur, and probabilities of the possible outcomes are assessed. 5. For each decision and each possible outcome, a payoff is received or a cost is incurred. 6. A “best” decision must be chosen using an appropriate decision criterion. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-2 Elements of Decision Analysis (slide 2 of 3)  Identifying the problem  When something triggers the need to solve a problem, the problem that needs to be solved should be carefully identified.  Possible decisions  The possible decisions depend on how the problem is specified.  Possible outcomes  One of the main reasons why decision making under uncertainty is difficult is that decisions have to be made before uncertain outcomes are revealed. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-2 Elements of Decision Analysis (slide 3 of 3)  Probabilities of outcomes  There is no easy way to assess the probabilities of the possible outcomes. Sometimes they will be determined at least partly by historical data. Other estimates will necessarily contain a heavy subjective component, such as when a new product is being introduced. To complicate matters, probabilities sometimes change as more information becomes available.  Payoffs and costs  Decisions and outcomes have consequences, either good or bad, and may be monetary or nonmonetary. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Decision Criterion (slide 1 of 2)  Look at the worst possible outcome for each decision and choose the decision that has the best (or least bad) of these.  Look at the 5th percentile of the distribution of outcomes for each decision and choose the decision that has the best of these.  Look at the best possible outcome for each decision and choose the decision that has the best of these.  Look at the variance of the distribution of outcomes for each decision and choose the decision that has the smallest of these.  Look at the downside risk of the distribution of outcomes for each decision and choose the decision with the smallest of these. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Decision Criterion (slide 2 of 2)  The expected monetary value, or EMV, for any decision is a weighted average of the possible payoffs for this decision, weighted by the probabilities of the outcomes.  The expected monetary value criterion, or EMV criterion, is generally regarded as the preferred criterion in most decision problems.  This approach assesses probabilities for each outcome of each decision and then calculates the expected payoff, or EMV, from each decision based on these probabilities.  Using this criterion, you choose the decision with the largest EMV—which is sometimes called “playing the averages.” © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  More about the EMV Criteria (slide 1 of 2)  Value a decision with a given EMV the same as a sure monetary outcome with the same EMV.  The EMV criterion doesn’t guarantee good outcomes.  The EMV criterion is easy to operationalize in a spreadsheet.  List the possible payoff/cost values and their probabilities, and calculate EMV with SUMPRODUCT. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  More about the EMV Criteria (slide 2 of 2)  The advantage to calculating EMVs in a spreadsheet is that you can easily perform sensitivity analysis on any of the inputs.  Here, the EMV for decision 2 is the largest of the three EMVs, so it is the best decision. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-3 EMV and Decision Trees (slide 1 of 4)  A graphical tool called a decision tree has been developed to represent decision problems.  It is particularly useful for more complex decision problems.  It clearly shows the sequence of events (decisions and outcomes), as well as probabilities and monetary values. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Decision Tree: Conventions (slide 2 of 4)  Decision trees are composed of nodes (circles, squares, and triangles) and branches (lines).  The nodes represent points in time. A decision node (a square) represents a time when the decision maker makes a decision.  A probability node (a circle) represents a time when the result of an uncertain outcome becomes known.  An end node (a triangle) indicates that the problem is completed—all decisions have been made, all uncertainty has been resolved, and all payoffs and costs have been incurred.  Time proceeds from left to right. Any branches leading into a node (from the left) have already occurred. Any branches leading out of a node (to the right) have not yet occurred. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Decision Trees (slide 3 of 4)  Branches leading out of a decision node represent the possible decisions; the decision maker can choose the preferred branch.  Branches leading out of probability nodes represent the possible outcomes of uncertain events; the decision maker has no control over which of these will occur.  Probabilities are listed on chance branches. These probabilities are conditional on the events that have already been observed (those to the left).  Probabilities on branches leading out of any chance node must sum to 1.  Monetary values are shown to the right of the end nodes.  EMVs are calculated through a “folding-back” process. They are shown above the various nodes. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Decision Trees (slide 4 of 4)  The decision tree allows you to use the following folding-back procedure to find the EMVs and the optimal decision:  Starting from the right of the decision tree and working back to the left: At each chance node, calculate an EMV—a sum of products of monetary values and probabilities. At each decision node, take a maximum of EMVs to identify the optimal decision. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-4 One-Stage Decision Problems  In single stage decision problems, one stage is made, right now.  They all unfold the same way. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.1: New Product Decisions at ACME (slide 1 of 4)  Objective: To use the EMV criterion to help Acme decide whether to go ahead with the product.  Solution: Acme’s cost accountants estimate the monetary inputs: the fixed costs ($6,000) and the unit margin ($18).  The uncertain sales volume is really a continuous variable but, as in many decision problems, Acme has replaced the continuum by three representative possibilities: great (45%), fair (35%) and awful (20%)  Each sales volume is multiplied by the unit margin to obtain the net revenues.  The formula for the EMV is the sum of the net revenues minus the fixed costs. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.1: New Product Decisions at ACME (slide 2 of 4) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.1: New Product Decisions at ACME (slide 3 of 4) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.1: New Product Decisions at ACME (slide 4 of 4)  Usually, the main purpose of sensitivity analysis is to see whether the best decision changes as one or more inputs change.  In this case, we will see whether the best decision continues to be “proceed with marketing” if the total market decreases. Specifically, we let each of the potential sales volumes decrease by the same percentage and we keep track of the EMV from marketing the product. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-5 The PrecisionTree Add-In (slide 1 of 2)  Decision trees present a challenge for Excel ®.  PrecisionTree, a powerful add-in developed by Palisade Corporation, makes the process relatively straightforward.  It enables you to draw and label a decision tree.  It performs the folding-back procedure automatically.  It allows you to perform sensitivity analysis on key input parameters.  See your text for a detailed description of its use. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-5 The PrecisionTree Add-In (slide 2 of 2) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-6 Multistage Decision Problems (slide 1 of 2)  Many real-world decision problems evolve through time in stages.  The objective is again to maximize EMV, but now we are searching for an EMV-maximizing strategy, often called a contingency plan, that specifies which decision to make at each stage.  A contingency plan tells the company which decision to make at the first stage, but the company won’t know which decision to make at the second stage until the information from the first uncertain outcome is known. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-6 Multistage Decision Problems (slide 2 of 2)  An important aspect of multistage decision problems is that probabilities can change through time.  Specifically, after you receive the information from the first-stage uncertain outcome, you might need to reassess the probabilities of future uncertain outcomes.  Another important aspect of multistage decision problems is the value of information.  Sometimes the first-stage decision is to buy information that will help in making the second-stage decision. The question then is how much this information is worth. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.2: New Product Decisions with Technological Uncertainty (slide 1 of 5)  Objective: To use a decision tree to find Acme’s EMV- maximizing strategy for this two-stage decision problem.  Solution: The probability of technological failure might be based partly on historical data (the technological failure rate of similar products in the past) but it is probably partly subjective, based on how the product’s development has proceeded so far. The reason this is a two-stage decision problem is that Acme can decide right away to stop development and abandon the product, thus saving further fixed costs of development. However, if Acme decides to continue development and the product turns out to be a technological success, a second decision on whether to market the product must still be made. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.2: New Product Decisions with Technological Uncertainty (slide 2 of 5)  The first decision is whether to continue development.  If “Yes,” the fixed development cost is incurred, so it is entered on this branch.  Then there is a probability node for the technological success or failure.  If it’s a failure, there are no further costs, but the fixed development cost is lost.  If it’s a success, Acme must decide whether to market the product. From this point, the tree is exactly like the single-stage tree, except that the fixed development cost is gone. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.2: New Product Decisions with Technological Uncertainty (slide 3 of 5) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.2: New Product Decisions with Technological Uncertainty (slide 4 of 5)  By following the TRUE branches, you can see Acme’s best strategy.  The company should continue development, and if the product is a technological success, it should be marketed. The EMV, again the weighted average of all possible monetary outcomes with this strategy, is $59,200.  However, this is only the expected value, or mean, of the probability distribution of monetary outcomes. You can see the full probability distribution by requesting a risk profile from PrecisionTree (through the Decision Analysis dropdown). © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.2: New Product Decisions with Technological Uncertainty (slide 5 of 5) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.3: New Product Decisions with Option to Buy Information (slide 1 of 2)  Suppose now that Acme has just about finished the development process on the new product, so that fixed development costs are no longer an issue, and technological failure is no longer a possibility. The only question is whether Acme should market the product, given the uncertainty about the eventual sales volume. If the company decides to market the product, it will incur fixed marketing costs of $4 million. To keep the model simple, we now assume that there are only two possible market outcomes, good or bad. The sales volumes for these two possible outcomes are 600,000 units and 100,000 units, and Acme assesses that their probabilities are 0.4 and 0.6. However, before making the ultimate decision, Acme has the option to hire a well-respected marketing research firm for $150,000. If Acme decides to use this option, the result will be a prediction of good or bad. That is, the marketing research firm will predict that either “We think the market for this product will be good” or “We think the market for this product will be bad.” Acme has used this firm before, so it has a sense of the prediction Accuracy. If the actual market is good, the prediction will be Actual/ Good Bad good with probability 0.8 and Predicted bad with probability 0.2. If the actual market is bad, the prediction will be bad with probability 0.7 and good with probability 0.3. WhatGood should Acme do0.8to maximize its0.2 EMV? Bad 0.3 0.7 © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.3: New Product Decisions with Option to Buy Information (slide 1 of 2)  Objective: To use a decision tree to see whether the marketing research firm is worth its cost and whether the product should be marketed.  Solution: Acme must first decide whether to hire the marketing research firm. If it decides not to, it can then immediately decide whether to market the product. On the other hand, if it decides to hire the firm, it must then wait for the firm’s prediction. After the prediction is received, Acme can then make the ultimate decision on whether to market the product. However, when making this ultimate decision, Acme should definitely take the firm’s prediction into account. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Example 6.3: New Product Decisions with Option to Buy Information (slide 2 of 2) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 1 of 7)  Bayes’ rule: Frequency approach  Bayes’ rule is a formal mathematical mechanism for updating probabilities as new information becomes available. The original probabilities are called prior probabilities. Then information is observed and Bayes’ rule is used to update the prior probabilities to posterior probabilities. The actual updating mechanism can be done in two ways: with frequencies (counts) or with probabilities. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule: Frequency Approach (Slide 2 of 7) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 3 of 7)  Bayes’ rule: Probability approach  For any possible outcome O, we let P(O) be the probability of O.  If we want to indicate that new information, I, is available, we write the probability as P(O|I). This is called a conditional probability.  The typical situation is that there are several outcomes such as “good market” and “bad market.” In general, denote these outcomes as O1 to On, assuming there are n possibilities. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 4 of 7)  We start with prior probabilities P(O1) to P(On), n probabilities that sum to 1.  Next, we observe new information, I, such as a market prediction, and we want the posterior probabilities P(O1|I) to P(On|I), an updated set of n probabilities that sum to 1.  We assume that the “opposite” conditional probabilities, P(I|O1) to P(I|On), are given. In Bayesian terminology, these are called likelihoods. Unfortunately, these likelihoods are not what we need in the decision tree. Bayes’ rule is a formal rule for turning these conditional probabilities around. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 5 of 7)  Bayes’ rule is given by  The denominator in Bayes’ rule is the probability P(I) of the information outcome. It is sometimes called the law of total probability.  In the case where there are only two Os, labeled as O and Not O, Bayes’ rule takes the following form:  These formulas can all be implemented in Excel®. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 6 of 7) © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6.6a Bayes’ Rule (Slide 7 of 7)  The results can then be displayed in a decision tree. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  6-6c Sensitivity Analysis (slide 1 of 2)  A strategy region graph shows how the EMV varies with the conditions, for example, whether Acme hires a marketing firm.  This type of chart is useful for seeing whether the optimal decision changes over the range of the input variable.  It does so only if the two lines cross. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning  Sensitivity Analysis (slide 2 of 2)  A two-way sensitivity chart shows how the selected EMV varies as each pair of inputs varies simultaneously. © 2020 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, 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 or school-approved learning