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Decision analysis: part 2 BSAD 30 Dave Novak Source: Anderson et al., 2013 Quantitative Methods for Business 12 th edition – some slides are directly from J. Loucks © 2013 Cengage Learning 1

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Overview Risk analysis Risk profile Sensitivity analysis Changes in states of nature Changes in payoffs EVPI calculation EOL calculation Building and using decision trees 2

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Risk analysis Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative, and the payoff that might actually occur Recall that a payoff is the result of a combination of: 1) a decision alternative (you control this), and 2) a state of nature probability (you do not control this) 3

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Risk analysis The risk profile for a decision alternative shows the possible payoffs for the decision alternative along with their associated probabilities We want to identify the probability or likelihood that a particular payoff will occur Basically, we want to list out ALL possible payoffs, and their probabilities of occurrence 4

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PDC example - lecture 15 Payoff table with P(s 1 ) = 0.8 and P(s 2 ) = 0.2 PAYOFF TABLE States of Nature Strong Demand Weak Demand Decision Alternative s 1 s 2 Small complex, d 1 8 7 Medium complex, d 2 14 5 Large complex, d 3 20 -9 5

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PDC example – lecture 15 1 1.8.2.8.2.8.2 d1d1 d2d2 d3d3 s1s1 s1s1 s1s1 s2s2 s2s2 s2s2 Payoffs $8 mil $7 mil $14 mil $5 mil $20 mil -$9 mil 2 2 3 3 4 4 6

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PDC example - lecture 15 1 1 small d 1 medium d 2 large d 3 2 2 3 3 4 4 7

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Risk profile d 3 (90 unit) decision alternative versus d 2 (60 unit) decision alternative 8

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Value of perfect information Calculate EV assuming MOST OPTIMISTIC payoff for both states of nature (does not need to be the same decision) = EVwPI Take the EV associated with your decision (this is the largest EV value across all decisions) = EVwoPI Given imperfect information, this is what we would choose to do 9

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Value of perfect information 10

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Expected opportunity loss Using the regret table from lecture #15, we can calculate “the expected opportunity lost” (EOL) associated with each decision 11 REGRET TABLE States of Nature Strong Demand Weak Demand Decision Alternative s 1 s 2 Small complex, d 1 12 0 Medium complex, d 2 6 2 Large complex, d 3 0 16

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Expected opportunity loss 12

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Expected opportunity loss The minimum of the EOL values always provides the optimal decision Notice that EVPI = Expected Opportunity Loss (EOL) for decision d 3 (90 units) EVPI is ALWAYS equal to the EOL for the optimal decision 13

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Sensitivity analysis Sensitivity analysis can be used to determine how changes to the following inputs affect the recommended decision alternative: probabilities for the states of nature can be subjective, and therefore subject to change values of the payoffs 14

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Sensitivity analysis If a small change in the value of one of the inputs (state of nature probabilities or payoff values) causes a change in the recommended decision alternative, extra effort and care should be taken in estimating the input value If changes to inputs do not really impact your decision, you can feel more confident about this decision 15

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Sensitivity analysis One way to address the sensitivity question is to select different values for either the state of nature probabilities or the payoff values, and then do some “what if” calculations Say we flip our state of nature probabilities for the PDC problem… 16

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Modified PDC example 1 1.2.8.2.8.2.8 d1d1 d2d2 d3d3 s1s1 s1s1 s1s1 s2s2 s2s2 s2s2 Payoffs $8 mil $7 mil $14 mil $5 mil $20 mil -$9 mil 2 2 3 3 4 4 17

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Modified PDC example 1 1 small d 1 medium d 2 large d 3 2 2 3 3 4 4 18

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Modified PDC example 1 1.5 d1d1 d2d2 d3d3 s1s1 s1s1 s1s1 s2s2 s2s2 s2s2 Payoffs $8 mil $7 mil $14 mil $5 mil $20 mil -$9 mil 2 2 3 3 4 4 19

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Modified PDC example 1 1 small d 1 medium d 2 large d 3 2 2 3 3 4 4 20

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EV comparison

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Graphing for 2 state of nature problem Like a LP with two decision variables, if we only have two states of nature, we can perform sensitivity analysis graphically Generalize relationship for P(s 1 ) and P(s 2 ) 22

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EV calculations for decision variables 23

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Sensitivity graph 24

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Sensitivity graph 25 d 1 provides highest EV d 2 provides highest EV d 3 provides highest EV Solve for each intersection point way we solved for internal points in LP Set two linear equations equal to one another and solve for p

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Solving for inflection points 26

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Solving for inflection points 27

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Sensitivity graph 28 d 1 provides highest EV d 2 provides highest EV d 3 provides highest EV p = 0.25 p = 0.7

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What are managerial implications? 29 If probability of strong demand, P(s 1 ) < 0.25, then choose d 1 (30 units) If probability of strong demand, P(s 1 ) = 0.25, then choose either d 1 (30 units) or d 2 (60 units) If probability of strong demand, 0.25 < P(s 1 ) < 0.7, then choose d 2 (60 units) If probability of strong demand, P(s 1 ) = 0.7, then choose either d 2 (60 units) or d 3 (90 units) If probability of strong demand, P(s 1 ) > 7 then choose d 3 (90 units)

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What about changes in payoff values? 30 From the PDC problem, we have: EV(d 1 ) = 7.8 EV(d 2 ) = 12.2 EV(d 3 ) = 14.2 So, we conclude that building 90 units is the optimal decision (d 3 ) as long as EV(d 3 ) ≥ 12.2

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What about changes in payoff values? 31 Let’s look at changing one of the payoff values for decision alternative d 3 (90 units) Hold the state of nature probabilities constant for both s 1 (strong demand) and s 2 (weak demand) P(s 1 ) = 0.8, and P(s 2 ) = 0.2 Let S = payoff value for d 3 assuming s 1 W= payoff value for d 3 assuming s 2

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What about changes in payoff values? 32 We can write EV(d 3 ) as: Examine a change in one of the payoff values for a particular decision alternative Here, we will hold payoff for weak demand constant at -9

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What about changes in payoff values? 33 Solve for S 0.8S – 1.8 ≥ 12.2 0.8S ≥ 14 S ≥ 17.5 What does this mean? As long as our original state of nature probabilities hold, we should build d 3, as long as the payoff under the strong demand scenario is ≥ 17.5 mil

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What about changes in payoff values? 34 Examine a change in the other payoff value for decision alternative d 3 we will hold payoff for strong demand constant at 20, and investigate changes in weak demand

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What about changes in payoff values? 35 Solve for W 16 + 0.2W ≥ 12.2 0.2W ≥ -3.8 W ≥ -19 What does this mean? As long as our original state of nature probabilities hold, we should build d 3, as long as the payoff under the weak demand scenario is ≥ -19 mil

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What about changes in payoff values? 36 When we hold the state of nature probabilities constant at P(s 1 ) = 0.8, and P(s 2 ) = 0.2, the d 3 decision does not seem to be particularly sensitive to variations in the payoff Why? Probability that demand is strong, P(s 1 ), is very high AND expected payoff is very high Using the EV approach, this combination leads us to choose d 3

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Decision trees 37 Just a graphical representation of the decision-making process Shows a progression over time Squares: decision nodes that we control Circles: chance nodes that we do not control

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Decision tree 1 1.8.2.8.2.8.2 d 1 -build 30 units s1s1 s1s1 s1s1 s2s2 s2s2 s2s2 Payoffs $8 mil $7 mil $14 mil $5 mil $20 mil -$9 mil 2 2 3 3 4 4 38 d 2 -build 60 units d 3 -build 90 units Given each decision, we are then subject to demand, which we cannot control For each decision alternative and state of nature pair, we have an expected payoff

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Decision trees 39 Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product.

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Decision trees 40 If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility.

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Decision trees 41 Identify the “pieces” or nodes associated with this problem We have to present this information in a time dependent sequence of events

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Decision trees 42 1. Make a decision whether to start the R&D project or not a) Start R&D project (cost of $5 mil) proceed b) Do not start R&D project (cost of zero) stop

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Decision trees 43

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Decision trees 44 2. If we start R&D, there is a state of nature or chance event that the project will be successful, where: a) P(R&D success) = 0.5 proceed b) P(R&D failure) = 0.5 stop and lose $5 mil

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Decision trees 45

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Decision trees 46 3. If R&D is successful, we make a decision whether to: a) Build the production facility (cost of $20 mil) proceed b) Sell the rights to the product for $20 mil stop

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Decision trees 47

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Decision trees 48 4. If we decide to build the facility, we are subject to state of nature or chance events regarding demand for the product: a) P(high demand) = 0.5, and the corresponding payoff is $34 mil b) P(med demand) = 0.3, and the corresponding payoff is $20 mil c) P(low demand) = 0.2, and the corresponding payoff is $10 mil

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Decision tree

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Decision trees 50 Populate the decision tree with probabilities, so we can calculate EV for different scenarios We work BACKWARDS to calculate EV for each chance or state of nature node EV (node 4) EV (node 2)

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Decision trees 51

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Decision tree

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Using the decision tree to guide decision-making 53 Should the company undertake the R&D project? If R&D is successful, what should company do, sell or build?

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Using the decision tree to guide decision-making 54 What is EV of your decision strategy? What would selling price need to be for company to consider selling? What about for recovering R&D cost?

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Using the decision tree to guide decision-making 55 Developing a risk profile for the optimal strategy Possible ProfitCorresponding probability $34 M $20 M $10 M -$5 M

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What would the payoff table look like? 56 PAYOFF TABLE States of Nature High Demand Med Demand Low Demand Decision Alternatives Build Sell 34 2010 20

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What would the regret table look like? 57 REGRET TABLE States of Nature High Demand Med Demand Low Demand Decision Alternatives Build Sell 0 010 14 0 0

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Value of perfect information EVwPI = EVwoPI = EVPI = 58

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Expected opportunity loss Using the regret table REGRET TABLE States of Nature High Demand Med Demand Low Demand Decision Alternatives Build Sell 0 010 14 0 0

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Summary Risk analysis Risk profile Sensitivity analysis Changes in states of nature Changes in payoffs EVPI calculation EOL calculation Building and using decision trees 60

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