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i want to know the answer of #3 and #4. subject is decision tree,-(Answered)


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i want to know the answer of #3 and #4.

subject is decision tree,

A Case Study: GPC?s New Product Decision ? Part 1


(Adapted from ?Making Hard Decisions? by Clemen and Reilly)


Note: Base parts 5 and 6 on the decision problem of parts 1-3, and not on the modified problem


of part 4.


The executives of the General Products Company (GPC) have to decide which of three products


to introduce: A, B, or C. Product C is essentially a risk-free proposition, from which the company


will obtain a net profit of $1 million. Product B is considerably more risky. Sales may be high,


with resulting net profit of $8 million, medium with net profit of $4 million, or low, in which case


the company just breaks even. The probabilities for these outcomes are:


P (Sales High for B) = 0.38


P (Sales Medium for B) = 0.12


P (Sales Low for B) = 0.50


Product A poses something of a difficulty: a problem with the production system has not yet


been solved. The engineering division has indicated its confidence in solving the problem, but


there is a slight (5%) chance that devising a workable solution may take a long time. In this


event, there will be a delay in introducing the product, and that delay will result in lower sales


and profits. Another issue is the price for Product A. The options are to introduce it at high or


low price, and the price will not be set until just before the product is to be introduced. Both of


these issues have an impact on the ultimate net profit.


Finally, once the product is introduced, sales can be either high or low. If the company decides


to set a low price, then low sales are just as likely as high sales. If the company sets a high price,


the likelihood of low sales depends on whether the product introduction is delayed due to the


production problem or not. If there is no delay and the company sets a high price, the


probability of high sales will be 0.4. However, if there is a delay and the price is set high, the


probability of high sales will only be 0.3. The following table summarizes the net profit figures


(in millions for Product A):




Time Delay


No Delay












High Sales


($ Millions)











Low Sales


($ Millions)













1. Use PrecisionTree to prepare an influence diagram for GPC?s problem. Specify the


possible outcomes and the probability distributions for each chance node. Specify the






possible alternatives for each decision node. Fill in the complete table for the


consequence node. What is the EMV for this decision problem?


2. Use PrecisionTree to prepare a decision tree for the problem:


a. Identify all the possible strategies.


b. Identify the best strategy based on the EMV criterion.


3. Use PrecisionTree to create the risk and cumulative risk profiles for the decision of


selecting a product (A, B or C). Note that in creating the profiles, PrecisionTree


evaluates the different values for the first decision (i.e., selection of products A, B or C),


but then sets the down line decisions based on the dominant EMV value. Discuss any


conclusions you can draw. Make sure to include a discussion of any observed


deterministic and/or stochastic dominance.


4. One of the executives of GPS is considerably less optimistic about Product B, and


assesses the probability of medium sales as 0.3, and the probability of low sales as 0.4.


Update the decision tree, to reflect the updated probabilities. Based on the new


expected value and risk profiles, what decision would this executive make? Should the


executives argue about the probabilities?





Suppose that the executives at GPC feel that their projected sales estimates for product


A, for the four possible scenarios (Delay-High Pricing, Delay-Low Pricing, No Delay-High


Pricing, No Delay-Low pricing) are too coarse. The executives reason that the table


below with minimum, target, and maximum profit levels better represent their current


assessment of the potential future sales for A. At this point in time, the executive are


really uncomfortable with reliably estimating any probabilities corresponding to these




Ranges for Sales for A -- Min/Base/Max ($ Millions)





No Delay



High Pricing







Low Pricing







GPC's executives are contemplating whether it would be worthwhile to conduct a


thorough, but expensive, market research study to obtain more refined sales estimates


(and corresponding profits) for A, along with associated probabilities. Before engaging


a market research firm for that purpose, they decided to first try to gain some


understanding as to which of the desired sales level estimates for A (Delay/High Pricing,


Delay/Low Pricing, No Delay/High Pricing, and No Delay/Low Pricing) would have the


most impact and, hence, should get the most attention in the study. This may allow


GPC to have a less-expensive and timelier study that, nonetheless, provides enhanced


estimates for the most important sales numbers.





Conduct one-way sensitivity analyses to help answer this question. Also, conduct a twoway sensitivity analysis for the two most important sales level estimates. Discuss the


insights provided by the sensitivity, spider and tornado charts you obtain. How would


you advise GPC to proceed?


Hint: You will need a new copy of the tree with the rightmost chance nodes for product


A removed. The last (rightmost) nodes for product A will now become the pricing


decisions (High or Low). For each of these decisions, you can assign the target sales


levels. For example if there is a delay, and the pricing is high, the payoff is $1.33 million.


Finally, the sensitivity analyses are conducted for these payoffs.


6. Suppose now that the GPC executives are uncertain about the estimated probabilities


for the Product B sales levels. Let p denote the probability of High sales, q the


probability of Medium sales and 1 - p - q the probability of Low sales. Using Precision


Tree conduct sensitivity analysis to assess the impact of varying p and q. Since


PrecisionTree does not allow requiring p + q to be ? 1, restrict the sensitivity analysis


such that 0 ? p ? 0.5 and 0 ? q ? 0.5. Show all steps, and discuss all your conclusions.







Paper#9210536 | Written in 27-Jul-2016

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