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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):

 

Price

 

Time Delay

 

No Delay

 


 

High

 

Low

 

High

 

Low

 


 

High Sales

 

($ Millions)

 

5.0

 

3.5

 

8.0

 

4.5

 


 

Low Sales

 

($ Millions)

 

(0.5)

 

1.0

 

0.0

 

1.5

 


 

Questions

 

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

 


 

1

 


 

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?

 

5.

 


 

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

 

levels.

 

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

 


 

Delay

 

No Delay

 


 

High Pricing

 

(1.5)/1.33/6.6

 

0/3.2/9

 


 

Low Pricing

 

0.5/2.25/4.0

 

1.0/3/4.5

 


 

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.

 

2

 


 

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.

 


 

3

 


 

 

Paper#9210536 | Written in 27-Jul-2016

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