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Quantitative Analysis for Management Mid-semester Test (Jul- Nov, 2010)

Decision Analysis and Forecasting

Completed by Zainap Asma Abdullah (2009618232)

CASE 1: SKI RIGHT

Question 1: Construct a Decision Tree and based on the analysis, what do you recommend?

Using POM for Windows, I inserted the relevant information and achieved the following results:

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Answer: By applying this technique we can see that the best option is to make the helmet with the help of Leadville Barts. It is worth much more to Bob to venture into business with Leadville Barts than of its other alternatives. And it's better for Bob to make helmets than to ignore his idea because he can make substantial profit even though it has certain risks and costs. So as a conclusion, based on the Decision Tree generated by POM for Windows using the Decision Analysis graphical approach, it suggests that Bob Guthrie’s best option is to align his helmet making business with Leadville Barts since they provide the best EMV of $2600 than of the other alternatives.

Question 2: What is the opportunity loss for this problem?

Answer: Expected Opportunity Loss (EOL) is the cost of not picking the best solution and whereby EOL will always result in the same decision as the maximum EMV. The following shows the summary of EOL computation also known as Expected Regret.

Excellent Good Average Poor Expecte

d MaximumProbability 0.2 0.4 0.3 0.1 Progressive Products (PP) 50000 18000 0 0 17200 50000Leadville Barts (LB) 43000 14000 2000 5000 15300 43000Talrad (TR) 42000 13000 8000 10000 17000 42000Cellestial Cellular (CC) 25000 10000 18000 25000 16900 25000Forget Progressive Products 0 0 33000 55000 15400 55000

Minimum 15300 25000

However, here is the manual method of computing EOL.

EOL (PP) = (0.2) ($50000) + (0.4) ($18000) + (0.3) ($0) + (0.1) ($0)

= $ 17200

EOL (LB) = (0.2) ($43000) + (0.4) ($14000) + (0.3) ($2000) + (0.1) ($5000)

= $ 15300

EOL (TR) = (0.2) ($42000) + (0.4) ($13000) + (0.3) ($8000) + (0.1) ($10000)

= $ 17000

EOL (CC) = (0.2) ($25000) + (0.4) ($10000) + (0.3) ($18000) + (0.1) ($25000)

= $ 16900

EOL (FPP) = (0.2) ($0) + (0.4) ($00) + (0.3) ($33000) + (0.1) ($55000)

= $ 15400

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Question 3: Compute the expected value of perfect information.

Answer: Expected value of perfect information (EVPI) places an upper bound on what to pay for information. EVPI is the expected value with perfect information minus the maximum EMV. The following shows the summary of EVPI computation generated from the POM for Windows software.

DataProfit Excellent Good Average Poor EMV Minimum MaximumProbability 0.2 0.4 0.3 0.1 Progressive Products (PP) 5000 2000 -2000 -5000 700 -5000 5000Leadville Barts (LB) 12000 6000 -4000 -10000 2600 -10000 12000Talrad (TR) 13000 7000 -10000 -15000 899.9999 -15000 13000Cellestial Cellular (CC) 30000 10000 -20000 -30000 999.9999 -30000 30000Forget Progressive Products 55000 20000 -35000 -60000 2500 -60000 55000

Maximum 2600 -5000 55000Expected Value of Perfect InformationColumn best 55000 20000 -2000 -5000

17900.00025 <-Expected value under certainty2600.000009 <-Best expected value15300.00024 <-Expected value of perfect information

Question 4: Was Bob completely logical in how he approached this decision problem?

Answer: Decision analysis and tools like the Decision Tree represent the alternatives available to the decision maker in this case Bob Guthrie, the uncertainty he faces, and evaluation measures representing how well he can achieve his objective of making ski helmets more safe, fun and useful in the final outcome. Uncertainties are represented through probabilities and probability distributions. Therefore, Bob’s attitude to risk is represented by utility functions and his attitude to trade-offs between conflicting objectives can be made using multi-attribute value functions or multi-attribute utility functions (if there is risk involved) therefore he is minimizing risks and overseeing potential profits. In some cases, utility functions can be replaced by the probability of achieving uncertain aspiration levels. Decision analysis advocates choosing that decision whose consequences have the maximum expected utility (or which maximize the probability of achieving the uncertain aspiration level)so as to answer whether or not Bob was completely logical or not in approaching his decision problem, well then the answer is yes.

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CASE 2: AKRON ZOOLOGICAL PARK

Question 1: The president of the Akron Zoo asked you to calculate the expected gate admittance figures and revenues for both 1999 and 2000. You can use at least three forecasting methods to estimate the forecast values and compare the results. Recommend the best method to the president of Akron Zoo.

1. Moving average (three year average) for year 1999

By using the moving average method, the forecasts of admittance for the year 1999 is 123,363 and the value of MAD is 17,969.

Given that the total attendance for 1999 is 123,363 people and of that number; 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 1999 is as follows:

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Total Attendance (1999)

Group Total Attendance in 1999 Group Percentage Total People by GroupAdult 123,363 0.35 43,177.05

Children 123,363 0.50 61,681.5Group 123,363 0.15 18,504.5

Total 1 123,363

Total Revenue by Group of Attended People (1999)

Group Number of People Price ($) Total Revenue by GroupAdult 43,177.05 4 172,708.20

Children 61,681.5 2.50 154,203.8Group 18,504.5 1.50 27,756.7

Total Revenue $ 354,668.63

* Note: All values are rounded up to the closest number

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1.1 Moving average (three year average) for year 2000

By using the moving average method, the forecasts of admittance for the year 2000 is 122,200 and the value of MAD is 15,723.75.

Given that the total attendance for 2000 is 122,200 people and of that number; 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 2000 is as follows:

Total Attendance (2000)

Group Total Attendance in 2000 Group Percentage Total People by GroupAdult 122,200 0.35 42,770

Children 122,200 0.50 61,100Group 122,200 0.15 18,330

Total 1 122,200

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Total Revenue by Group of Attended People (1999)

Group Number of People Price ($) Total Revenue by GroupAdult 42,770 4 171,080

Children 61,100 2.50 152,750Group 18,330 1.50 2,749.5

Total Revenue 351,325.29

* Note: All values are rounded up to the closest number

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2. Weighted Moving Average (three year average) for 1999

Using POM for Windows, I was able to generate the forecast of admittance to Akron for year 1999. The following shows the summary of the forecasts and other related information needed to help Akron’s current position.

Weight Applied Period3 Last year2 2 years ago1 3 years ago

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By using the weighted moving average method, the forecasts of admittance for the year 1999 is 121,867 and the MAD is 15,752 (rounded to the closest round number).

Given that 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 1999 is:

Total Attendance (1999)

Group Total Attendance in 1999 Group Percentage Total People by GroupAdult 121,867 0.35 42,653.45

Children 121,867 0.50 60,933.5Group 121,867 0.15 18,280.1

Total 1 121,867

Total Revenue by Group of Attended People (1999)

Group Number of People Price ($) Total Revenue by GroupAdult 42,653.45 4 170,613.80

Children 60,933.5 2.50 152,333.8Group 18,280.1 1.50 27,420.1

Total Revenue 350,367.63

* Note: All values are rounded up to the closest number

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2.1 Weighted Moving Average (three year average) for 2000

Using POM for Windows, I was able to generate the forecast of admittance to Akron for year 2000. The following shows the summary of the forecasts and other related information needed to help Akron’s current position.

Weight Applied Period3 Last year2 2 years ago1 3 years ago

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By using the weighted moving average method, the forecasts of admittance for the year 2000 is 121,119 and the MAD is 13,783 (rounded to the closest round number).

Given that 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 2000 is:

Total Attendance (2000)

Group Total Attendance in 2000 Group Percentage Total People by GroupAdult 121,119 0.35 42,391.65

Children 121,119 0.50 60,559.5Group 121,119 0.15 18,167.9

Total 1 121,119

Total Revenue by Group of Attended People (2000)

Group Number of People Price ($) Total Revenue by GroupAdult 42,653.45 4 169,566.60

Children 60,933.5 2.50 151,398.8Group 18,280.1 1.50 27,251.8

Total Revenue 348,217.13

* Note: All values are rounded up to the closest number

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3. Trend Analysis

Trend analysis could be used as well. Here, as with moving average and weighed moving average, we are using past attendance figures (historical data) to predict future values of attendance.

From the table above, we can see that the forecasted admittance for the year 1999 is 145,522.8 and year 2000 is 154,720.10.

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3.1 Trend Analysis (1999)

Given that 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 1999 is:

Total Attendance (1999)

Group Total Attendance in 1999 Group Percentage Total People by GroupAdult 145,522.80 0.35 50,932.98

Children 145,522.80 0.50 72,761.40Group 145,522.80 0.15 21,828.42

Total 1 145,522.80

Total Revenue by Group of Attended People (1999)

Group Number of People Price ($) Total Revenue by GroupAdult 50,932.98 4 203,731.92

Children 72,761.40 2.50 181,903.50Group 21,828.42 1.50 32,742.63

Total Revenue 418,378.05

* Note: All values are rounded up to the closest number

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3.2 Trend Analysis (2000)

Given that 35% of all the visitors are adults, 50% children while 15% is of group admittance. Therefore, the revenue for 2000 is:

Total Attendance (2000)

Group Total Attendance in 2000 Group Percentage Total People by GroupAdult 154,720.13 0.35 54,152.05

Children 154,720.13 0.50 77,360.07Group 154,720.13 0.15 23,208.02

Total 1 154,720.13

Total Revenue by Group of Attended People (2000)

Group Number of People Price ($) Total Revenue by GroupAdult 54,152.05 4 216,608.18

Children 77,360.07 2.50 193,400.16Group 23,208.02 1.50 34,812.03

Total Revenue 444,820.37

* Note: All values are rounded up to the closest number

Therefore based on the Trend Analysis method, the trend line is: Y = a + b (x) whereby

Y = 44,352.41 + 9197.31(x)

So forecast for the year 1999,

Y = 44,352.41 + 9197.31 (11)

= 145,522.82

Forecast for the year 2000,

Y = 44,352.41 + 9197.31 (12)

= 154,720.13

In which case the trend line “Y = 44,352.41 + 9197.31(x)” is deemed acceptable to give the given

forecast for years 1999 and 2000.

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Conclusion

In order to determine which forecasting method Akron Zoological Park should you as a reference for

annual admittance is influenced by the method’s Mean Absolute Deviation (MAD); the lowest MAD

value of the methods used in this case is ultimately the best method for Akron. The following table

illustrates which of the methods has the lowest MAD value.

Methods 1999 2000Simple Moving Average 17,696.95 15,723.71Weighted Moving Average 15,752.19 13,783.17Trend Analysis 9,662.59 9,662.59

Therefore, from the analysis of the three forecasting methods, which are moving average method,

weighted moving average method and trend analysis method, trend analysis is the best method for

Akron to use in forecasting the admittances figures and revenues for both years (1999 & 2000) since the

value of forecasting for both are 9,662.59 and 9,662.59

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Question 2: What factors other than admission price influences annual attendance and thus should be considered in the forecast?

There are numerous factors that may have an influence annual attendance, however not all of the factors listed below have a significant importance underlying the number of admittance per year. Some factors may be more important than others.

*Note: Factors listed with * have more significant influence on the number of attendance annually.Other factors that admission price that influences attendances include:

- number of new animals- number of active exhibits*- the weather*- advertising campaigns - public service advertising*- other types of attractions in the area,- disposable income levels in the area- area population shifts, Area’s birth rate- new attractions at the zoo*- new baby animals - quality of service- operating time of the zoo- employment trends- gasoline and automobile related prices- rate of tourism growth in the area- cleanliness- discount rates for groups- promotional events*- special animal exhibits- coverage on local news (the announcement of new born animals or new arrivals)- tour guides (to give background information on animals)- new and exotic animals*- renovations on older exhibits- other recreation in the town, competition, Barney tour, circus, fair

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