# Decision Modeling

June 10, 2016

Question
Chapter 1 – Introduction
R(x)=p.x

P(x)=R(x)-C(x)

Break even point: C(x)=R(x)

Chapter 2 – Introduction to Probability
P(A)+P(Ac)=1

Addition law P(A or B)=P(A)+P(B)-P(A and B)

Multiplication law P(A and B)=P(A).P(B/A)

Chapter 3 – Probability Distributions
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Chapter 4 – Decision Analysis
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Rij – the regret associated with di and sj

Vj – the payoff value corresponding to the best decision for sj

Vij – the payoff corresponding to di and sj

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Chapter 6 – Forecasting

equation of regression line: y=ax+b

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Exponential forecast: Ft+1=.0/msohtmlclip1/01/clip_image012.gif”>.Yt+(1-.0/msohtmlclip1/01/clip_image012.gif”>).Ft

1. The company knows that the city will build the new sports stadium in either the eastern or western suburb of the city, but the city has not made a final decision. The company needs to buy the land before the stadium final decision is made public, in order to save money on the purchase price of the land, which will probably increase substantially when the location for the new stadium is made public.The following payoff table shows profit for a decision analysis problem withfour different decision alternatives d1-d4 and 2 states of nature s1-s2. [3+3+5=11pts]…in each part draw a clear conclusion based on your calculations.

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a) What is the recommended decision using the optimistic approach?

b) What is the recommended decision using the conservative approach?

c) What is the recommended decision using the minimax regret approach?

2. InvestmentAdvisors, Inc., has three investment strategies under consideration. Profits from the strategies will depend on what happens to the prime interest rate over the next three months. Payoffs (in thousands of dollars) are shown.[ 3+4=7pts]

Decision alternative

Rate decrease (s1)

No change(s2)

Rate increase(s3)

Strategy d1

50

70

40

Strategy d2

55

35

80

Strategy d3

15

60

70

a) What is the recommended decision using the expected value approach if the demand probabilities are 0.2, 0.5, and 0.3?

b) Find the expected value of perfect information.

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3. The president of a small manufacturing firm has been concerned about the continual growth in manufacturing costs over the past several years. The following is a time series of the cost per unit (in dollars) for the firm’s leading product over the past 8 years. [5+2=7pts]

Year

1

2

3

4

5

6

7

8

Cost per unit (in \$)

20

24.5

28

27.5

26.6

30

31

36

a) Assuming that linear trend appears, develop the equation of regression line. Round values of coefficients to two decimal places.

b) Use the equation to prepare a forecast for costs in year 10.

4. Use graphical sensitivity analysis to determine the range of probabilities for which each decision alternative has the largest expected value. Write clear conclusion. Round values of p to 3 decimal places.[ 8 pts]

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5. Alabama building contracts for a 9-month period (in millions of dollars) are 240, 350, 230, 260, 280, 320, 220, 310, 240. [15+2=17pts]

a) Compare a four-month moving average forecast with an exponential smoothing forecast using .0/msohtmlclip1/01/clip_image012.gif”>=0.3. Which provides the better forecasts? Use two decimal places at least.

month

Time series value

4-month moving average forecast

Forecast error

Squared forecast error

1

240

2

350

3

230

4

260

5

280

6

320

7

220

8

310

9

240

month

Time series value

Exponential smoothing forecast.0/msohtmlclip1/01/clip_image012.gif”>=0.3

Forecast error

Squared forecast error

1

240

2

350

3

230

4

260

5

280

6

320

7

220

8

310

9

240

b) Using the better method from a) part, what is the forecast for the next month?

6. A large business has fixed costs of £250,000 per week. Its average sales revenue per item is £2, and its variable costs are on average 40p per item.[4+2+4+2=12pts]

a) What is breakeven point?

b) What profit or loss can be anticipated with a demand of 200 000 units?