Hurwicz alpha criterion is which approach

MGMT 2012- Introduction to Quantitative Methods-

Graded Assignment Two S2- 2014-15- Due April 10th – 10 percent Final Grade

Students should note that this assignment should be submitted in a Word document.

Question 1A

APC industries has been experiencing significant growth and has been having difficulty meeting customer demands recently. They are considering three options to address this issue. They can move to a larger facility, add a second shift or use a subcontractor to assist in production. The annual payoff of each option depends on if the current market continues to expand hold s steady or declines. The expected payoff for each combination is show in the table below Option Expand Steady Decline

Move to larger facility

250,000 125,000 -90,000

Add a second shift

175,000 80000 -45,000

Subcontract 90,000 15,000 -10,000

a) Which alternative should APC choose under the maximax criterion? (1 mark) b) Which option should APC choose under the maximin criterion? (1 mark) c) Which option should APC choose under the LaPlace criterion? (2 marks) d) Which option should APC choose with the Hurwicz criterion with α = 0.5? (2 marks) e) Using a minimax regret approach, what alternative should she choose? (4 marks) f) After reading about economic predictions , APC has assigned the probability that the market will

be expand , or be steady or be weak at 20%, 50% and 30 %. Using expected monetary values, what option should be chosen and what is that optimal expected value? (4 marks)

g) What is the most that the APC should be willing to pay for additional information? Use Expected Regret (3 marks)

h) Use the alternative method to verify EVPI (3 marks

Question 1B

A CEO of a multihospital system is planning to expand operations into various states. It will take several years to get certificate of need (CON) approvals so that the new facilities can be constructed. The eventual cost (in millions of dollars) of building a facility will differ among states, depending upon finances, labor, and the economic and political climate. An outside consulting firm estimated the costs for the new facilities as based on declining, similar, or improving economies, and the associated probabilities as shown in the Table below.

payoffs as costs states of nature decision alternatives

Declining Same Improving

Kentucky 44.00 38.00 30.00

Maryland 38.00 37.00 36.00

North carolina 39.00 34.00 31.00

Tennesee 46.00 34.00 28.00

Virginia 50.00 42.00 26.00 (a) Which alternative should the firm choose under the maximax criterion? (1 mark)

(b) Which option should the firm choose under the maximin criterion? (1 mark)

(c) Which option should the firm choose under the LaPlace criterion? (2 marks)

(d) Which option should the firm choose with the Hurwicz criterion with α = 0.4? (2 marks)

(e) Using a minimax regret approach, what alternative should the firm choose? (4 marks)

(f) Economists have assigned probabilities of 0.25, 0.40, and 0.35 to the possible economic climate

of declining, same and improving respectively. Using expected monetary values, what option

should be chosen and what is that optimal expected value? (4 marks)

(g) What is the most that the firm should be willing to pay for additional information? Use Expected

Regret (3 marks)

(h) Use the alternative method to verify EVPI (3 marks)

Question 1C

CWD Inc needs to decide how many of the new Samsung phone to purchase for the new store. The company has assumed that demand will be 60,110,180, or 220 samsung next month and they need to decide whether to order 60,110,180 or 220 Samsung for this period. Each Samsung cost CWD Inc $1250 and can be sold for $2000. Technology Inc can sell any unsold Samsung back to their supplier for $250.00

Number of Samsung demanded

Amount ordered 60 110 180 220

60

45,000

110 -5,000 180

135,000

220

-27,500

(a) Complete the Payoff table( 3 marks) (b) Using an optimistic approach (maximax), which option would you choose? 1 mark (c) Using a pessimistic approach (maximin), which option would you choose?1 mark (d) If you are a LaPlace decision maker, which option would you choose? 2 marks (e) If you are a Hurwicz decision maker, which option would you choose with α = 0.75?1 mark (f) Using a minimax regret approach, which option would you choose? 4 marks (g) Using the same probabilities of 0.20, 0.35, .25, and 0.20 for possible level of demand

respectively, Which decision alternative will maximise the expected profit? 4 marks g) What is the most the firm should be willing to pay to obtain further (perfect) information (EVPI)? 2 marks

h) Use the alternative method to verify EVPI (2 marks)

Question 2

A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm.

For $600, he could buy an expert weather forecast from CWD consulting.

States of Nature with Profits ($)

Does not include forecast cost

Decision Alternatives Warm weather(W)

Cold weather (C)

Ganja $16,000 $10,000

Coffee $14,000 $13000

Prior Probabilities P(W) = 0.60 P(C) = .40

Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20; P (G|C) = 0.10; P (B|C) = 0.90

After you have computed the revised probabilities round to two decimal places

a) Construct the appropriate decision tree to help the farmer make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs (5 marks). It also includes the revised probabilities (5 marks) (10 marks)

b) Fold back the decision tree (5 marks) to determine the best strategy for the farmer; you must state this strategy (1 mark). What is the final expected profit?( 1 mark)(7 marks)

c) What is the expected value of sample information(EVSI)- the most that should be paid to seismic testing firm for the test?( 1 mark)

d) Calculate the expected value of perfect information (EVPI)- the most that should be paid CWD for prediction of the uncertain outcomes.(1 mark)

e) What is the efficiency of sample information?(1 mark) Question 3 Data collected on the monthly demand for a certain product in thousands of dollars are shown in the following table.

Month Demand

1 145.5

2 160

3 71

4 99

5 194.5

6 206

7 135.5

8 152.5

9 246

10 259

11 181.5

12 194

a) Using a weighted moving average with three periods, determine the demand for period 13. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively b) Use exponential smoothing with a smoothing constant of 0.30 to forecast the sales. Assume that last period’s forecast for month 1 is equal to actual to begin the procedure. Which method do you think is best? Is this an improvement over the weighted average- use MAD only ( Six marks) c) Use regression analysis to estimate the line of best fit -use the manual method with the formulas shown below. (Eight marks)

Question four

A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks.

A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks. Activity Immediate

predecessors Optimistic time

Most likely time

Most pessimistic time

Variance

A - 2 3 4 0.11111

B - 2 4 6 0.44444

C A,B 1 2 3 0.11111

D B 1 3 5 0.44444

E A 2 3 4 0.11111

F C 1 4 7 1

G E,F 2 2 2 0

H D,F 2 5 8 1

I G,H 1 3 5 0.44444

J I 2 3 4 0.11111

You must use two decimal places at all times for expected times when they are not integer (you are not permitted to round off to integers). (a) Draw the activity network for this problem (6 marks) (b) Determine the Expected Times. (1 mark) (c) Determine the activity schedule (ES, EF, LS, and LF) as well as slack. (7 marks) (d) Determine and state the critical path for this project. (1 mark) (e) What are the expected time and the variance of the project? (2 marks) (f) What is the probability that the project is completed in 22 or fewer weeks(1 mark) (g) What date should be set such that there is a 94% chance of completion within that time? (2

marks)