Baøi taäp 2: ra quyeát ñònh trong moâi tröôøng baát ñònh. Phaân coâng baøi taäp:

stt Teân baøi taäp Nhoùm thöïc hieän1 1 Hoaøng Anh2 2 Minh Caûnh3 3 Vónh Taøi4 4 Traàn phöông Thaûo5 5 Ñoã Thaønh Trung6 5 Leâ phan phuù Haûi7 7 Hoaøi Chaâu8 8 Phaïm Anh Tuaán9 9 Nguyeãn V Höõu10 10 Döông Thu Höông11 11 Huyønh Thanh phong12 12 Nguyeãn Ñaéc Thoï13 13 Löông Troïng Quyeàn14 14 Xuaân Nöõ15 15 Dieãm Chaâu16 16 Phan hoaøng Khaùnh

Löu yù traû lôøi boå sung caâu hoûi sau trong quaù trình phaân tích: 1. If there is no knowledge of probability, how decisions are made

and why?2. If different criteria, such as EMV, EOL, RTRR are used, what are

the decisions to be made? Are they different? And why?3. In several given cases, what need to be added to answer all the

questions posed?

BT 1:An entrepreneur wants to determine whether it would be profitable to establish a gardening service in a local suburb. The entrepreneur believes that there are four possible levels of demand for this gardening service:Very low demand—1% of the households would use the service.Low demand—5% of the households would use the service.Moderate demand—10% of the households would use the service.High demand—25% of the households would use the service.

Based on past experiences in other suburbs, the entrepreneur assigns the following probabilities to the various demand levels:

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The entrepreneur has calculated the following profits or losses ($) of this garden service for each demand level (over a period of one year):

Before making a final decision, the entrepreneur conducts a survey to determine demand for the gardening service. A random sample of 20 households is selected, and 3 indicate that they would use this gardening service. Revise the prior probabilities in light of this sample information. (Hint: Use the binomial distribution to determine the probability of the outcome that occurred, given a particular level of demand.

BT 2A manufacturer of a brand of inexpensive felt-tip pens maintains a production process that produces 10,000 pens per day. In order to maintain the highest quality of this product, the manufacturer guarantees free replacement of any defective pen sold. Each defective pen produced costs 20 cents for the manufacturer to replace. Based on past experience, four rates of producing defective pens are possible:Very low—1% of the pens manufactured will be defective.Low—5% of the pens manufactured will be defective.Moderate—10% of the pens manufactured will be defective.High—20% of the pens manufactured will be defective.

The manufacturer can reduce the rate of defective pens produced by having a mechanic fix the machines at the end of each day. This mechanic can reduce the rate to 1%, but his services will cost $80.

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A payoff table based on the daily production of 10,000 pens, indicating the replacement costs ($) for each of the two alternatives (calling in the mechanic and not calling in the mechanic), is as follows:

Based on past experience, each defective rate is assumed to be equally likely to occur. If at the end of a day’s production, a sample of 15 pens is selected, and 2 are defective. Revise the prior probabilities in light of this sample information. (Hint: Use the binomial distribution to determine the probability of the outcome that occurred, given a particular defective rate.)

BT 3The manufacturer of a nationally distributed brand of potato chips wants to determine the feasibility of changing the product package from a cellophane bag to an unbreakable container. The product manager believes that there are three possible national market responses to a change in product package: weak, moderate, and strong. The projected payoffs, in millions of dollars, in increased or decreased profit compared to the current package are as follows:

Based on past experience, the product manager assigns the following probabilities to the different levels of national response:P (Strong national response) = 0.10

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P (Moderate national response) = 0.60P (Weak national response) = 0.30

Before making a final decision, the product manager would like to test market the new package in a selected city by substituting the new package for the old package. A determination can then be made about whether sales have increased, decreased, or stayed the same. In previous test marketing of other products, when there was a subsequent weak national response, sales in the test city decreased 60% of the time, stayed the same 30% of the time, and increased 10% of the time. Where there was a moderate national response, sales in the test city decreased 20% of the time, stayed the same 40% of the time, and increased 40% of the time. When there was a strong national response, sales in the test city decreased 5% of the time, stayed the same 35% of the time, and increased 60% of the time.

BT 4A vendor at a local baseball stadium must determine whether to sell ice cream or soft drinks at today’s game. The vendor believes that the profit made will depend on the weather. The payoff table (in $) is as follows:

Based on her past experience at this time of year, the vendor estimates the probability of warm weather as 0.60.

If prior to making her decision, she decides to listen to the local weather forecast. In the past, when it has been cool, the weather reporter has forecast cool weather 80% of the time. When it has been warm, the weather reporter has forecast warm weather 70% of the time. The local weather forecast is for cool weather. Revise the prior probabilities now that you know that the weather forecast is for cool weather.

BT 5An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits ($) of each investment under each economic condition are indicated in the following payoff table:

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Based on his own past experience, the investor assigns the following probabilities to each economic condition:P (Economy expands) = 0.20P (No change) = 0.50P (Economy declines) = 0.30

Prior to making his investment decision, the investor decides to consult with his financial adviser. In the past, when the economy has declined, the financial adviser has given a rosy forecast 20% of the time (with a gloomy forecast 80% of the time). When there has been no change in the economy, the financial adviser has given a rosy forecast 40% of the time. When there has been an expanding economy, the financial adviser has given a rosy forecast 70% of the time. The financial adviser in this case gives a gloomy forecast for the economy. a. Revise the probabilities of the investor based on this economic forecast by the financial adviser.

BT 6An author is trying to choose between two publishing companies that are competing for the marketing rights to her new novel. Company A has offered the author $10,000 plus $2 per book sold. Company B has offered the author $2,000 plus $4 per book sold. The author believes that five levels of demand for the book are possible: 1,000, 2,000, 5,000, 10,000, and 50,000 books sold.Given the results computed in that problem, suppose that the probabilities of the levels of demand for the novel are as follows:

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Prior to making a final decision, the author decides to have an experienced reviewer examine her novel. This reviewer has an outstanding reputation for predicting the success of a novel. In the past, for novels that sold 1,000 copies, only 1% received favorable reviews. Of novels that sold 5,000 copies, 25% received favorable reviews.Ofnovels that sold 10,000 copies, 60% received favorable reviews. Of novels that sold 50,000 copies, 99% received favorable reviews. After examining the author’s novel, the reviewer gives it an unfavorable review. a. Revise the probabilities of the number of books sold in light of the reviewer’s unfavorable review.

BT 7:

Your company is considering whether it should tender for two contracts (MS1 and MS2) on offer from a government department for the supply of certain components. The company has three options:

tender for MS1 only; or tender for MS2 only; or tender for both MS1 and MS2.

If tenders are to be submitted the company will incur additional costs. These costs will have to be entirely recouped from the contract price. The risk, of course, is that if a tender is unsuccessful the company will have made a loss.

The cost of tendering for contract MS1 only is £50,000. The component supply cost if the tender is successful would be £18,000.

The cost of tendering for contract MS2 only is £14,000. The component supply cost if the tender is successful would be £12,000.

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The cost of tendering for both contract MS1 and contract MS2 is £55,000. The component supply cost if the tender is successful would be £24,000.

For each contract, possible tender prices have been determined. In addition, subjective assessments have been made of the probability of getting the contract with a particular tender price as shown below. Note here that the company can only submit one tender and cannot, for example, submit two tenders (at different prices) for the same contract.

Option Possible Tender Prices (£)

Probability of getting contract

MS1 only 130,0000.20

115,000 0.85

130,000 0.20

MS2 only70,000

0.15

65,000 0.80

60,000 0.95

MS1 and MS2

190,0000.05

140,000 0.65

In the event that the company tenders for both MS1 and MS2 it will either win both contracts (at the price shown above) or no contract at all.

A consultant has approached your company with an offer that in return for £20,000 in cash she will ensure that if you tender £60,000 for contract MS2 only your tender is guaranteed to be successful. Should you accept her offer or not and why?

BT 8:

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The Metal Discovery Group (MDG) is a company set up to conduct geological explorations of parcels of land in order to ascertain whether significant metal deposits (worthy of further commercial exploitation) are present or not. Current MDG has an option to purchase outright a parcel of land for £3m.

If MDG purchases this parcel of land then it will conduct a geological exploration of the land. Past experience indicates that for the type of parcel of land under consideration geological explorations cost approximately £1m and yield significant metal deposits as follows:

manganese 1% chance gold 0.05% chance silver 0.2% chance

Only one of these three metals is ever found (if at all), i.e. there is no chance of finding two or more of these metals and no chance of finding any other metal.

If manganese is found then the parcel of land can be sold for £30m, if gold is found then the parcel of land can be sold for £250m and if silver is found the parcel of land can be sold for £150m.

MDG can, if they wish, pay £750,000 for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and past experience indicates that three-day test explorations cost £250,000 and indicate that significant metal deposits are present 50% of the time.

If the three-day test exploration indicates significant metal deposits then the chances of finding manganese, gold and silver increase to 3%, 2% and 1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding manganese, gold and silver decrease to 0.75%, 0.04% and 0.175% respectively.

A company working in a related field to MDG is prepared to pay half of all costs associated with this parcel of land in return for half of all revenues. Under these circumstances what would you recommend MDG should do and why?

BT 9:

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The decision sciences department is trying to determine which of two copying machines to purchase. Both machines will satisfy the department’s needs for the next ten years.

Machine 1 costs $2,000 and has a maintenance agreement, which, for an annual fee of $150, covers all repairs. Machine 2 costs $3,000, and its annual maintenance cost is a random variable.

At present, the decision sciences department believes there is a 40% chance that the annual maintenance cost for machine 2 will be $0, a 40% chance it will be $100, and a 20% chance it will be $200.

Before the purchase decision is made, the department can have a trained repairer evaluate the quality of machine 2.

If the repairer believes that machine 2 is satisfactory, there is a 60% chance that its annual maintenance cost will be $0 and a 40% chance it will be $100. If the repairer believes that machine 2 is unsatisfactory, there is a 20% chance that the annual maintenance cost will be $0, a 40% chance it will be $100, and a 40% chance it will be $200. If there is a 50% chance that the repairer will give a satisfactory report.

If the repairer charges $40, what should the decision sciences department do?

BT 10: BUYING A HOUSE

Debbie and George Calvert are thinking of making an offer to purchase a house in Shaker Heights, Ohio. Both George and Debbie saw the house this morning and fell in love with it.

The asking price for the house is $400,000, and it has been on the market for only one day. Their broker told them that there were more than 20 potential buyers who saw the house that day. She also added that another broker told her that an offer on the house was going to be presented by that broker this afternoon. Their broker has advised them that if they decide to make an offer on the house, they should offer very close to the asking price of $400,000. She also added that if there are competing offers on the house that are close in value, then it is common practice for the seller to ask the potential buyers to submit their final offers the following day.

Trying to be objective about this decision, Debbie has decided to construct a decision tree to help her with this decision. She has assumed that the “fair market value” of the house under consideration is $400,000. She has assigned an “emotional value” of $10,000 if she

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and George are successful in purchasing the house. That is, whereas the fair market value of the house is $400,000, the house is worth $410,000 to Debbie and George. Thus, if they were to be successful in purchasing the house for $390,000, the value of this outcome would be $20,000. Of course, if they were not successful in purchasing the house, the value of this outcome would be simply $0. Debbie has also assigned a probability of 0.30 that they will be the only bidders on the house.

Debbie has decided to consider making one of only three offers: $390,000,$400,000, or $405,000. She estimates that if they are the only bidders, the probability that an offer of $390,000 is accepted is 0.40, the probability that an offer of $400,000 is accepted is 0.60, and the probability that an offer of $405,000 is accepted is 0.90. If, however, there are other bidders, Debbie assumes that the seller will ask them to submit a final offer the following day. In such a scenario, she will then have to rethink what to do: She can withdraw her offer, submit the same offer, or increase her offer by $5,000. She feels that in the event of multiple bids, the probability that an offer of $390,000 is accepted is 0.20, the probability that an offer of $395,000 is accepted is 0.30, the probability that an offer of $400,000 is accepted is 0.50, the probability that an offer of $405,000 is accepted is 0.70, and the probability that an offer of $410,000 is accepted is 0.80.

BT 11:

Nova Ltd is considering whether to spend a further £30K to develop a new product. If the development program is successful two alternative sizes of plant are likely to be considered:

Plant Production capacity Capital cost Running cost (tonnes) (£K) (£K per year)Small 2,000 100 50Large 5,000 200 100

The development program, which is thought to have a 70% chance of success, will take a year to complete. After completing that program it would take one year to build a small plant and two years to build a large plant. It is believed that one other major company in this field is developing a competing product and the marketing intelligence unit of Nova believe that there is a 25% chance that this company will have their product on the market 3 years from now, a 50% chance that they will have their product on the market 4 years from now and a 25%

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chance that it will take them 5 years to get their product onto the market.

The following estimates of Nova's possible selling price have been obtained from the marketing department:

Small LargeOutput (per year) 2,000 tonnes 5,000 tonnesMonopoly price £50 per tonne £30 per tonneCompetitive price £30 per tonne £25 per tonne

where the monopoly price applies whilst Nova is without competition and the competitive price applies once the competitor company have their product on the market.

If the likely lifetime of the Nova product is 10 years (once released onto the market) what should Nova do?

BT 12:

Company X is deciding whether it should invest £750,000 in a program of major improvements for a particular product which, with or without these major improvements, will remain in production for just one more year. Company Y produces an almost identical product which is in direct competition with X's and it is predicted that there is a 50/50 chance (irrespective of any action X takes) that Y will institute similar major improvements to its own product.

If X improves and Y does not then for X the probabilities are 0.6, 0.3 and 0.1 of sales improving by 15%, 10% and 5% respectively.

If X and Y both improve then the total market will increase and X would expect its sales to rise by 8%.

If neither X nor Y improve then the present demand is expected to continue and this for X is 500,000 units a year.

If X doesn't improve and Y does then the probabilities are 0.8, 0.1 and 0.1 of X's sales falling by 15%, 10% and 5% respectively.

If X decides not to invest £750,000 in the program of major improvements it has the option, in the event that Y does carry out major improvements, of instituting either a normal program of minor improvements or a crash program of minor improvements (instead of the program of major improvements).

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A crash program could be instituted very quickly but would cost 50% more than the normal program. The normal program is certain of success, the crash program however has a 10% chance of failure and the sales if the crash program fails would be the same as if X had done nothing in response to Y's major improvements. If, however, X is successful with its crash program it could expect to attain a 7% increase in sales. The normal program would attain a 5% increase in sales.

The contribution to profit of each unit sold by X is £40. The cost of the normal program of minor improvements for X is estimated to be £400,000.

BT 13:

Chelsea Bush is an emerging candidate for her party's nomination for president of the US. She is considering whether or not to run in the Super Tuesday (ST) primaries. If she enters the ST primaries, she and her advisors believe that she will either do well (finish 1st or 2nd) or do poorly (finish 3rd or worse) with probabilities of 0.40 and 0.60, respectively. Doing well on Super Tuesday will net her campaign approximately $16 million in new contributions, whereas a poor showing will mean a loss of $10 million after numerous TV ads are paid for. Alternatively, she may choose not to run at all on Super Tuesday and incur no costs.

Chelsea's advisors realize that her chances of success on Super Tuesday may be affected by the outcome of the smaller New Hampshire (NH) primary occurring three weeks earlier. The cost of entering and campaigning in the NH primary is estimated to be $1.6 million. Political analysts feel that the results of the NH primary are correct two-thirds of the time in predicting the results of the ST primaries. Among Chelsea's advisors is a "quant" expert who has computed the following probabilities: (1) she has a 0.47 chance of doing well in the NH primary; (2) if she does well in NH, she has a 0.57 chance of doing well on Super Tuesday; and (3) if she does poorly in NH, she has a 0.25 chance of doing well on Super Tuesday.

BT 14A company must decide whether to build a small plant or build a large plantto manufacture a new product with a market life of ten years.Demand for the product may possibly be high during the first two years but, if many of the initial users find it unsatisfactory, the demand could then fall to a low level thereafter. High initial demand could

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indicate the possibility of a sustained high-volume market. Low demand for full ten years.If the demand is initially high and remains so, and the company finds itself with insufficient capacity within the first two years, competing products will certainly be introduced by other companies.If the company initially builds a big plant, it must live with it for the whole tenyears, whatever the size of the market demand.If it builds a small plant, there is the option of expanding the plant in two years time, an option that it would only take up if demand were high during the introductory period.If a small plant is built initially and demand is low during the introductory period, the company will maintain operations in the small plant, and make a good profit on the low-volume throughput.

Marketing Information:60% chance of a large market in the long run, and 40% of a long-term low demand developing initially as follows:Initially High, sustained High 60%Initially High, long-term Low 10%Initially Low, continuing Low 30%Initially Low, long-term High 0%Capital Costs:A large plant would cost £3m to build.A small plant would cost £1.3m initially, and an additional £2.2m if expanded after two years.Annual Income:A large plant with high market volume would yield £1m annually for ten years.A large plant with low market volume would yield only £0.1m annually.A small plant with low market demand would yield a cash income of £0.4m p.a.A small plant during an initial period of high demand would yield £0.45m p.abut, because of competition, this would drop to £0.25m per annum in the long run, if high demand continued.

If an initial small plant were expanded after two years to meet sustained high demand, it would yield £0.7m annually for the remaining eight years.If an initial small plant were expanded after two years, but high demand were not sustained, the estimated annual income for the remaining eight years would be £0.05m.

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BT 15The Grimm Group presents in-house training seminars to organizations throughout the United States. The company currently presents seminarson three topics: quality control, material management, and just-in-time (JIT) manufacturing. The quality control seminar costs each participant $500,and the Grimm Group’s gross margin (revenue –direct expenses) is 40% of this amount. The material-management seminar costs $450 for each attendee and also has a 40% gross margin; the JIT seminar costs $600 and has a 35% gross margin.

After 5 years of expansion, attendance at the seminars has declined more than 10% in the past year. The revenues from the three operations last yearwere quality control, $1,200,000; material management, $900,000; and JIT, $1,400,000.

At the yearly forecasting meeting, Graciela Grimm, the company’s founder, projects that if no changes are made in marketing philosophy, revenues will be stagnant this year. She is, however, considering two options that should increase demand for the three seminars. The first option is to incorporate a computer simulation game as part of each seminar. Projections indicate that adding this type of game will increase the demand for the quality control seminar by 10% and the demand for the other two seminars by 15% each. Adding a game will increase the cost associated with each seminar participant by $50; but because the market is very competitive, the company will have to hold the line on the price change. The second option is to offer 3-day training seminars on the same topics but at 60% of the price of the 5-day seminars.

Unfortunately, the cost of presenting the 3-day seminars will be reduced by only 20% from the cost of the original seminars. The president estimates the demand for the shorter seminars this year will generate revenues equal to 50% of the revenues realized from each 5-day seminar in the past year. Also, adding the shorter seminars will reduce the projected demand for the original seminars to 75% of last year’s level.

An initial market survey of the acceptance of simulation games indicates they are so popular that there is a 70% chance the Grimm Group will be able to raise the price of the seminars by enough to maintain its previous margins without affecting the demand.

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BT 16

Rockstone International is one of the world’s largest diamond brokers. The firm purchases rough stones and has them cut and polished for sale in the United States and Europe. The diamond business has been very profitable, and from all indications it will continue to be so. However, R. B. Randall,president and chief executive officer for Rockstone, has stressed the need for effective management decisions throughout the organization if the firm is to remain profitable and competitive.Normally, R. B. does not involve herself in personnel decisions, but today’s situation is not typical. Beth Harkness, Rockstone’s personnel manager, is considering whether to hire Hans Marquis, a world-famous diamond cutter, toreplace Omar Barboa, who broke both his hands in a freak skateboard accident almost a month ago. If he is hired, Hans Marquis will be paid on a commission basis at the rate of $5,000 for each stone he cuts successfully. (Because of his professional pride, Hans will accept no fee if he is unsuccessful in cutting a stone.)In the past, the decision of whether to hire Hans would have been simple. If he was available, he would be hired. However, 6 months ago, the Liechtenstein Corporation introduced the world’s first diamond-cutting machine. This machine, which can be leased for $1,000,000 per year, isguaranteed to cut stones successfully 90% of the time.

Although Hans Marquis has an excellent reputation, Rockstone International cannot be sure about his success rate because of the extreme secrecy among people in the diamond business. Hans claims that his success rate is 95%, but he has been known to exaggerate. Rockstone executives have made the following assessments, based on all the information they could obtain:

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Rockstone purchases gemstones at a cost of $15,000 each. A successful cut yields four diamonds that can be sold at an average price of $35,000 each. Harry Winkler, sales and purchasing manager, reports that his projections for the next year indicate a need for 100 stones to be cut.R. B. Randall knows there must be a way to decide whether to hire Hans Marquis or lease the new cutting machine.

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