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A

Decision Making Tools

QUANTITATIVE MODULE

DISCUSSION QUESTIONS Discussion questions 1 through 10 appear in the hardcover version of the text. 11.

Identify the six steps in the decision process.

12.

What should be considered when deciding between building a large facility and a small facility that can be expanded later?

13.

What is a decision tree?

14.

What is the expected value under certainty?

15.

Identify the five steps in analyzing a problem using a decision tree.

16.

Why are the maximax and maximin strategies considered to be optimistic and pessimistic, respectively?

17.

The expected value criterion is considered to be the rational criterion on which to base a decision. Is this really true? Is it rational to consider risk?

18.

When are decision trees most useful?

PROBLEMS Problems A.1 through A.22 appear in the hardcover version of the text. P

A.23 Given the following conditional value table, determine the appropriate decision under uncertainty using (a) maximax (b) maximin (c) equally likely States of Nature Alternatives Build new plant Subcontract Overtime Do nothing

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Very Favorable Market

Average Market

Unfavorable Market

$350,000 $180,000 $110,000 $0

$240,000 $90,000 $60,000 $0

$300,000 $20,000 $10,000 $0

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A.24 A decision-maker has two alternative courses of action, A1 and A2. There are three possible states of nature, S1, S2, and S3. The table of conditional profits, as well as the probabilities for the states of nature, appear below. Based on this decision table, which decision alternative produces the higher EMV? States of Nature Alternatives Probability A1 A2

P

S1 .3 10,000 5,000

S2 .5 20,000 30,000

S3 .2 6,000 15,000

A.25 The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Doug Blocher’s software firm: Demand Alternative 1 Alternative 2 Alternative 3

Low

High

$10,000 $5,000 $2,000

$30,000 $40,000 $50,000

The probability of low demand is 0.4, whereas the probability of high demand is 0.6. (a) What is the highest possible expected monetary value? (b) What is the expected value under certainty? (c) Calculate the expected value of perfect information for this situation. P

A.26 A decision-maker is faced with the selection of new manufacturing technologies. The three choices are Alternatives A, B, and C. Possible consumer demand levels are the states of nature: Scenarios 1, 2, and 3. Probabilities of these scenarios are in the table below. This table also contains the matrix of conditional profits. What is the EMV of each decision alternative? What is the best choice, using EMV as the criterion? How good is EMV as a criterion for this problem? Which decision alternative would YOU select? Support your choice.

Probability Alternative A Alternative B Alternative C P

Scenario 1

Scenario 2

Scenario 3

.1 $25,000,000 $500,000 $2,000,000

.5 $1,000,000 $1,800,000 $500,000

.4 $1,500,000 $1,000,000 $500,000

A.27 Chung Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosing a process that is inappropriate. Chen Chung is V.P.-Operations. He can choose among batch manufacturing, custom manufacturing, or he can invest in group technology. Chen won’t be able to forecast demand accurately until after he makes the process choice. Demand will be classified into four compartments: poor, fair, good, and excellent. The table below indicates the payoffs (profits) associated with each process/demand combination, as well as the probabilities of each long-term demand level. Poor Probability .1 Batch $200,000 Custom 100,000 Group Technology 1,000,000 Heizer/Render/Operations Management

Fair

Good

Excellent

.4 $1,000,000 300,000 500,000

.3 $1,200,000 700,000 500,000

.2 $1,300,000 800,000 2,000,000 Q-73

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Based on expected value, what choice offers the greatest gain? What would Chen Chung be willing to pay for a forecast that would accurately determine the level of demand in the future?

A.28 The University of Dallas bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and pre-registration records to determine how many copies of a text are needed. Pre-registration shows 90 operations management students enrolled, but bookstore manager Raymond Lutz has second thoughts, based on his intuition and some historical evidence. Lutz believes that the distribution of sales may range from 70 to 90 units, according to the following probability model: Demand Probability

70 .15

75 .30

80 .30

85 .20

90 .05

This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $36. (a) Construct the table of conditional profits. (b) How many copies should the bookstore stock, in order to achieve highest expected value? P

P

A.29 Joseph Biggs owns his own Sno-Cone business and lives 30 miles from a California beach resort. The sale of Sno-Cones is highly dependent upon his location and upon the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40 percent chance of foul weather. (a) Construct Joseph’s decision tree. (b) What decision is recommended by the expected value criterion? A.30 James Lawson’s Bed and Breakfast, in a small historic Mississippi town, must decide how to subdivide (remodel) the large old home that will become its inn. There are three alternatives: Option A would modernize all baths and combine rooms, leaving the inn with four suites, each suitable for two to four adults each. Option B would modernize only the second floor; the results would be six suites, four for two to four adults, two for two adults only. Option C (the status quo option) leaves all walls intact. In this case, there are eight rooms available, but only two are suitable for four adults, and four rooms will not have private baths. Below are the details of profit and demand patterns that will accompany each option. Annual profit under various demand patterns Alternatives A (Modernize all) B (Modernize 2nd) C (Status Quo) (a) (b)

P

High

p

Average

p

$90,000 $80,000 $60,000

.5 .4 .3

$25,000 $70,000 $55,000

.5 .6 .7

Draw the decision tree for Lawson. Which option has the highest expected value?

A.31 Louisiana is busy designing new lottery “scratch-off” games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal “Loser,” “Win $1,” or “Win $50.” B can reveal “Loser” or “Take a Second Chance.” C can reveal “Loser” or “Win $500.” On the Second Chance, the player is instructed to scratch off D or E. D can reveal “Loser” or “Win $1.” E can reveal “Loser” or “Win $10.” The probabilities at A are .9, .09, and .01. The probabilities at B are .8 and .2. The probabilities at C are .999 and .001. The probabilities at D are .5 and .5. Finally, the probabilities at E are .95 and .05. Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game. Q-74

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P A.32 Using the data in Problem A.8 on text page 731–732, provide the following: (a) The appropriate decision tree showing payoffs and probabilities. (b) The best alternative using expected monetary value (EMV).

CASE STUDY SKI RIGHT After retiring as a physician, Bob Guthrie became an avid downhill skier on the steep slopes of the Utah Rocky Mountains. As an amateur inventor, Bob was always looking for something new. With the recent deaths of several celebrity skiers, Bob knew he could use his creative mind to make skiing safer and his bank account larger. He knew that many deaths on the slopes were caused by head injuries. Although ski helmets have been on the market for some time, most skiers considered them boring and basically ugly. As a physician, Bob knew that some type of new ski helmet was the answer. Bob’s biggest challenge was to invent a helmet that was attractive, safe, and fun to wear. Multiple colors, using the latest fashion designs would be a must. After years of skiing, Bob knew that many skiers believed that how you looked on the slopes was more important than how you skied. His helmets would have to look good and fit in with current fashion trends. But attractive helmets were not enough. Bob had to make the helmets fun and useful. The name of the new ski helmet, Ski Right, was sure to be a winner. If Bob could come up with a good idea, he believed that there was a 20% chance that the market for the Ski Right Helmet would be excellent. The chance of a good market should be 40%. Bob also knew that the market for his helmet could be only average (30% chance) or even poor (10% chance). The idea of how to make ski helmets fun and useful came to Bob on a gondola ride to the top of a mountain. A busy executive on the gondola ride was on his cell phone trying to complete a complicated merger. When the executive got off of the gondola, he dropped the phone and it was crushed by the gondola mechanism. Bob decided that his new ski helmet would have a built-in cell phone and an AM/FM Stereo radio. All of the electronics could be operated by a control pad worn on a skier’s arm or leg. Bob decided to try a small pilot project for Ski Right. He enjoyed being retired and didn’t want a failure to cause him to go back to work. After some research, Bob found Progressive Products (PP). The company was willing to be a partner in developing the Ski Right and sharing any profits. If the market were excellent, Bob would net $5,000 per month. With a good market, Bob would net $2,000. An average market would result in a loss of $2,000, and a poor market would mean Bob would be out $5,000 per month. Another option for Bob was to have Leadville Barts (LB) make the helmet. The company had extensive experience in making bicycle helmets. Progressive would then take the helmets made by Leadville Barts and do the rest. Bob had a greater risk. He estimated that he could lose $10,000 per month in a poor market or $4,000 in an average market. A good market for Ski Right would result in a $6,000 profit for Bob, while an excellent market would mean a $12,000 profit per month. A third option for Bob was to use TalRad TR, a radio company in Tallahassee, Florida. TalRad had extensive experience in making military radios. Leadville Barts could make the helmets, and Progressive Products could do the rest. Again, Bob would be taking on greater risk. A poor market would mean a $15,000 loss per month, while an average market would mean a $10,000 loss. A good market would result in a net profit of $7,000 for Bob. An excellent market would return $13,000 per month. Bob could also have Celestial Cellular (CC) develop the cell phones. Thus, another option was to have Celestial make the phones and have Progressive do the rest of the production and distribution. Because the cell phone was the most expensive component of the helmet, Bob could lose $30,000 per month in a poor market. He could lose $20,000 in an average market. If the market were good or excellent, Bob would see a net profit of $10,000 or $30,000 per month, respectively. Bob’s final option was to forget about Progressive Products entirely. He could use Leadville Barts to make the helmets, Celestial Cellular to make the phones, and TalRad to make the AM/FM stereo radios. Bob could then hire some friends to assemble everything and market the finished Ski Right helmets. With this final alternative, Bob could realize a net profit of $55,000 a month in an excellent market. Even if the market were just good, Bob would net $20,000. An average market, however, would mean a loss of $35,000. If the market were poor Bob would lose $60,000 per month. Heizer/Render/Operations Management

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DISCUSSION QUESTIONS 1.

What do you recommend?

2.

Compute the expected value of perfect information.

3.

Was Bob completely logical in how he approached this decision problem? Source: B. Render, R.M. Stair, and M. Hanna, Quantitative Analysis for Management, 8th ed. Upper Saddle River, N.J.: Prentice-Hall (2003). Reprinted by permission of Prentice-Hall, Inc.

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