The expected utility implies that the decision maker regards this option as being equivalent to a lottery offering a same chance of the best/best outcome (and a complementary probability of the worst/worst outcome)

The expected utility implies that the decision maker regards this option as being equivalent to a lottery offering a same chance of the best/best outcome (and a complementary probability of the worst/worst outcome)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 46P

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It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
11. Bakery Products is considering the introduction of a new line of pastries. In order to produce the new line, the bakery is considering either a major or a minor renovation of its current plant. Bill Wicker, head of operations, has developed the following conditional values table: Alternatives Favorable Market Unfavorable Market Major renovation $100,000 -$90,000Minor renovation $40,000 -$20,000 Do nothing $0 $0 Assume that the probability of a favorable market is equal to the probability of an unfavorable market.Part 2a) Choose the appropriate decision tree showing payoffs and probabilities.A.MinorFavorable40,000Unfavorable-20,000UnfavorableFavorableMajor100,000-90,000Do…
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Joseph Biggs owns his own ice cream truck and lives 30 miles from a Florida beach resort. The sale of his products is highly dependent on his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $30per day in bad weather. At home, his profit will be $80 in fair weather and $50 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. a) The correct decision tree for Joseph is shown in Figure ___________ . b) To maximize the return, for selling ice cream, Joseph's decision should be to use the ______ . Expected monetary value for Joseph = $______
Option 2: Raise prices by 50%. If this occurs, there is a 75% chance that an Entrepreneur will set up in competition this year. The board’s estimate of its annual profit in this situation would be as follows: 2A: With new competitor 2B: Without new competitor Probability Profit (Sh.) Probability Profit (Sh.) 0.25 150,000 0.5 200,000 0.5 120,000 0.3 150,000 0.25 80,000 0.2 100,000 Option 3: Expand the car park quickly at a cost of Sh. 50,000 keeping prices theSame. The profits are then estimated to be like 2B above, except that the probabilities would be 0.6, 0.3 and 0.1 respectively. Required: Draw a decision tree for the above problem, including all the relevant data. Using expected values analyze the decision tree and recommend the best option to the owners of the car park.
Global Logistics needs to rent space for storing product for the next three years. The following information regarding the demand and spot price is available. Current demand for the product is 150,000. Historically, Global Logistics has required 1500 square feet to store 1500 units of the product. Demand for the product can go up by 20% with a probability of 0.7 or down by 20% with a probability of 0.3. Global Logistics can sign a three-year fixed lease to rent 150,000 square feet of space at $1.00 per square foot per year. The firm may also choose to obtain warehousing space on the spot market. The current spot market price is $1.20 per square foot per year. The spot price can go up by 10% with a probability of 0.8 and can decrease by 10% with a probability of 0.2. The firm receives a revenue of $1.22 for each unit of demand. a) Create a decision tree showing period 0, 1 and 2 for the scenario described above. b) Calculate the NPV for the option when the firm decides to sign a…
On a decision tree, at each state-of-nature node: a) the alternative with the greatest EMV is selected. b) an EMV is calculated. c) all probabilities are added together. d) the branch with the highest probability is selected.
Downtown Health Clinic needs to order influenza vaccines for the next flu season. The Clinic charges its patients $15.00 per vaccination and each dose of vaccine costs the clinic $4.00 to purchase. The Center for Disease Control has a long standing policy of buying back unused vaccines for $1.00 per dose. The Clinic estimates the following probability distribution for the season’s demand:Demand Probability2,000 0.053,000 0.204,000 0.255,000 0.406,000 0.10a. How many vaccines should the Clinic order to maximize its expected profit?b. The Clinic is trying to determine if they should participate in a new Federal program in which the cost of each dose is reduced to $2.00. However, to participate in the program, they can charge no more than $10.00 per vaccine. On strictly a profit maximizing basis, should the Clinic agree to participate?