Decision Analysis A decision maker has prepared the following payoff table.5States of NatureAlternativeHighLowBuy75|-10Rent7030Lease5035Using the Maximin criterion, what is the best decision and the expected payoff?Best decisionPayoff

Decision Table Alternatives High Low Buy 75 -10 Rent 70 30 Lease 50 35

Answered: A decision maker has prepared the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 76P

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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.
A payoff table is given as: S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 (a) What choice should be made by the optimistic decision maker? (b) What choice should be made by the conservative decision maker? (c) What decision should be made under minimal regret? (d) If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?
A landlord can either lease for one or two years or sell offices outrightly for K100 million with payoffs as follows: Lease -100 50 150 Sell 100 100 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. Required: What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S1 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Required: Find EMV and recommend the course of action Find the…
A television network earns an average of $1.6 million each season from a hit program and loses an averageof $400,000 each season on a program that turns out to be a flop, and of all programs picked up by thisnetwork in recent years, 25% turn out to be hits and 75% turn out to be flops. a) Construct a decision tree to help the television network identify the strategy that maximizes itsexpected profit in responding to a newly proposed television program. Make sure to label all decisionand chance nodes and include appropriate costs, payoffs and probabilities. b) What should the network do? What is their expected profit? c) The network can conduct market research to determine whether a program will be a hit or a flop. Ifthe market research report is perfectly reliable, what is the most the network should be willing to payfor it? Can you please include pictures of excel sheets. Having trouble determining what the excel sheet should look like
The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million. Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain. Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?
Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tire products. Carlisle’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. The market for this particular tire product may expand, remain stable, or contract. Carlisle’s marketing department estimates the probabilities of these market outcomes to be 0.25, 0.35, and 0.40, respectively. The file P06_31.xlsx (picture of given excel file is attached) contains Carlisle’s payoffs and costs for the various combinations of decisions and outcomes. Identify the strategy that maximizes this tire manufacturer’s expected profit. Perform a sensitivity analysis on the optimal decision, letting each of the monetary inputs vary one at a time plus or minus 10% from its base value, and summarize your findings. Which of the inputs appears to have the largest effect on the best solution?
Dwayne Whitten, president of Whitten Industries, is considering whether to build a manufacturing plant in north Texas. His decision is summarized in the following table: Alternatives Favorable Market Unfavorable Market Build large plant $400,000 −$300,000 Build small plant $120,000 −$15,000 Don't Build $0 $0 Market Probability 0.40 0.60 a) The correct decision tree for Dwayne is shown in Figure ____ (all payoffs are in thousands). b) To maximize the return, Dwayne's decision should be to ______ . c) For Dwayne, the expected value of perfect information (EVPI) = $___________ (enter your answer as a whole num
An oil company must decide whether or not to drill an oil well in a particular area that they already own. The decision maker (DM) believes that the area could be dry , reasonably good or a bonanza. See data in the table which shows the gross revenues for the oil well that is found. Decision Dry (D) Reasonably good(G) Bonanza(B) Drill $0 $85 $200 m Abandon $0 $0 $0 Probability 0.3 0.3 0.4 Drilling costs 40M. The company can take a series of seismic soundings ( at a cost of 12M) to determine the underlying geological structure. The results will be either “no structure”, “open structure or “closed structure”. The reliability of the testing company is as follows that is, this reflects their historical performance. Note that if the test result is “no structure” the company can sell the land to a developer for 50 m, otherwise (for the other results) it can abandon the drilling idea at no benefit to itself.…
A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the tablebelow. Which alternative should be selected if the decision criterion is:a. Maximax?b. Maximin?c. Laplace?d. Minimax regret?NEXT YEAR’SDEMANDAlternative Low HighDo nothing $50* $60Expand 20 80Subcontract 40 70
Consider the following payoff table for three product decisions (A, B, and C) and three future market conditions (payoffs = P millions) Assume that is now possible for the company to estimate a probability of 0.40 that market condition1 will exist, 0.40 for market condition 2 and a probability of 0.20 that market condition 3 will exist in the future. Determine the best decision using expected value. Determine the expected value of perfect information (EVPI)?Determine the best decision using expected opportunity loss.

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A decision maker has prepared the following payoff table. States of Nature Alternative High 75 Low Buy -10 Rent 70 30 Lease 50 35 Using the Maximin criterion, what is the best decision and the expected payoff? Best decision Payoff