Reference no: EM132207207

Making Decisions Under Certainty, Uncertainty, and Risk

Different methods can be used for approaching and solving decision problems. These methods depend on the amount of uncertainty associated with the parameters of the decisions and the likelihoods of the outcomes.

In this week's Assignment, you will solve business decision problems presented in the in your Resources. The problems under consideration this week are framed in terms of money and the impact on the bottom line, as opposed to determining the utility of alternatives. These problems range from making decisions in which information about the parameters of the problem are known with certainty, unknown, or determined probabilistically. Specific techniques for solving these decision problems under these conditions are discussed. Before you begin, watch the video "Managerial Decisions," which provides an introduction to this Assignment.

Be sure to provide your rationale and explanations for your solutions.

Also, articulate any questions or challenges you experienced when completing the problems in the Assignment. Explain how these problems can be applied to decision making; provide an example that is different from the ones or anything in the text.

Question 1. A small building contractor has recently experienced two successive years in which work opportu¬nities 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 table below. Which alternative should be selected if the decision criterion is
a. Maximax?
b. Maximin?
c. Laplace?
d. Minimax regret?

                                                  NEXT YEAR'S DEMAND

Alternative                                   Low                        High

Do nothing                                   550*                       $60

Expand                                         20                        80

Subcontract                                   40                        70

'Profit in $ thousands.

Question 2. The lease of Theme Park, Inc., is about to expire. Management must decide whether to renew the lease for another 10 years or to relocate near the site of a proposed motel. The town planning board is currently debating the merits of granting approval to the motel. A consultant has estimated the net present value of Theme Park's two alternatives under each state of nature as shown on the fol¬lowing page.

What course of action would you recommend using?
a. Maximax.
b. Miximin.
c. Laplace.
d. Minimax regret.

Options          Approved         Rejected
Renew           $500.0100        $4.000.00
Relocate          5.000,000         100.00

Question 3. Refer to Problem 6. Suppose that the management of Theme Park, Inc., has decided that there is a 35 probability that the motel's application will be approved.
a. If management uses maximum expected monetary value as the decision criterion, which alter¬native should it choose?
b. Represent this problem in the form of a decision tree.
c. If management has been offered the option of a temporary lease while the town planning board considers the motel's application, would you advise management to sign the lease? The lease will cost $24,000.

Question 4. A firm must decide whether to construct a small, medium, or large stamping plant. A consultant's report indicates a .20 probability that demand will be low and an .80 probability that demand will be high.
If the firm builds a small facility and demand turns out to be low, the net present value will be $42 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $42 million or expand greatly for a net present value of $48 million.
The firm could build a medium-size facility as a hedge: If demand turns out to be low, its net present value is estimated at S22 million; if demand turns out to be high, the firm could do nothing and realize a net present value of $46 million, or it could expand and realize a net present value of $50 million.
If the firm builds a large facility and demand is low, the net present value will be -$20 million, whereas high demand will result in a net present value of $72 million.
a. Analyze this problem using a decision tree.
b. What is the maximin alternative?
c. Compute the EVPI and interpret it.
d. Perform sensitivity analysis on P(high).

Question 5. A logistics provider plans to have a new warehouse built to handle increasing demands for its services. Although the company is unsure of how much demand there will be, it must decide now on the size (large or small) of the warehouse. Preliminary estimates are that if a small warehouse is built and demand is low, the monthly income will be $700,000. If demand is high, it will have to either expand the facility or lease additional space. Leasing will result in a monthly income of $100,000 while expanding will result in a monthly income of $500,000.
If a large warehouse is built and demand is low, monthly income will only be $40,000, while if demand is high, monthly income will be $2 million.
a. Construct a tree diagram for this decision.
b. Using your tree diagram. Identify the choice that would be made using each of the four approaches for decision making under uncertainty.