OSCM 471/571 Optimization and Decision Support Modeling for Business

OSCM 471/571 Optimization and Decision Support Modeling for Business

Homework 5, Spring 2022

Notice for Homework 5

Instructor: Seokjun Youn ( [email protected] )

· Due date: Thursday 4/20, 11:59 pm

· Please submit your files to D2L > Assignments > Homework 5

1. A Word file (or PDF) with your answers combined into a single document.

2. An Excel spreadsheet template with your answers (for some sub-questions).

· This homework is made up of 7 questions (20 pts):

· Lecture Note 7: Decision Making under Uncertainty

· Q1 (2 pts), Q2 (3 pts), Q3 (5 pts)

· Lecture Note 8: Intro to Simulation

· Q4 (2.5 pts) Q5 (2.5 pts)

· Reading Articles

· Q6A (2.5 pts), Q7A (2.5 pts)

· Students may choose either handwriting or word processing (or both).

· Handwriting: please properly scan or take photos and organize them into one file before uploading in D2L.

· Please write down your solutions step-by-step for partial credit.

· You may use:

· Your textbook and notes from the class.

· Notes or sources from a related class or internet source.

· Discussion with the instructor.

· Voluntary, mutual, and cooperative discussion with other students currently taking the class.

· You may not use:

· Solution manuals (printed or electronic).

· Copying from other students in this class, including expecting them to reveal their solutions in “discussion.”

· It is fine if your answer is not 100% correct. However, if you do not put enough effort to the assignment, your score for this homework will be lower than your expectation. So, please try to convince your logic to instructor.

Your Name:

Lecture Note 7: Decision Making under Uncertainty

1. You are given the following decision tree, with the probabilities at event nodes shown in parentheses and with the payoffs at terminal points shown on the right. Analyze this decision tree to obtain the optimal policy (Use TreePlan Excel Add-in or Do it by Hand).

Answer:

2. An athletic league does drug testing of its athletes, 10 percent of whom use drugs. The test, however, is only 95 percent reliable. That is, a drug user will test positive with probability 0.95 and negative with probability 0.05, and a nonuser will test negative with probability 0.95 and positive with probability 0.05.

a. Determine the posterior probability of each of the following outcomes of testing an athlete.

i. The athlete is a drug user, given that the test is positive.

ii. The athlete is not a drug user, given that the test is positive.

iii. The athlete is a drug user, given that the test is negative.

iv. The athlete is not a drug user, given that the test is negative.

Answer:

b. Use the corresponding Excel template to check your answers in the preceding parts.

Answer:

3. Management of the Telemore Company is considering developing and marketing a new product. It is estimated to be twice as likely that the product would prove to be successful as unsuccessful. If it were successful, the expected profit would be $1,500,000. If unsuccessful, the expected loss would be $1,800,000. A marketing survey can be conducted at a cost of $100,000 to predict whether the product would be successful. Past experience with such surveys indicates that successful products have been predicted to be successful 80 percent of the time, whereas unsuccessful products have been predicted to be unsuccessful 70 percent of the time.

a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the market survey is not conducted.

Answer:

b. Assuming the market survey is not conducted, use Bayes’ decision rule to determine which decision alternative should be chosen.

Answer:

c. Find the expected value of perfect information. Does this answer indicate that consideration should be given to conducting the market survey?

Answer:

d. Assume now that the market survey is conducted. Find the posterior probabilities of the respective states of nature for each of the two possible predictions from the market survey.

Answer:

e. Use TreePlan Excel Add-in to construct and solve the decision tree for this entire problem.

Answer:

Lecture Note 8: Intro to Simulation

4. Reconsider the coin-flipping game introduced in Section 12.1 and analyzed with computer simulation in Figures 12.1, 12.2, and 12.3 ( Section and Figure #s from the textbook pdf file).

a. Revise the spreadsheet model in Figure 12.1 by using Excel’s VLOOKUP function instead of the IF function to generate each simulated flip of the coin. Then perform a computer simulation of one play of the game.

Answer:

b. Use this revised spreadsheet model to generate a data table with 14 replications like Figure 12.2.

Answer:

c. Repeat part c with 1,000 replications (like Figure 12.3).

Answer:

5. Jessica Williams, manager of kitchen appliances for the Midtown Department Store, feels that her inventory levels of stoves have been running higher than necessary. Before revising the inventory policy for stoves, she records the number sold each day over a period of 25 days, as summarized below.

a. Use these data to estimate the probability distribution of daily sales.

Answer:

b. Calculate the mean of the distribution obtained in part a.

Answer:

c. Describe how random numbers can be used to simulate daily sales.

Answer:

d. Use the random numbers 0.4476, 0.9713, and 0.0629 to simulate daily sales over three days. Compare the average with the mean obtained in part b.

Answer:

e. Formulate a spreadsheet model for performing a computer simulation of the daily sales. Perform 300 replications and obtain the average of the sales over the 300 simulated days.

Answer:

· Reading Articles

6. Read the referenced article: Federal Aviation_Interfaces-2009.pdf. Briefly describe how computer simulation was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study (200~300 words).

Answer:

7. Read the referenced article: Merill Lynch_Interfaces-2002.pdf. Briefly describe how computer simulation was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study (200~300 words).

Answer:

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