Homework Assignment 8 MGSC 609 Murphy Spring 2015
Due: Tuesday, May 12, 2015 by 11:59p
Worth 20 points; All parts of all problems are equally weighted as given below.
Please Submit: A single MS Excel workbook for all problems created that is clearly and cleanly formatted with answers clearly indicated via Blackboard. See “Homework Assignment” tool. There should be one spreadsheet tab for each problem below.
Please name each of your workbooks “hw8_lastname_firstname.xlsx”.
Homework 8 Exercises
- (Winston and Albright, 4th) A buyer for a large department store chain must place order with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. In particular, the buyer must decide on November 1 how many pairs of the manufacturer’s newest model of tennis shoes to order for sale during the coming summer season. Assume the each pair of this new brand of tennis shoes costs the department store chain $45 per pair. Furthermore, assume that each pair of these shoes can then be sold to the chain’s customers for $70 per pair. Any pairs of these shoes that remain unsold at the end of the summer season will be sold in a closeout sale next fall for $30 each. The probability distribution of the consumer demand for these tennis shoes during the coming summer season has been assessed by market research specialists and is provided in the file under the tab 8.1. Assume that the department store chain must purchase these tennis shoes from the manufacturer in lots of 100 pairs.
- Create a payoff matrix that specifies the contribution to profit from the sale of the tennis shoes by this department store chain for possible purchase decision and each random outcome with respect to consumer demand.
- Evaluate the payoff matrix using the minimax, maximax, and minimax regret criteria. What is the best decision in each case?
- Evaluate the payoff matrix using the expected value approach. What this expected monetary return. Which order quantity maximizes expected monetary return?
- Compute and interpret the EVPI in the context of this procurement setting.
- Create a data table that varies the closeout price over the range of $5 to $45
- (Winston and Albright, 4th) A company, Kenchel Industries, is considering whether or market a new product that it has already spent $200,000 developing or to sell the idea to a competitor. If the company does choose to market the product, it will cost the company $250,000 in marketing fees, and the probability of the product’s success is estimated to be about 40%. If the product is marketed and the product turns out to be a failure the company will have $0 revenue, while if it is a success, the company will have an estimated $1,500,000 in revenue. The company can also sell its idea to its competition. The competing company will either pay $300,000, $400,000 or $450,000 with equal probabilities to Kenchel for the intellectual property. What should Kenchel Industries decide in order to maximize profit?
- Enter the data into a new spreadsheet tab
- Use the Decision Tree tool in Analytical Solver (or another tool) to build the decision tree representing this problem. What is the best decision and the EMV based on this tree.
- Create a data table that shows the sensitivity of Kenchel’s decision to the $450,000 figure given above (the upper end of what the competitor is willing to pay). Vary this figure from $400,000 to $600,000 in increments of $25,000. Include in the table, this value, the expected monetary value and the best decision.
- (Lind, Marchal and Wathen, 16th) ABC Auto classifies drivers as good, medium, or poor risks. Drivers, who apply for insurance with ABC, fall into these three groups in the approximate proportions of 30%, 50% and 20%, respectively. The probability that a good driver will have an accident in a year period is 0.01. The similar probabilities of an annual accident for medium and poor drivers are 0.03 and 0.10, respectively. Suppose the company sells Dr. M. a policy and he has an accident.
- Define the relevant events (in words) and associate the given probabilities with these events.
- What is the probability that Dr. M. is a good driver? Medium driver? Poor driver?