BUS 220 - Introduction to Decision Sciences Assignment 4 due on Thursday 11/12/2015 Fall 2015 NOTE: 10% of your grade will be deducted if the work is not presented in a clear and neat manner. NOTE: The assignment could be done jointly by (at most) 2 students. (Of course, it can be done by a single person.) In any case, the cover page indicating only student(s) names and student id(s) should be attached to each assignment. I will keep this page for my recording purposes. The first page of the solutions to the assignment should also include student(s) names and student number(s), so that you can get the solutions back. Problem 1 (15 points) Use a worksheet to simulate the rolling of dice. Use the VLOOKUP function to select the outcome for each die. Place the number for the first die in column B and the number for the second die in column C. Show the sum in column D. Repeat the simulation for 1000 rolls of the dice. What is your simulation estimate of the probability of rolling a7? Problem 2 (20 points) South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $100 profit on each passenger on the flight. When South Central takes 30 reservations for the flight, experience has shown that on average, two passengers do not show up. As a result, with 30 reservations, South Central is averaging 28 passengers with a profit of 28(100) = $2800 per flight. The airline operations office has asked for an evaluation of an overbooking strategy where they would accept 32 reservations even though the airplane holds only 30 passengers. The probability distribution for the number of passengers showing up when 32 reservations are accepted is as follows. Passengers Showing Up Probability 28 0.05 29 0.25 30 0.5 31 0.15 32 0.05 The airline will receive a profit of $100 for each passenger on the flight up to the capacity of 30 passengers. The airline will incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $150 per passenger. Develop a worksheet model that will simulate the performance of the overbooking system. Simulate the number of passengers showing up for each of 500 flights by using the VLOOKUP function. Use the results to compute the profit for each flight. a. (15 points) Does your simulation recommend the overbooking strategy? What is the mean profit per flight if overbooking is implemented? b. (5 points) Explain how your simulation model could be used to evaluate other overbooking levels such as 31, 33, 34 and for recommending a best overbooking strategy. 1 Problem 3 (45 points) Chicago Air Express has decided to offer direct service from Islip to Chicago. Management must decide between a full price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Chicago Air offers. Management has developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Chicago: strong and weak. The following table shows the estimated quarterly profits ($1000s). Service Full Price Discount Demand for Service Strong Weak $ 960 $ -490 [Note: negative value!] $ 670 $ 320 a. (5 points) What is the decision to be made, what is the chance event and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event? b. (15 points) If nothing is known about the probabilities of the chance of outcomes, what is the recommended decision using the optimistic, conservative and minimax regret approaches? c. (5 points) Suppose that management of Chicago Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision. d. (5 points) Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach? e. (15 points) use graphical sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value. Problem 4 (20 points) In the following profit payoff table for a decision problem with two states of nature and three decision alternatives, the probabilities for s1 and s2 are: p(s1)=0.8 and p (s2)= 0.2 Decision Alternatives d1 d2 d3 State of Nature s1 s2 15 10 10 12 8 20 a. (10 points) What is the optimal decision? b. (10 points) Find the EVPI 2