Joanna Johnson is planning a vacation to Spain to celebrate her upcoming graduation from her MS program in business analytics. She will be traveling alone, and is therefore particularly cost conscious as she will not be able to split the cost of lodging with a travel partner. In her MS program, she learned about how travel and lodging firms leverage dynamic pricing to improve their revenues by adjusting their prices in response to supply and demand dynamics. She would like to incorporate her knowledge about this strategy into her decision-making on when to purchase her flight and hotel for her trip.
It is now three months from the timeframe for which she would like to travel. Round trip airfare from her home city of Charlotte, North Carolina to Barcelona is currently $1200, and lodging for 4 nights at the Grand Hotel Central would total $1000. Joanna could decide to purchase her airfare and lodging now, or she could decide to wait in the hopes that prices would decrease in subsequent months. If she decides to wait one month, there is a 20% chance that her airfare will decrease by $200, a 40% chance that it will stay the same, otherwise, the price will increase by $200. If she decides to wait two months, there is a 20% chance that her airfare will decrease by $400, a 20% chance it will stay the same, and a 60% chance that it will increase by $200. The cost of her lodging will remain the same if she waits for one month to make her decision. However, if she waits two months, there is a 40% chance the cost will decrease by $300, a 30% chance it will stay the same, and a 30% chance it will increase by $100. You may assume that she will purchase her airfare and lodging at the same time, and all price changes are in reference to the initial prices.
a. (8 points) What decision will Joanna make if she is an expected monetary value (EMV) maximizer? Build the decision tree in PrecisionTree and report the following results.
i. (4 points) Produce a high-resolution PDF Exhibit A of your decision tree (do not submit an Excel file), fit to one page in landscape orientation. All decision and chance nodes, as well as all branches should be appropriately labeled and readable.
ii. (2 points) Report the optimal decision policy and the EMV for each of your initial decisions (i.e., the EMV of your optimal decision and any other decisions initially considered).
iii. (2 points) Given your optimal decision policy, report the possible monetary outcomes and their associated probabilities. What is the most likely outcome? What is the probability that Joanna?s outcome is at least as good as purchasing her travel arrangements immediately?
b. (2 points) Joanna is concerned about her estimation of the price change probabilities for airfare one month out. Perhaps the chances that the price will decrease or stay the same could be substantially different from her estimations. Should she be concerned? Why or why not? Justify your answers with appropriate results produced from your decision tree.
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