1. Although no-shows are an ever growing issue that can slash 10-20% of revenues from an all-booked day, few hotels actually do charge any fees for them. Instead, just like airlines, many overbook their rooms. This means that they book more rooms than they have, in the eort to reduce the number of empty rooms while at the same time hoping that not all guests show up. Please, describe and explain
(i) what and what type of decision variables/parameters should a hotel use/estimate in order to maximize prots and minimize losses. Now, assume that a fully booked hotel faces between 0 and 10 no- shows daily with uniform probability. Assume also that the hotel wants to minimize the total loss of empty rooms ($70 each for cost of opportunity) and overbooked customers ($50 each for loss of goodwill) so that revenues and sales prots are disregarded. Please,
(ii) create a spreadsheet table that helps determine the optimal overbooking level for the day. Finally, (iii) change the loss of goodwill estimate so that the optimal solution x increases by two. Provide a mathematical and a managerial explanation for the change.
2. A company has to decide whether to invest in a large and expensive new plant or in a small and cheaper new plant or in no plant at all. With the big and expensive plant and a favorable market, they estimated a $350,000 net present revenue over the next 5 years. If the market will not be favorable, they estimated a $100,000 net present total revenue.
With the small plant, they estimated a $250,000 and $80,000 net present total revenue, respectively. The two plants costs $200,000 and $150,000, respectively. If the company estimates that the market will be favorable with 60% probability and unfavorable with 40% probability, (iv) advise them on which plant to invest on. The company could also commission a $20,000 survey that can predict with more precision the future of the market. If the survey predicts a favorable market (you may still use the 60% probability for this), the market will be be favorable with a 80% probability, and if the survey predicts an unfavorable market (you may still use the 40% probability for this), the market will be be favorable with a 90% probability 1. In other words, the company would be paying a few dollars for a survey to give them more condence before they decide whether or not to commit to a big dollar investment. Should the survey be
commissioned?
3. The queue simulation.xlsx" le on Blackboard shows one simulation run of a daily customer schedule. The customers to service for the day are 48 and their appointments are scheduled 10 minutes apart. Suppose that the business wants to increase the number of customers to see by 12, and still schedule them at regular intervals and in the same amount of time. Advice the business whether or not to make the change. Please, (iv) suggest all the parameters that they should consider and illustrate the model that should be created, with specic detail to the prots, losses, and trade-os involved, the metrics to use, and the number of simulations to run in order to obtain some accurate enough problem solution. No Excel work is needed here.