A Tourist Bus Can Accommodate 80 People and Currently Books

Essay

A tourist bus can accommodate 80 people and currently books up to 80 reservations. Past data shows that the tourist bus always accommodates all 80 reservations but that, on average, two people do not show up. To capture additional profit, the travel agent is considering an overbooking strategy in which he would accept 82 reservations even though the tourist bus can accommodate only 80 people. The travel agent believes that he will be able to always book all 82 reservations. The probability distribution for the number of people showing up when 82 reservations are accepted is estimated as follows:
​ $$\begin{array} { c | c } \text { People Showing Up } & \text { Probability } \\\hline 78 & 0.05 \\79 & 0.3 \\80 & 0.5 \\81 & 0.1 \\82 & 0.05\end{array}$$ ​
The travel agent receives a marginal profit of $110 for each passenger who books a reservation (regardless whether they show up). The travel agent will also incur a cost for any passenger denied seating on the bus. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $160 per passenger. Develop a spreadsheet simulation model for this overbooking system. Simulate the number of passengers showing up.
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a. What is the average net profit for each tourist bus with the overbooking strategy?
b. What is the probability that the net profit with the overbooking strategy will be less than the net profit without overbooking (80 × $110 = $8,800)?
c. Explain how your simulation model could be used to evaluate other overbooking levels such as 81, 83, and 84 and for recommending a best overbooking strategy.