{"id":614,"date":"2024-03-14T21:15:37","date_gmt":"2024-03-14T21:15:37","guid":{"rendered":"https:\/\/sites.rutgers.edu\/yasai\/?page_id=614"},"modified":"2024-03-14T21:15:37","modified_gmt":"2024-03-14T21:15:37","slug":"airline-overbooking-problem","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/yasai\/airline-overbooking-problem\/","title":{"rendered":"Airline Overbooking Problem"},"content":{"rendered":"

You are taking reservations for an airline flight. This particular flight uses an aircraft with 50 first-class seats and 190 economy-class seats.<\/p>\n

First-class tickets on the flight cost $600, with demand to purchase them distributed like a Poisson random variable with mean 50. Each passenger who buys a first-class ticket has a 93% chance of showing up for the flight. If a first-class passenger does not show up, he or she can return their unused ticket for a full refund. Any first class passengers who show up for the flight with tickets but are denied boarding are entitled to a full refund plus a $500 inconvenience penalty.<\/p>\n

Economy tickets cost $300. Demand for them is Poisson distributed with a mean of 200, and is independent of the demand for first-class tickets. Each ticket holder has a 96% chance of showing up for the flight, and “no shows” are not entitled to any refund. If an economy ticket holder shows up and is denied a seat, however, they get a full refund plus a $200 penalty. If there are free seats in first class and economy is full, economy ticket holders can be seated in first class.<\/p>\n

The airline allows itself to sell somewhat more tickets than it has seats. This is a common practice called “overbooking”.\u00a0 The firm is considering the 18 possible polices obtained through all possible combinations of<\/p>\n