STATS Module 2 Problem 2

While vacationing in England, you decide to take an impromptu trip outsideof London to see some of the country. You phone several hotels in the area but aretold that all rooms are reserved. You and your friends decide to go anyway, vowingthat if worse comes to worse you will all sleep in the car. Having driven the 100miles from London, you stop at the first hotel you see, Ye Olde Ox and Bow, and aresurprised to find that rooms are available. Having settled in, you go down to theHotel Pub for a drink and strike up a conversation with the Hotel Manager. Youinform him of your experience and he points out that it is not uncommon. Theproblem is that about 20% of the people with reservations either call back andcancel or just dont show up. He tells you that there is a great deal of uncertainty inhow long guests will stay. From experience he has found that about half of theguests who stayed the night will stay for another night irrespective of their originalplans. He therefore adds half the number of rooms rented to the number of vacantrooms to come up with his estimate of the number of rooms that will be available (ifthere are 92 rooms rented, one half is 46 to which he adds the 8 vacant rooms tocome up with an estimated 54 vacant rooms the next night). He then will take amaximum of 54 reservations. Of course, many of the reservations become no-showsso that he usually has rooms available.You point out that airlines regularly overbook flights since they have asimilar no-show problem. He has never tried this approach and is worried sinceif a person with a reservation showed up, he would feel compelled to pay for asimilar room at a competitor and provide the inconvenienced party with a freedinner and breakfast.You wake up the next morning to a terribly rainy English day, which ruinsall of your plans. Your friends decide to see the sites of the town, which is aMuseum dedicated to Quilting. You beg off and find yourself with most of themorning and afternoon free. Your thoughts return to the previous eveningsconversation and you think that you might be able to help the owner make a bitmore profit by changing his reservation procedure.Using the following: Poisson and Binomial distributionsAssignment:By using simulation techniques compare the current reservation system withan open reservation system where anyone who calls for a reservation is given one.Specifically determine if the open reservation system is more or less profitable thanthe current system. Your simulation should be no smaller than one year in length.Facts and Assumptions:1) The hotel has 100 rentable rooms:2) Assume that of the n rooms that are occupied on a given night, the numberthat will vacate the next day follows the Binomial Distribution withparameters n and p = :3) Assume that the number of new reservations follows the Poissondistribution with mean equal to 60:4) If m is the number of reservations made, assume that the number of noshows will follow the Binomial Distribution with parameters m and p=. 2:5) The profit break-even point is 50 rented rooms:6) The net profit is $90 per room for each rented room over 50:7) If a person with a reservation cannot be accommodated, the cost to put theperson up at another hotel plus dinner and breakfast is $270.8) In your simulation you may assume that holidays and weekend lodgingand reservations are the same as on any other day.Hints:a) Assume that the hotel starts off with 92 rented rooms.b) Use the day as your basic unit, i.e. use the previous days occupancy as thestarting point from which you will determine vacancies and, in the case of thepresent reservation system, the number of reservations you will take. Thendetermine how many reservations in fact show up and compute the final number ofrooms rented. In the case of the present reservation system, use this figure as thestarting point for the next day.Is this More Or Less Profitable?Facts:100 Total Rooms Available, starting off with 92 rented roomsn=?p = .560 new reservations