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[null,"Airline Overbooking"]
[null,null,null,null,null,null,null,null,null,null,"year","load factor"]
[null,"The following passages are extracts from the cited websites (as of September 21, 2004).",null,null,null,null,null,null,null,null,1990,0.62]
[null,null,null,null,null,null,null,null,null,null,2000,0.71]
[null,"Air Transport Association (airlines.org)",null,null,null,null,null,null,null,null,2005,0.77]
[null,"Airline Handbook, Chapter 4: Airline Economics",null,null,null,null,null,null,null,null,2006,0.79]
[null,null,null,null,null,null,null,null,null,null,2007,0.8]
[null,"Break-Even Load Factors",null,null,null,null,null,null,null,null,2008,0.8]
[null,null,null,null,null,null,null,null,null,null,2009,0.81,null,"Source: Air Transport Association"]
[null,"Every airline has what is called a break-even load factor. That is the percentage of the",null,null,null,null,null,null,null,null,2010,0.87]
[null,"seats the airline has in service that it must sell at a given yield, or price level, to cover"]
[null,"its costs. "]
[null,null,null,null,null,null,null,null,null,null,"Less Free To Move About The Cabin"]
[null,"Since revenue and costs vary from one airline to another, so does the break-even load"]
[null,"factor. Escalating costs push up the break-even load factor, while increasing prices for",null,null,null,null,null,null,null,null,"Flights Growing More Crowded"]
[null,"airline services have just the opposite effect, pushing it lower. Overall, the break-even"]
[null,"load factor for the industry in recent years has been approximately 66 percent. ",null,null,null,null,null,null,null,null,"By Del Quentin Wilber"]
[null,null,null,null,null,null,null,null,null,null,"Washington Post Staff Writer"]
[null,"Airlines typically operate very close to their break-even load factor. The sale of just one",null,null,null,null,null,null,null,null,"Monday, December 3, 2007; Page A01 "]
[null,"or two more seats on each flight can mean the difference between profit and loss for an"]
[null,"airline. ",null,null,null,null,null,null,null,null,"Federal data show that planes have grown steadily more packed in the past two"]
[null,null,null,null,null,null,null,null,null,null,"decades. In 1990, U.S. air carriers' planes were about 62 percent full. By 2000, the"]
[null,"Overbooking ",null,null,null,null,null,null,null,null,"figure had climbed to 71 percent. Through the first eight months of this year, planes"]
[null,null,null,null,null,null,null,null,null,null,"were 81 percent full, according to the Bureau of Transportation Statistics."]
[null,"Airlines occasionally overbook flights, meaning that they book more passengers for a"]
[null,"flight than they have seats on the same flight. ",null,null,null,null,null,null,null,null,"Just 10 years ago, airlines could make money on a flight that was a little over half full,"]
[null,null,null,null,null,null,null,null,null,null,"because business travelers were willing to pay thousands of dollars for a ticket,"]
[null,"The practice is rooted in careful analysis of historic demand for a flight, economics and",null,null,null,null,null,null,null,null,"compensating for unsold seats. But when the tech bubble burst in 2000, business travel"]
[null,"human behavior. Historically, many travelers, especially business travelers buying",null,null,null,null,null,null,null,null,"and demand for expensive seats declined. The 2001 terrorist attacks also hurt leisure"]
[null,"unrestricted, full-fare tickets, have not traveled on the flights for which they have a",null,null,null,null,null,null,null,null,"travel. Both trends forced many carriers to slash costs and try to find ways to fly more"]
[null,"reservation. Changes in their own schedules may have made it necessary for them to",null,null,null,null,null,null,null,null,"efficiently."]
[null,"take a different flight, maybe with a different airline, or to cancel their travel plans"]
[null,"altogether, often with little or no notice to the airline. Some travelers, unfortunately,",null,null,null,null,null,null,null,null,"Meanwhile, such low-cost carriers as Southwest Airlines and AirTran Airways continued"]
[null,"reserve seats on more than one flight. ",null,null,null,null,null,null,null,null,"to grow, spurring demand for air travel from people who may not have flown much, or as"]
[null,null,null,null,null,null,null,null,null,null,"much, before. That prodded traditional carriers to match cheap fares to remain"]
[null,"Both airlines and customers are advantaged when airlines sell all the seats for which",null,null,null,null,null,null,null,null,"competitive. Travel-booking Web sites such as Orbitz and Travelocity also made it"]
[null,"they have received reservations. An airline's inventory is comprised of the seats that it",null,null,null,null,null,null,null,null,"easier for passengers to compare fares, further reducing ticket prices."]
[null,"has on each flight. If a customer does not fly on the flight which he or she has a"]
[null,"reservation, his or her seat is unused and cannot be returned to inventory for future use",null,null,null,null,null,null,null,null,"The lower fares meant airlines could no longer rely on a few expensive tickets to keep a"]
[null,"as in other industries. This undermines the productivity of an airline's operations; it is",null,null,null,null,null,null,null,null,"flight profitable. They altered their tactics to concentrate on filling planes with more"]
[null,"increasing productivity, of course, that contributes to lower airfares and expanded",null,null,null,null,null,null,null,null,"passengers on cheaper tickets to offset the loss of steeper fares."]
[null,"service. Consequently, airlines sometimes overbook flights. "]
[null,null,null,null,null,null,null,null,null,null,"Surging fuel prices have also encouraged airlines to carry as many passengers as"]
[null,"Importantly for travelers, airlines do not overbook haphazardly. They examine the history",null,null,null,null,null,null,null,null,"possible on each plane and to better match routes with the appropriate-size aircraft. The"]
[null,"of particular flights, in the process determining how many no-shows typically occur, and",null,null,null,null,null,null,null,null,"high fuel costs made it too expensive to fly jets not loaded to the gills, leading"]
[null,"then decide how much to overbook that particular flight. The goal is to have the",null,null,null,null,null,null,null,null,"carriers to reduce capacity, hold it steady or slow growth plans."]
[null,"overbooking match the number of no-shows. In most cases the practice works"]
[null,"effectively. Occasionally, however, when more people show up for a flight than there are",null,null,null,null,null,null,null,null,"Airlines also upgraded their technology and ticketing systems, allowing them to book"]
[null,"seats available, airlines offer incentives to get people to give up their seats. Free tickets",null,null,null,null,null,null,null,null,"flights more efficiently."]
[null,"are the usual incentive; those volunteering are booked on another flight. "]
[null,null,null,null,null,null,null,null,null,null,"The trend of packed planes is not likely to change anytime soon, executives said,"]
[null,"Normally, there are more volunteers than the airlines need, but when there are not",null,null,null,null,null,null,null,null,"because most airlines are not going to add planes to their fleets in the near future."]
[null,"enough volunteers, airlines must bump passengers involuntarily. In the rare cases where"]
[null,"this occurs, federal regulations require the airlines to compensate passengers for their"]
[null,"trouble and help them make alternative travel arrangements. The amount of"]
[null,"compensation is determined by government regulation. "]
[]
[]
[null,"The U.S. Department of Transportation's \"Fly Rights, A Consumer Guide to Air Travel\""]
[null,"(airconsumer.dot.gov)"]
[]
[null,"Airline Overbooking"]
[]
[null,"Overbooking is not illegal, and most airlines overbook their schedules flights to a certain"]
[null,"extent in order to compensate for \"no-shows.\" Passengers are sometimes left behind or"]
[null,"\"bumped\" as a result. When an oversale occurs, the Department of Transportation"]
[null,"(DOT) requires airlines to ask people who aren't in a hurry to give up their seats"]
[null,"voluntarily, in exchange for compensation. Those passengers bumped against their will"]
[null,"are, with a few exceptions, entitled to compensation. "]
[]
[null,"Voluntary Bumping"]
[]
[null,"Almost any group of airline passengers includes some people with urgent travel needs"]
[null,"and others who may be more concerned about the cost of their tickets than about"]
[null,"getting to their destination on time. Federal rules require airlines to seek out people who"]
[null,"are willing to give up their seats for some compensation before bumping anyone"]
[null,"involuntarily. Here's how this works. "]
[]
[null,"At the check-in or boarding area, airline employees will look for volunteers when it"]
[null,"appears that the flight has been oversold. If you're not in a rush to arrive at your next"]
[null,"destination, you can give your reservation back to the airline in exchange for"]
[null,"compensation and a later flight. "]
[]
[null,"But before you do this, you may want to get answers to these important questions: "]
[]
[null,"When is the next flight on which the airline can confirm your seat? The alternate flight"]
[null,"may be just as acceptable to you. On the other hand, if they offer to put you on a"]
[null,"standby on another flight that's full, you could be stranded. "]
[]
[null,"Will the airline provide amenities such as free meals, a hotel room, phone calls, or"]
[null,"ground transportation? If not, you might have to spend the money they offer you on food"]
[null,"or lodging while you wait for the next flight. "]
[]
[null,"The Department of Transportation has not said how much the airline has to give"]
[null,"volunteers. This means carriers may negotiate with their passengers for a mutually"]
[null,"acceptable amount of money-- or maybe a free trip or other benefits. Airlines give"]
[null,"employees guidelines for bargaining with passengers, and they may select those"]
[null,"volunteers willing to sell back their reservations at the lowest price. "]
[]
[null,"If the airline offers you a free ticket, ask about restrictions. How long is the ticket good"]
[null,"for? Is it blacked out during holiday periods when you might want to use it? Can it be"]
[null,"used for international flights? Most importantly, can you make a reservation, and if so,"]
[null,"how far before departure are you permitted to make it? "]
[]
[null,"Involuntary Bumping"]
[]
[null,"DOT requires each airline to give all passengers who are bumped involuntarily a written "]
[null,"statement describing their rights and explaining how the carrier decides who gets on an"]
[null,"oversold flight and who doesn't. Those travelers who don't get to fly are frequently"]
[null,"entitled to an on-the- spot payment of denied boarding compensation. The amount"]
[null,"depends on the price of their ticket and the length of the delay: "]
[]
[null,"If you are bumped involuntarily and the airline arranges substitute transportation that is"]
[null,"scheduled to get you to your final destination (including later connections) within one"]
[null,"hour of your original scheduled arrival time, there is no compensation. "]
[]
[null,"If the airline arranges substitute transportation that is scheduled to arrive at your"]
[null,"destination between one and two hours after your original arrival time (between one and"]
[null,"four hours on international flights), the airline must pay you an amount equal to your"]
[null,"one-way fare to your final destination, with a $200 maximum. "]
[]
[null,"If the substitute transportation is scheduled to get you to your destination more than two"]
[null,"hours late (four hours internationally), or if the airline does not make any substitute travel"]
[null,"arrangements for you, the compensation doubles (200% of your fare, $400 maximum). "]
[]
[null,"You always get to keep your original ticket and use it on another flight. If you choose to"]
[null,"make your own arrangement, you can request an \"involuntary refund\" for the ticket for"]
[null,"the flight you were bumped from. The denied boarding compensation is essentially a"]
[null,"payment for your inconvenience. "]
[]
[null,"Like all rules, however, there are a few conditions and exceptions: "]
[]
[null,"To be eligible for compensation, you must have a confirmed reservation. An \"OK\" in the"]
[null,"Status box of your ticket qualified you in this regard even if the airline can't find your"]
[null,"reservation in the computer, as long as you didn't cancel your reservation or miss a"]
[null,"reconfirmation deadline. You must meet the airline's deadline for buying your ticket."]
[null,"Discount tickets must usually be purchased within a certain number of days after their"]
[null,"reservation was made. Other tickets normally have to be picked up no later than 30"]
[null,"minutes before the flight. "]
[]
[null,"In addition to the ticketing deadline, each airline has a check-in deadline, which is the"]
[null,"amount of time before scheduled departure that you must present yourself to the airline"]
[null,"at the airport. For domestic flights most carriers have a deadline of 10 minutes before"]
[null,"scheduled departure, but some can be an hour or longer. (Many airlines require"]
[null,"passengers with advance seat assignments to check in 30 minutes before scheduled"]
[null,"departure, even if they already have advance boarding passes. If you miss this deadline"]
[null,"you may lose the specific seats you were promised, although not the reservation itself.)"]
[null,"Check-in deadlines on international flights can be as much as three hours before"]
[null,"scheduled departure time, due partially to security procedures. Some airlines may"]
[null,"simply require you to be at the ticket/baggage counter by this time; most, however,"]
[null,"require that you get all the way to the boarding area. If you miss the ticketing or check-"]
[null,"in deadline, you may have lost your reservation and your right to compensation if the"]
[null,"flight is oversold. "]
[]
[null,"As noted above, no compensation is due if the airline arranges substitute transportation"]
[null,"which is scheduled to arrive at your destination within one hour of your originally"]
[null,"scheduled arrival time. If the airline must substitute a smaller plane for the one it"]
[null,"originally planned to use, the carrier isn't required to pay people who are bumped as a"]
[null,"result. "]
[]
[null,"The rules do not apply to charter flights, or to scheduled flights operated with planes that"]
[null,"hold 60 or fewer passengers. They don't apply to international flight inbound to the"]
[null,"United States, although some airlines on these routes may follow them voluntarily. Also,"]
[null,"if you are flying between two foreign cities--from Pairs to Rome, for example--these rules"]
[null,"will not apply. The European Community has a rule on bumpings that occur in an EC"]
[null,"country; ask the airline for details, or contact DOT. "]
[]
[null,"The most effective way to reduce the risk of being bumped is to get to the airport early."]
[null,"On oversold flights the last passengers to check in are usually the first to be bumped,"]
[null,"even if they have met the check-in deadline. Allow extra time; assume that the airport"]
[null,"access road is backed up, the parking lot is full, and there is a long line at the check-in"]
[null,"counter. However, if you arrive so early that your airline has another flight to your"]
[null,"destination leaving before the one that you are booked on, either switch to the earlier"]
[null,"flight or don't check your bag until after the first flight leaves. If you check your bag right"]
[null,"away, it might get put on the earlier flight and remain unattended at your destination"]
[null,"airport for hours. "]
[]
[null,"Airlines may offer free transportation on future flights in place of a check for denied"]
[null,"boarding compensation. However, if you are bumped involuntarily you have the right to"]
[null,"insist on a check if that is your preference. Once you cash the check (or accept the free"]
[null,"flight), you will probably lose the right to demand more money from the airline later on."]
[null,"However, if being bumped costs you more money than the airline will pay you"]
[null,"at the airport, you can try to negotiate a higher settlement with their complaint"]
[null,"department. If this doesn't work you usually have 30 days from that day on the check to"]
[null,"decide if you want to accept the amount of the check. You are always free to decline"]
[null,"the check and take the airline to court to try to obtain more compensation. The "]
[null,"government's denied boarding regulation spells out the airline's minimum obligation to"]
[null,"people they bump involuntarily. "]
[]
[null,"Finally, don't be a \"no-show.\" If you are holding confirmed reservation you don't plan to"]
[null,"use, notify the airline. If you don't, they will cancel all onward or return reservations on"]
[null,"your trip."]
[]
[]
[null,"The U.S. Supreme Court ruling on NADER v. ALLEGHENY AIRLINES "]
[null,"http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=US&vol=426&invol=290"]

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[null,"Airline Overbooking"]
[]
[null,"World Airways runs daily flights from Chicago to Tokyo.  They face a fixed cost of $80,000"]
[null,"for each flight (basically independent of the actual number of passengers), and there are"]
[null,"300 seats available on their planes.  One-way tickets generate revenues (after agent"]
[null,"commissions and the like are deducted) of $500 apiece when used, but are fully refundable"]
[null,"if not used.  The Thursday flight typically has between 5 and 95 no-shows; all intermediate"]
[null,"values are equally likely.  WA is allowed (by law) to overbook its flights, but must give"]
[null,"compensation of $250 to all ticketed passengers not allowed to board, and must provide"]
[null,"those passengers with alternative transportation on another carrier (the cost of providing the"]
[null,"alternative transportation just wipes out the $500 revenue). How many tickets should they"]
[null,"be willing to sell for the Thursday flight?"]
[]
[null,"[The precise distribution of N, the number of no-shows, is chosen here to simplify classroom"]
[null,"discussion. On the following pages, any distribution could be entered. The only critical"]
[null,"assumption we'll make is that the number of no-shows varies independently of the number"]
[null,"of seats sold.)"]

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[null,"Flight Overbooking: Brute Force"]
[]
[null,null,null,null,null,80000,"operating expense"]
[null,null,null,null,null,500,"revenue/seat"]
[null,null,null,null,null,250,"cost/bump",5,"minimum no-shows"]
[null,"number of",null,null,null,300,"capacity",95,"maximum no-shows"]
[null,"no-shows","prob","profit"]
[null,{"$f":"MIN_NS","v":5},{"$f":"1/91","v":1.098901098901099E-2},{"$f":"-EXPENSE+SEAT_REV*MIN(SALES-B8,CAPACITY)-BUMP_CST*MAX((SALES-B8)-CAPACITY,0)","v":66250},null,320,"tickets sold"]
[null,{"$f":"B8+1","v":6},1.098901098901099E-2,{"$f":"-EXPENSE+SEAT_REV*MIN(SALES-B9,CAPACITY)-BUMP_CST*MAX(SALES-CAPACITY-B9,0)","v":66500}]
[null,7,1.098901098901099E-2,66750]
[null,8,1.098901098901099E-2,67000,null,{"$f":"showformula(D8)","v":"=-EXPENSE+SEAT_REV*MIN(SALES-B8,CAPACITY)-BUMP_CST*MAX((SALES-B8)-CAPACITY,0)"}]
[null,9,1.098901098901099E-2,67250]
[null,10,1.098901098901099E-2,67500,null,"We're out $80,000 for sure."]
[null,11,1.098901098901099E-2,67750]
[null,12,1.098901098901099E-2,68000,null,"SALES-B8 = \"tickets sold\" - \"no-shows\" is the number of passengers who show up at the gate."]
[null,13,1.098901098901099E-2,68250]
[null,14,1.098901098901099E-2,68500,null,"We seat 300 … unless \"tickets sold\" - \"no-shows\" is smaller than 300."]
[null,15,1.098901098901099E-2,68750]
[null,16,1.098901098901099E-2,69000,null,"We only bump passengers if the number of passengers who show up,"]
[null,17,1.098901098901099E-2,69250,null,"\"tickets sold\" - \"no-shows\", exceeds the capacity,"]
[null,18,1.098901098901099E-2,69500,null,"i.e., if \"tickets sold\" - \"capacity\" - \"no-shows\" is positive."]
[null,19,1.098901098901099E-2,69750]
[null,20,1.098901098901099E-2,70000]
[null,21,1.098901098901099E-2,69500]
[null,22,1.098901098901099E-2,69000]
[null,23,1.098901098901099E-2,68500]
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[null,30,1.098901098901099E-2,65000]
[null,31,1.098901098901099E-2,64500]
[null,32,1.098901098901099E-2,64000]
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[null,35,1.098901098901099E-2,62500]
[null,36,1.098901098901099E-2,62000]
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[null,{"$f":"B40+1","v":38},1.098901098901099E-2,61000]
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[null,40,1.098901098901099E-2,60000]
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[null,45,1.098901098901099E-2,57500]
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[null,52,1.098901098901099E-2,54000]
[null,53,1.098901098901099E-2,53500]
[null,54,1.098901098901099E-2,53000]
[null,55,1.098901098901099E-2,52500]
[null,56,1.098901098901099E-2,52000]
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[null,60,1.098901098901099E-2,50000]
[null,61,1.098901098901099E-2,49500]
[null,62,1.098901098901099E-2,49000]
[null,63,1.098901098901099E-2,48500]
[null,64,1.098901098901099E-2,48000]
[null,65,1.098901098901099E-2,47500]
[null,66,1.098901098901099E-2,47000]
[null,67,1.098901098901099E-2,46500]
[null,68,1.098901098901099E-2,46000]
[null,69,{"$f":"1/91","v":1.098901098901099E-2},45500]
[null,{"$f":"B72+1","v":70},1.098901098901099E-2,{"$f":"-EXPENSE+SEAT_REV*MIN(SALES-B73,CAPACITY)-BUMP_CST*MAX(SALES-CAPACITY-B73,0)","v":45000}]
[null,71,1.098901098901099E-2,44500]
[null,72,1.098901098901099E-2,44000]
[null,73,1.098901098901099E-2,43500]
[null,74,1.098901098901099E-2,43000]
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[null,76,1.098901098901099E-2,42000]
[null,77,1.098901098901099E-2,41500]
[null,78,1.098901098901099E-2,41000]
[null,79,1.098901098901099E-2,40500]
[null,80,1.098901098901099E-2,40000]
[null,81,1.098901098901099E-2,39500]
[null,82,1.098901098901099E-2,39000]
[null,83,1.098901098901099E-2,38500]
[null,84,1.098901098901099E-2,38000]
[null,85,1.098901098901099E-2,37500]
[null,86,1.098901098901099E-2,37000]
[null,87,1.098901098901099E-2,36500]
[null,88,1.098901098901099E-2,36000]
[null,89,1.098901098901099E-2,35500]
[null,90,1.098901098901099E-2,35000]
[null,91,1.098901098901099E-2,34500]
[null,92,1.098901098901099E-2,34000]
[null,93,1.098901098901099E-2,33500]
[null,94,1.098901098901099E-2,33000]
[null,95,1.098901098901099E-2,32500]

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[null,"Flight Overbooking: Brute Force"]
[]
[null,null,null,null,null,80000,"operating expense"]
[null,null,null,null,null,500,"revenue/seat"]
[null,null,null,null,null,250,"cost/bump",5,"minimum no-shows"]
[null,"number of",null,null,null,300,"capacity",95,"maximum no-shows"]
[null,"no-shows","prob","profit"]
[null,{"$f":"MIN_NS","v":5},{"$f":"1/91","v":1.098901098901099E-2},{"$f":"-EXPENSE+SEAT_REV*MIN(CAPACITY,SALES-B8)-BUMP_CST*MAX(SALES-B8-CAPACITY,0)","v":55000.001299744639},null,364.99999480102144,"tickets sold",null,null,"The data table shows, explicitly, the manner in which expected"]
[null,{"$f":"B8+1","v":6},1.098901098901099E-2,{"$f":"-EXPENSE+SEAT_REV*MIN(CAPACITY,SALES-B9)-BUMP_CST*MAX(SALES-B9-CAPACITY,0)","v":55250.001299744639},null,null,null,null,null,"profit varies with our booking policy."]
[null,{"$f":"B9+1","v":7},1.098901098901099E-2,55500.001299744639,null,null,{"$f":"SUMPRODUCT(C8:C98,D8:D98)","v":62417.582389016643},"expected profit"]
[null,8,1.098901098901099E-2,55750.001299744639,null,null,{"$f":"SEAT_REV*CAPACITY-EXPENSE","v":70000},"certainty profit",null,"Alternatively, Solver can be used to find the optimal policy:"]
[null,9,1.098901098901099E-2,56000.001299744639,null,null,{"$f":"G11-G10","v":7582.417610983357},"uncertainty cost",null,"Change the policy (F8) to something else, such as 350, and select"]
[null,10,1.098901098901099E-2,56250.001299744639,null,null,null,null,null,"Tools / Solver to see the setup, and then Solve to find the best policy."]
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{"sheet":"Simulation","index":4,"n_rows":98,"n_cols":9,"rows_kept":98,"cut":false,"hidden":false,"merged":[[0,1,0,6]]}
[null,"Flight Overbooking: Simulation"]
[]
[null,null,null,null,null,80000,"operating expense"]
[null,null,null,null,null,500,"revenue/seat"]
[null,null,null,"cumulative",null,250,"cost/bump",5,"minimum no-shows"]
[null,"number of",null,"prob",null,300,"capacity",95,"maximum no-shows"]
[null,"no-shows","prob",0]
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[null,{"$f":"B8+1","v":6},1.098901098901099E-2,{"$f":"C9+D8","v":2.197802197802198E-2},null,{"$f":"LOOKUP(RAND(),D7:D97,B8:B98)","v":90},"no-shows",{"$f":"showformula(F9)","v":"=LOOKUP(RAND(),D7:D97,B8:B98)"}]
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{"sheet":"Overbooking 2","index":5,"n_rows":98,"n_cols":11,"rows_kept":98,"cut":false,"hidden":false,"merged":[[0,1,0,6],[7,8,8,8],[7,9,8,9]]}
[null,"Flight Overbooking: Simulation"]
[null,null,null,null,null,null,null,null,"Load Simulation.xls in another Excel window in order"]
[null,null,null,null,null,80000,"operating expense",null,"to add the \"Simulation\" option to the Excel menu."]
[null,null,null,null,null,500,"revenue/seat"]
[null,null,null,"cumulative",null,250,"cost/bump",5,"minimum no-shows"]
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[null,{"$f":"B8+1","v":6},1.098901098901099E-2,{"$f":"C9+D8","v":2.197802197802198E-2},null,{"$f":"LOOKUP(RAND(),D7:D97,B8:B98)","v":20},"no-shows",null,null,null,"error (95%)"]
[null,7,1.098901098901099E-2,3.2967032967032968E-2,null,{"$f":"-EXPENSE+SEAT_REV*MIN(CAPACITY,SALES-F9)-BUMP_CST*MAX(0,SALES-F9-CAPACITY)","v":58750},"profit",null,{"$f":"F13","v":325},{"$f":"F15","v":55731.73},{"$f":"1.96*F16/SQRT(F19)","v":68.186926462639136}]
[null,8,1.098901098901099E-2,4.3956043956043959E-2,null,null,null,null,{"$f":"F21","v":350},{"$f":"F23","v":61473.404999999999},{"$f":"1.96*F24/SQRT(F27)","v":36.63693640527039}]
[null,9,1.098901098901099E-2,5.4945054945054951E-2,null,null,null,null,{"$f":"F29","v":375},{"$f":"F31","v":62004.6875},{"$f":"1.96*F32/SQRT(F35)","v":30.645034439037506}]
[null,10,1.098901098901099E-2,6.5934065934065936E-2,null,325,"tickets sold",null,{"$f":"F37","v":390},{"$f":"F39","v":59875.334999999999},{"$f":"1.96*F40/SQRT(F43)","v":39.558443089345168}]
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[null,12,1.098901098901099E-2,8.7912087912087919E-2,null,55731.73,"mean"]
[null,13,1.098901098901099E-2,9.8901098901098911E-2,null,11001.326238181013,"sample standard deviation"]
[null,14,1.098901098901099E-2,0.1098901098901099,null,35000,"minimum"]
[null,15,1.098901098901099E-2,0.12087912087912089,null,70000,"maximum"]
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[null,17,1.098901098901099E-2,0.14285714285714285]
[null,18,1.098901098901099E-2,0.15384615384615383,null,350,"tickets sold"]
[null,19,1.098901098901099E-2,0.1648351648351648,null,"$F$10","monitored cell"]
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[null,21,1.098901098901099E-2,0.18681318681318676,null,5911.0288536426624,"sample standard deviation"]
[null,22,1.098901098901099E-2,0.19780219780219774,null,47500,"minimum"]
[null,23,1.098901098901099E-2,0.20879120879120872,null,70000,"maximum"]
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[null,25,1.098901098901099E-2,0.23076923076923067]
[null,26,1.098901098901099E-2,0.24175824175824165,null,375,"tickets sold"]
[null,27,1.098901098901099E-2,0.25274725274725263,null,"$F$10","monitored cell"]
[null,28,1.098901098901099E-2,0.26373626373626363,null,62004.6875,"mean"]
[null,29,1.098901098901099E-2,0.27472527472527464,null,4944.2912143703543,"sample standard deviation"]
[null,30,1.098901098901099E-2,0.28571428571428564,null,52500,"minimum"]
[null,31,1.098901098901099E-2,0.29670329670329665,null,70000,"maximum"]
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[null,33,1.098901098901099E-2,0.31868131868131866]
[null,34,1.098901098901099E-2,0.32967032967032966,null,390,"tickets sold"]
[null,35,1.098901098901099E-2,0.34065934065934067,null,"$F$10","monitored cell"]
[null,36,1.098901098901099E-2,0.35164835164835168,null,59875.334999999999,"mean"]
[null,37,{"$f":"1/91","v":1.098901098901099E-2},0.36263736263736268,null,6382.3867781876761,"sample standard deviation"]
[null,{"$f":"B40+1","v":38},1.098901098901099E-2,0.37362637362637369,null,48750,"minimum"]
[null,39,1.098901098901099E-2,0.38461538461538469,null,70000,"maximum"]
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[null,42,1.098901098901099E-2,0.41758241758241771,null,363,"tickets sold"]
[null,43,1.098901098901099E-2,0.42857142857142871,null,"$F$10","monitored cell"]
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[null,45,1.098901098901099E-2,0.45054945054945073,null,4406.4501549211554,"sample standard deviation"]
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[null,47,1.098901098901099E-2,0.47252747252747274,null,70000,"maximum"]
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[null,67,1.098901098901099E-2,0.69230769230769185]
[null,68,1.098901098901099E-2,0.7032967032967028]
[null,69,{"$f":"1/91","v":1.098901098901099E-2},0.71428571428571375]
[null,{"$f":"B72+1","v":70},1.098901098901099E-2,{"$f":"C73+D72","v":0.7252747252747247}]
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{"sheet":"Marginal Analysis","index":6,"n_rows":97,"n_cols":11,"rows_kept":97,"cut":false,"hidden":false,"merged":[[0,1,0,7]]}
[null,"Flight Overbooking: Marginal Analysis"]
[]
[null,null,"probability",null,null,{"$f":"SEAT_REV/(SEAT_REV+BUMP_CST)","v":0.66666666666666663},"critical fractile"]
[null,null,"that last",null,null,{"$f":"305+CRIT.FRACTILE*91","v":365.66666666666669},"number to sell"]
[null,"tickets","sold is","marginal",null,{"$f":"TRUNC(F4)","v":365},"(really)"]
[null,"sold","seated","profit"]
[null,{"$f":"CAPACITY+MIN_NS","v":305},{"$f":"SUM('Overbooking 1'!C8:$C$98)","v":0.99999999999999845},{"$f":"C7*SEAT_REV-(1-C7)*BUMP_CST","v":499.99999999999881},null,"Our per-unit cost of being \"over\" is the net difference in cost between"]
[null,{"$f":"B7+1","v":306},{"$f":"SUM('Overbooking 1'!C9:$C$98)","v":0.9890109890109875},491.75824175824062,null,"selling a ticket to a passenger who ends up being bumped, and not"]
[null,307,{"$f":"SUM('Overbooking 1'!C10:$C$98)","v":0.97802197802197655},483.51648351648242,null,"selling that ticket, i.e, $250."]
[null,308,{"$f":"SUM('Overbooking 1'!C11:$C$98)","v":0.9670329670329656},475.27472527472423]
[null,309,{"$f":"SUM('Overbooking 1'!C12:$C$98)","v":0.95604395604395465},467.03296703296598,null,"Our per-unit cost of being \"under\" is the net difference in cost between"]
[null,310,{"$f":"SUM('Overbooking 1'!C13:$C$98)","v":0.9450549450549437},458.79120879120779,null,"not selling a ticket to a passenger who would have filled a seat, and"]
[null,311,{"$f":"SUM('Overbooking 1'!C14:$C$98)","v":0.93406593406593275},450.54945054944955,null,"selling that passenger a ticket, i.e, $500."]
[null,312,{"$f":"SUM('Overbooking 1'!C15:$C$98)","v":0.9230769230769218},442.30769230769135]
[null,313,{"$f":"SUM('Overbooking 1'!C16:$C$98)","v":0.91208791208791085},434.06593406593311,null,"The \"critical fractile is"]
[null,314,{"$f":"SUM('Overbooking 1'!C17:$C$98)","v":0.9010989010988999},425.82417582417492]
[null,315,{"$f":"SUM('Overbooking 1'!C18:$C$98)","v":0.89010989010988895},417.58241758241672]
[null,316,{"$f":"SUM('Overbooking 1'!C19:$C$98)","v":0.879120879120878},409.34065934065853,null,"We should \"order\" enough passengers - that is, sell enough tickets - that"]
[null,317,{"$f":"SUM('Overbooking 1'!C20:$C$98)","v":0.86813186813186705},401.09890109890028,null,"our chance of being \"over\" - ending up with too many"]
[null,318,{"$f":"SUM('Overbooking 1'!C21:$C$98)","v":0.8571428571428561},392.85714285714209,null,"passengers - is equal to (or just below) the critical fractile."]
[null,319,{"$f":"SUM('Overbooking 1'!C22:$C$98)","v":0.84615384615384515},384.61538461538385]
[null,320,{"$f":"SUM('Overbooking 1'!C23:$C$98)","v":0.8351648351648342},376.37362637362565,null,"If we sell 365 tickets, our chance of being \"over\" - having"]
[null,321,{"$f":"SUM('Overbooking 1'!C24:$C$98)","v":0.82417582417582325},368.13186813186741,null,"less than 65 no-shows - is …",null,null,null,null,{"$f":"SUM('Overbooking 1'!C8:C67)","v":0.659340659340659}]
[null,322,{"$f":"SUM('Overbooking 1'!C25:$C$98)","v":0.8131868131868123},359.89010989010922,null,"If we sell 366 tickets, our chance of being \"over\" is …",null,null,null,null,{"$f":"SUM('Overbooking 1'!C8:C68)","v":0.67032967032966995}]
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[null,384,{"$f":"SUM('Overbooking 1'!C87:$C$98)","v":0.13186813186813187},-151.09890109890108]
[null,385,{"$f":"SUM('Overbooking 1'!C88:$C$98)","v":0.12087912087912089},-159.34065934065933]
[null,386,{"$f":"SUM('Overbooking 1'!C89:$C$98)","v":0.1098901098901099},-167.58241758241758]
[null,387,{"$f":"SUM('Overbooking 1'!C90:$C$98)","v":9.8901098901098911E-2},-175.82417582417582]
[null,388,{"$f":"SUM('Overbooking 1'!C91:$C$98)","v":8.7912087912087919E-2},-184.06593406593407]
[null,389,{"$f":"SUM('Overbooking 1'!C92:$C$98)","v":7.6923076923076927E-2},-192.30769230769232]
[null,390,{"$f":"SUM('Overbooking 1'!C93:$C$98)","v":6.5934065934065936E-2},-200.54945054945057]
[null,391,{"$f":"SUM('Overbooking 1'!C94:$C$98)","v":5.4945054945054951E-2},-208.79120879120879]
[null,392,{"$f":"SUM('Overbooking 1'!C95:$C$98)","v":4.3956043956043959E-2},-217.03296703296704]
[null,393,{"$f":"SUM('Overbooking 1'!C96:$C$98)","v":3.2967032967032968E-2},-225.27472527472526]
[null,394,{"$f":"SUM('Overbooking 1'!C97:$C$98)","v":2.197802197802198E-2},-233.51648351648353]
[null,395,{"$f":"SUM('Overbooking 1'!C98:$C$98)","v":1.098901098901099E-2},-241.75824175824178]

{"sheet":"Overbooking 3","index":7,"n_rows":97,"n_cols":8,"rows_kept":97,"cut":false,"hidden":false,"merged":[[0,1,0,7]]}
[null,"Flight Overbooking: Marginal Analysis"]
[]
[null,null,"probability",null,null,{"$f":"SEAT_REV/(SEAT_REV+BUMP_CST)","v":0.66666666666666663},"critical fractile"]
[null,null,"that last",null,null,{"$f":"305+CRIT.FRACTILE*91","v":365.66666666666669},"number to sell"]
[null,"tickets","sold is","marginal",null,{"$f":"TRUNC(F4)","v":365},"(really)"]
[null,"sold","seated","profit"]
[null,{"$f":"CAPACITY+MIN_NS","v":305},{"$f":"SUM('Overbooking 1'!C8:$C$98)","v":0.99999999999999845},{"$f":"C7*SEAT_REV-(1-C7)*BUMP_CST","v":499.99999999999881},null,{"$f":"AVERAGE(1,F5-305)","v":30.5},"E[bumped | bump]"]
[null,{"$f":"B7+1","v":306},{"$f":"SUM('Overbooking 1'!C9:$C$98)","v":0.9890109890109875},491.75824175824062,null,{"$f":"(F5-305)/91","v":0.65934065934065933},"Pr[bump]"]
[null,{"$f":"B8+1","v":307},{"$f":"SUM('Overbooking 1'!C10:$C$98)","v":0.97802197802197655},483.51648351648242,null,{"$f":"AVERAGE(1,395-F5)","v":15.5},"E[empty | empty]"]
[null,308,{"$f":"SUM('Overbooking 1'!C11:$C$98)","v":0.9670329670329656},475.27472527472423,null,{"$f":"(395-F5)/91","v":0.32967032967032966},"Pr[empty]"]
[null,309,{"$f":"SUM('Overbooking 1'!C12:$C$98)","v":0.95604395604395465},467.03296703296598]
[null,310,{"$f":"SUM('Overbooking 1'!C13:$C$98)","v":0.9450549450549437},458.79120879120779,null,{"$f":"F7*F8*BUMP_CST+F9*F10*SEAT_REV+(1-F8-F10)*0","v":7582.4175824175818},"uncertainty cost"]
[null,311,{"$f":"SUM('Overbooking 1'!C14:$C$98)","v":0.93406593406593275},450.54945054944955]
[null,312,{"$f":"SUM('Overbooking 1'!C15:$C$98)","v":0.9230769230769218},442.30769230769135,null,"The formulas used above work"]
[null,313,{"$f":"SUM('Overbooking 1'!C16:$C$98)","v":0.91208791208791085},434.06593406593311,null,"for the given problem, where all"]
[null,314,{"$f":"SUM('Overbooking 1'!C17:$C$98)","v":0.9010989010988999},425.82417582417492,null,"no-show levels are equally likely."]
[null,315,{"$f":"SUM('Overbooking 1'!C18:$C$98)","v":0.89010989010988895},417.58241758241672,null,"=","=","="]
[null,316,{"$f":"SUM('Overbooking 1'!C19:$C$98)","v":0.879120879120878},409.34065934065853,null,"The formulas below show how we"]
[null,317,{"$f":"SUM('Overbooking 1'!C20:$C$98)","v":0.86813186813186705},401.09890109890028,null,"can handle the general case"]
[null,318,{"$f":"SUM('Overbooking 1'!C21:$C$98)","v":0.8571428571428561},392.85714285714209,null,"where the probabilities are not"]
[null,319,{"$f":"SUM('Overbooking 1'!C22:$C$98)","v":0.84615384615384515},384.61538461538385,null,"equal."]
[null,320,{"$f":"SUM('Overbooking 1'!C23:$C$98)","v":0.8351648351648342},376.37362637362565]
[null,321,{"$f":"SUM('Overbooking 1'!C24:$C$98)","v":0.82417582417582325},368.13186813186741,null,{"$f":"LOOKUP(CRIT.FRACTILE,1-C7:C97,B7:B97)","v":365},"number to sell"]
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[null,{"$f":"B24+1","v":323},{"$f":"SUM('Overbooking 1'!C26:$C$98)","v":0.80219780219780135},351.64835164835102,null,{"$f":"SUMPRODUCT((F23-CAPACITY-'Overbooking 1'!B8:B98>0)*(F23-CAPACITY-'Overbooking 1'!B8:B98)*'Overbooking 1'!C8:C98)/F26","v":30.500000000000004},"E[bumped | bump]"]
[null,324,{"$f":"SUM('Overbooking 1'!C27:$C$98)","v":0.7912087912087904},343.40659340659283,null,{"$f":"SUMPRODUCT(('Overbooking 1'!B8:B98<F23-CAPACITY)*'Overbooking 1'!C8:C98)","v":0.659340659340659},"Pr[bump]"]
[null,325,{"$f":"SUM('Overbooking 1'!C28:$C$98)","v":0.78021978021977945},335.16483516483459,null,{"$f":"SUMPRODUCT((CAPACITY+'Overbooking 1'!B8:B98-F23>0)*(CAPACITY+'Overbooking 1'!B8:B98-F23)*'Overbooking 1'!C8:C98)/F28","v":15.499999999999998},"E[empty | empty]"]
[null,326,{"$f":"SUM('Overbooking 1'!C29:$C$98)","v":0.7692307692307685},326.92307692307634,null,{"$f":"SUMPRODUCT(('Overbooking 1'!B8:B98>F23-CAPACITY)*'Overbooking 1'!C8:C98)","v":0.32967032967032966},"Pr[empty]"]
[null,327,{"$f":"SUM('Overbooking 1'!C30:$C$98)","v":0.75824175824175755},318.68131868131815]
[null,328,{"$f":"SUM('Overbooking 1'!C31:$C$98)","v":0.7472527472527466},310.43956043955995,null,{"$f":"F25*F26*BUMP_CST+F27*F28*SEAT_REV+(1-F26-F28)*0","v":7582.4175824175809},"uncertainty cost"]
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[null,332,{"$f":"SUM('Overbooking 1'!C35:$C$98)","v":0.7032967032967028},277.47252747252713]
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[null,337,{"$f":"SUM('Overbooking 1'!C40:$C$98)","v":0.64835164835164805},{"$f":"C39*SEAT_REV-(1-C39)*BUMP_CST","v":236.26373626373601}]
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[null,{"$f":"B40+1","v":339},{"$f":"SUM('Overbooking 1'!C42:$C$98)","v":0.62637362637362615},219.78021978021962]
[null,340,{"$f":"SUM('Overbooking 1'!C43:$C$98)","v":0.6153846153846152},211.53846153846143]
[null,341,{"$f":"SUM('Overbooking 1'!C44:$C$98)","v":0.60439560439560425},203.29670329670319]
[null,342,{"$f":"SUM('Overbooking 1'!C45:$C$98)","v":0.5934065934065933},195.05494505494497]
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[null,347,{"$f":"SUM('Overbooking 1'!C50:$C$98)","v":0.53846153846153855},153.84615384615392]
[null,348,{"$f":"SUM('Overbooking 1'!C51:$C$98)","v":0.5274725274725276},145.60439560439573]
[null,349,{"$f":"SUM('Overbooking 1'!C52:$C$98)","v":0.51648351648351665},137.36263736263749]
[null,350,{"$f":"SUM('Overbooking 1'!C53:$C$98)","v":0.5054945054945057},129.12087912087927]
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[null,{"$f":"B56+1","v":355},{"$f":"SUM('Overbooking 1'!C58:$C$98)","v":0.45054945054945073},87.912087912088055]
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[null,364,{"$f":"SUM('Overbooking 1'!C67:$C$98)","v":0.35164835164835168},13.736263736263766]
[null,365,{"$f":"SUM('Overbooking 1'!C68:$C$98)","v":0.34065934065934067},5.4945054945054892]
[null,366,{"$f":"SUM('Overbooking 1'!C69:$C$98)","v":0.32967032967032966},-2.7472527472527588]
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[null,368,{"$f":"SUM('Overbooking 1'!C71:$C$98)","v":0.30769230769230765},-19.230769230769226]
[null,369,{"$f":"SUM('Overbooking 1'!C72:$C$98)","v":0.29670329670329665},{"$f":"C71*SEAT_REV-(1-C71)*BUMP_CST","v":-27.472527472527503}]
[null,370,{"$f":"SUM('Overbooking 1'!C73:$C$98)","v":0.28571428571428564},-35.714285714285779]
[null,{"$f":"B72+1","v":371},{"$f":"SUM('Overbooking 1'!C74:$C$98)","v":0.27472527472527464},-43.956043956044027]
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[null,374,{"$f":"SUM('Overbooking 1'!C77:$C$98)","v":0.24175824175824165},-68.681318681318771]
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[null,{"$f":"B88+1","v":387},{"$f":"SUM('Overbooking 1'!C90:$C$98)","v":9.8901098901098911E-2},-175.82417582417582]
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[null,394,{"$f":"SUM('Overbooking 1'!C97:$C$98)","v":2.197802197802198E-2},-233.51648351648353]
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