Northwest Airlines runs daily flights from Detroit to Amsterdam. They face a fix

Question

Northwest Airlines runs daily flights from Detroit to Amsterdam. They face a fixed cost of $70,000 for each flight independent of the actual number of passengers on the plane. There are 310 seats available on a plane. One-way tickets generate revenues of $600 apiece when used but are fully refundable if not used. On a typical weekday, the airline estimates that the number of no-shows will range between 0 and 20; all intermediate values are equally likely. By law, an airline is allowed to overbook flights, but must give compensation of $250 to all ticketed passengers not allowed to board. In addition, it must provide those passengers with alternative transportation on another carrier (the cost of providing the alternative transportation just wipes out the $600 revenue). How many tickets should Northwest book on its flight from Detroit to Amsterdam?

Explanation / Answer

Overbook No Show Probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.05 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 $103,250 $102,400 $101,550 $100,700 $99,850 2 0.05 $115,400 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 $103,250 $102,400 $101,550 $100,700 3 0.05 $114,800 $115,400 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 $103,250 $102,400 $101,550 4 0.05 $114,200 $114,800 $115,400 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 $103,250 $102,400 5 0.05 $113,600 $114,200 $114,800 $115,400 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 $103,250 6 0.05 $113,000 $113,600 $114,200 $114,800 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 $104,100 7 0.05 $112,400 $113,000 $113,600 $114,200 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 $104,950 8 0.05 $111,800 $112,400 $113,000 $113,600 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 $105,800 9 0.05 $111,200 $111,800 $112,400 $113,000 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 $106,650 10 0.05 $110,600 $111,200 $111,800 $112,400 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 $107,500 11 0.05 $110,000 $110,600 $111,200 $111,800 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 $108,350 12 0.05 $109,400 $110,000 $110,600 $111,200 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 $109,200 13 0.05 $108,800 $109,400 $110,000 $110,600 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 $110,050 14 0.05 $108,200 $108,800 $109,400 $110,000 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 $110,900 15 0.05 $107,600 $108,200 $108,800 $109,400 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 $111,750 16 0.05 $107,000 $107,600 $108,200 $108,800 $108,800 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 $112,600 17 0.05 $106,400 $107,000 $107,600 $108,200 $108,200 $108,800 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 $113,450 18 0.05 $105,800 $106,400 $107,000 $107,600 $107,600 $108,200 $108,800 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 $114,300 19 0.05 $105,200 $105,800 $106,400 $107,000 $107,000 $107,600 $108,200 $108,800 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 $115,150 20 0.05 $104,600 $105,200 $105,800 $106,400 $106,400 $107,000 $107,600 $108,200 $108,800 $109,400 $110,000 $110,600 $111,200 $111,800 $112,400 $113,000 $113,600 $114,200 $114,800 $116,000 Total Profit (A) $2,206,000 $2,216,550 $2,225,650 $2,233,300 $2,230,500 $2,235,850 $2,239,750 $2,242,200 $2,243,200 $2,242,750 $2,240,850 $2,237,500 $2,232,700 $2,226,450 $2,218,750 $2,209,600 $2,199,000 $2,186,950 $2,173,450 $2,158,500 Expected Profit (A/20) $110,300 $110,828 $111,283 $111,665 $111,525 $111,793 $111,988 $112,110 $112,160 $112,138 $112,043 $111,875 $111,635 $111,323 $110,938 $110,480 $109,950 $109,348 $108,673 $107,925 Since Expected Profit is highest in 9 overbookings, so overbook 9 Example Calculation for No Show - 3 passengers Overbooking No Show Seats Empty Opportunity Cost Expected Revenue Expected Profit A B C = B - A D = If C>0, C*600, IF C

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