Star Airlines Flight 123 is one of the popular morning departure flights from NY

Question

Star Airlines Flight 123 is one of the popular morning departure flights from NY to LA. The aircraft is Boeing 737-800, with a capacity of 175 economy class seats. If the flight is overbooked, then the airline has to book the passenger in the next available flight with a different airline at a cost of $100 and pay the passenger a credit voucher worth $400. The cost of $100 to book in another airline is less than the profit of $270 because of agreement between the airlines – note that the other airline may do the same with Star. The incremental profit is $270 per passenger. Historical indicates the following probability distribution for the number of no shows.

       Determine the optimal number of seats that Star should overbook.

No-Shows 0 1 2 3 4 5 6 7 8 9 10 11 12 Probability % 2 4 5 6 8 10 16 20 12 7 5 3 2

Explanation / Answer

Overbook No Show Probability 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0.02 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 $4,000.00 $4,500.00 $5,000.00 $5,500.00 $6,000.00 1 0.04 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 $4,000.00 $4,500.00 $5,000.00 $5,500.00 2 0.05 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 $4,000.00 $4,500.00 $5,000.00 3 0.06 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 $4,000.00 $4,500.00 4 0.08 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 $4,000.00 5 0.10 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 $3,500.00 6 0.16 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 $3,000.00 7 0.20 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 $2,500.00 8 0.12 $2,160.00 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 $2,000.00 9 0.07 $2,430.00 $2,160.00 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 $1,500.00 10 0.05 $2,700.00 $2,430.00 $2,160.00 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 $1,000.00 11 0.03 $2,970.00 $2,700.00 $2,430.00 $2,160.00 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 $500.00 12 0.02 $3,240.00 $2,970.00 $2,700.00 $2,430.00 $2,160.00 $1,890.00 $1,620.00 $1,350.00 $1,080.00 $810.00 $540.00 $270.00 $0.00 Total Cost (A) $21,060.00 $18,320.00 $16,350.00 $15,150.00 $14,720.00 $15,060.00 $16,170.00 $18,050.00 $20,700.00 $24,120.00 $28,310.00 $33,270.00 $39,000.00 Expected Cost (A/12) $1,755.00 $1,526.67 $1,362.50 $1,262.50 $1,226.67 $1,255.00 $1,347.50 $1,504.17 $1,725.00 $2,010.00 $2,359.17 $2,772.50 $3,250.00 Overbooking No Show Seats Empty Cost A B C = B - A If C>0, C*270, IF C

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