1Airport and Steamboat Springs, Colorado, is considering overbooking its flights

Question

1Airport and Steamboat Springs, Colorado, is considering overbooking its flights to avoid flying with empty seats. For exam ple, the ticket agent is thinking of taking seven reservations for an airplane that has only six seats. During the past month, the no-show experience has been No-shows 0 2 4 Percentage30 25201510 The operating costs associated with each flight are pilot, $150; first officer, $100; fuel, $30; and landing fee, $20 What would be your recommendation for overbooking if a one-way ticket sells for $80 and the cost of not honoring a reservation is a free lift ticket worth S50 plus a seat on the next flight? What is the expected profit per flight for your overbooking choice?

Explanation / Answer

Airline profit by selling six seats = 80*6 - (150+100+30+20) = $ 180

Payoff table for incremental profit based on various overbooking decisions is as follows

Incremental profit = D*80 - MAX(0,D-S)*(80+50) , where D indicates each decision (overbooking =0,1,2,3,4,)

and S denotes state of no shows (0,1,2,3,4)

Expected Value of each decision is computed by finding SUMPRODUCT of the respective payoffs and their probabilities

EV of D0 = 0

EV of D1 = 41

EV of D2 = 49.5 (=-100*.30+30*0.25+160*0.20+150*0.15+160*0.10)

EV of D3 = 32

EV of D4 = -5

EV is maximum for overbooking of 2 seats.

Expected profit per flight with the above overbooking choice = 180 + 49.2 = $ 229.5

No Shows 0 1 2 3 4 Overbooking 0.3 0.25 0.2 0.15 0.1 0 0 0 0 0 0 1 -50 80 80 80 80 2 -100 30 160 160 160 3 -150 -20 110 240 240 4 -200 -70 60 190 320

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