A charter fishing boat operating out of Port Aransas on the Gulf coast has recor

Question

A charter fishing boat operating out of Port Aransas on the Gulf coast has recorded the no-show experience show below over the past 20 excursions. To avoid the opportunity of losing the $50 fee charged per fisherman, the boat captain is considering a policy of accepting more reservations than his boat has capacity. When this policy results in turning away disappointed fishermen, he plans to hire his brother to accommodate the overbooked fishermen at $120 apiece.

No-show 0 1 2 3 4

Frequency 4 5 6 3 2

a. Using the "critical fractile" probability, P(d<x), how many reservations would you recommend overbooking?

b. What is the expected loss per excursion, if only two reservations are overbooked?

Explanation / Answer

Cu - Underbooking Cost = $50 Co - Overbookinh Cost = $120 Increase the booking so long as P Cu / Cu + Co P 50 / 50 + 120 = 0.2941 Hence, overbook 1 Overbook No Show Probability Cum Prob 0 1 2 3 4 0 0.20 0.20 $0.00 $120.00 $240.00 $360.00 $480.00 1 0.25 0.45 $50.00 $0.00 $120.00 $240.00 $360.00 2 0.30 0.75 $100.00 $50.00 $0.00 $120.00 $240.00 3 0.15 0.90 $150.00 $100.00 $50.00 $0.00 $120.00 4 0.10 1.00 $200.00 $150.00 $100.00 $50.00 $0.00 Expected Cost $500.00 $420.00 $510.00 $770.00 $1,200.00 Since Expected Cost is lowest in 1 overbooking, so overbook 1 Example Calculation for No Show - 1 passenger Overbooking No Show Seats Empty Cost A B C = B - A If C>0, C*50, IF C

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