Question

Case 7.2

Skyhigh Airlines

Skyhigh Airlines flight 708 from New York to Los Angeles is a popular flight that is

usually sold out. Unfortunately, some ticketed passengers change their plans at the last

minute and cancel or re-book on another flight. Subsequently, the airline loses the $450

for every empty seat that the plane flies.

To limit their losses from no-shows, the airline routinely overbooks flight 708, and hopes

that the number of no-shows will equal the number of seats oversold. However, things

seldom work out that well. Sometimes flight 708 has empty seats, and other times there

are more passengers than the airplane has seats. When the latter happens, the airline must

“bump” pre-ticketed passengers; they estimate that this will cost them $275 in later

accommodations to bumped passengers.

Fortunately for the airline, hopeful passengers usually show up at flight time without

tickets and want to get on the flight. The airline classifies these passengers as standbys

while it waits to determine how many seats, if any will be available. Standby passengers

can help offset the loss associated with flying an empty seat, but the airline suffers no

penalty when a standby passenger is not able to receive a seat.

Airline records indicate that the number of No-shows and Standbys will vary according

to the probability tables below: (see bottom of page)

Simulate 25 flights with each of several different overbooking decisions (assume that the

best overbooking number will be between 1 and 6) to determine the optimal number of

seats to overbook this flight, to minimize the airline’s losses. Tabulate your results and

use them to justify your recommendations. You should report, for each scenario, the

average loss per flight, and the percentage of flights that suffer a loss.

No. of No Show	Relative Frequency
0	.04
1	.08
2	.14
3	.25
4	.30
5	.13
6	.06

No. Of Standy-Byes	Relative Frequency
0	.26
1	.34
2	.24
3	.11
4	.05

Answer 1

SOLLUTION:-

NO	Per Ticket Cost	Probability	loss after probability
1)	$340	100%	$340
2)	$350	99%	$347
3)	$360	98%	352.8
4)	$370	97%	358.9
5)	$380	96%	364.8
6)	$380	95%	361
7)	$390	94%	366.6
8)	$430	93%	399.9
9)	$420	92%	386.4
10)	$410	91%	373.1
11)	$440	90%	396
12)	$450	89%	400.5
13)	$470	88%	413.6
14)	$460	87%	400.2
15)	$480	86%	412.8
16)	$490	85%	416.5
17)	$500	84%	420
18)	$510	83%	423.3
19)	$520	82%	426.4
20)	$530	81%	429.3
21)	$540	80%	432
22)	$550	79%	434.5
23)	$560	78%	436.8
24)	$580	77%	446.6
25)	$600	76%	456
Average	$460	88%	$400

	NUMBER OF NO SHOWS
	0
	1
	2
	3
	4
	5
	6
Total	21
Average	3
s.d	2.160246899

determine the optimal number of seats =NORMINV(Probability, Mean, Standard deviation)

= 2.235449(0.3617,3, 2.160246899)

average loss per flight =

and the percentage of flights that suffer a loss.

so, empty seat over booked loss is = 2

B / B+C

$340 / $340 +$600

$340 / $940

=0.3617

B= low cost for empty seat taken from simulation

C=high cost for empty seat taken from simulation

Average loss per flight= $400( from simulation cost average loss has taken)(see last line from the table)

Percentage of flights that suffer a loss is 88%. (see last line from the table)

________________________________________________________________

NO	Bumb cost	Probability	cost after probability
1)	$120	100%	120
2)	$130	99%	128.7
3)	$140	98%	137.2
4)	$150	97%	145.5
5)	$160	96%	153.6
6)	$170	95%	161.5
7)	$180	94%	169.2
8)	$195	93%	181.35
9)	$201	92%	184.92
10)	$210	91%	191.1
11)	$220	90%	198
12)	$230	89%	204.7
13)	$240	88%	211.2
14)	$250	87%	217.5
15)	$260	86%	223.6
16)	$270	85%	229.5
17)	$280	84%	235.2
18)	$290	83%	240.7
19)	$300	82%	246
20)	$310	81%	251.1
21)	$320	80%	256
22)	$330	79%	260.7
23)	$340	78%	265.2
24)	$350	77%	269.5
25)	$360	76%	273.6
Average	$240	88%	206.2228

	NUMBER of Standbys	Probability
	0	0.26
	1	0.34
	2	0.24
	3	0.11
	4	0.05
Total	10	1
Average	2
s.d	1.58113883

determine the optimal number of seats =NORMINV(Probability, Mean, Standard deviation)

= 0.9335 (0.25,2, 1.58113883)

average bump   per flight = 1

B / B+C

$120 / $120 +$360

$120 / $480

=0.25

B= low cost for empty seat taken from simulation

C=high cost for empty seat taken from simulation

Average bump cost per flight= $206

Percentage of flights is 88%. (see last line from the table)