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 |
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)
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