Question

  

  Ashcroft Airlines flies a six-passenger commuter flight once a day to Gainesville, Florida.         A non-refundable one-way fare with a reservation costs $129. The daily demand for this         flight is given in the table below, along with the probability distribution of no-shows. A         no-show has a reservation but does not arrive on time at the gate and forfeits the fare.         Ashcroft currently overbooks at most three passengers per flight. If there are not         enough seats for all the passengers at the gate, each passenger that cannot board the         flight is refunded the passenger’s fare and also $150 voucher good on any other trip.         The fixed cost for a flight is $450.

Demand	Probability		No-shows	Probability
5	0.05		0	0.15
6	0.11		1	0.25
7	0.20		2	0.26
8	0.18		3	0.23
9	0.16		4	0.11
10	0.12
11	0.10
12	0.08

        i) Set up a flow chart showing the logical sequence of events for simulating Ashcroft’s              expected profit for this flight. Provide all the details of the formulas used for relevant         calculations.                                                                                         [20%]

        ii) Using the two-digit random numbers below (in the order as they appear),                         calculate Ashcroft’s profit per flight and replicate your calculations 10 times.                     Organise all your calculation in a table. Calculate the expected profit, the                           occupancy rate of the plane and the probability that Ashcroft profit per flight is                  higher than $400? Briefly comment on the reliability of your results.             [50%]

           Random number sequence: 69 56 30 32 66 79 55 24 80 35 10 98 92 92 88            82 13 04 86 31 12 23 40 93 13 42 51 16 17 29 62 08 59 41 47 72 25            96 58 14 68 15 18 99 13 05 03 83 34 78 50 89 98 93 70 11

        iii) Explain how you could use this model to investigate Ashroft’s overbooking strategy             (no calculations required).                                                                    [15%]

Answer 1

The flow chart with required explanation is below

ii. The spreadsheet with the calculation shown in the flow chart is given below

With formula used

The expected profit is the average of profit in 10 simulation and is $412.5

The average occupancy rate is 92%

Out of 10 simulation runs, there are 5 instances in which the profit is greater than $400. The probability that Ashcroft profit per flight is higher than $400 is 5/10=0.5

The standard deviation of the profit calculated using excel formula =STDEV.S(H2:H11). The standard error of the profit is standard deviation/sqrt(n) where n=10

The standard error of profit = 232.62/sqrt(10)=73.56

That margin of error in the point estimate of profit at 95% confidence (z value is 1.96 for significance level 0.05) is

which is pretty high. As we increase the number of simulations the margin of error decreases. For example for 100 simulations the standard error of profit is 232.62/sqrt(100)=23.26

the margin of error is +-1.96*23.26=+- $45.59

Hence it makes sense to increase the number of simulation runs.

iii. the current number of overbooked passengers is a maximum of 3. Ashroft can run this simulation with different number of over bookings and go for the strategy which yields the maximum expected profit.