Question 1 (20 points: 6, 7, 7) An airline offers two types of one-way air fares

Question

Question 1 (20 points: 6, 7, 7) An airline offers two types of one-way air fares for the route from Chicago to San Francisco: full-coach fare ($450/seat) and discount fare ($200/seat). The aircraft used for the route has 100 seats. The company needs to consider the tradeoff between the "spoilage" and the "spill" (refer to the lecture slides for the definitions of these two terms) to decide on the number of seats they should allocate and reserve for the full-coach passengers in order to maximize its expected revenue. Assume that the demand for the discount fares is very large (well more than 100 seats). Based on the past data and information from the market, the airline estimates the demand for full-coach fares and uses it for analysis. Find the optimal (best) number of seats the airline should allocate for full-coach passengers for the cases below: a. The demand for full-coach fares can be anywhere between 10 and 40, i.e. it has uniform distribution: U[10,40] b. The demand for full-coach has normal distribution with the mean of 30 (seats) and the standard deviation of 20. The demand for full coach fares has the following distribution: c. Demand Probabilit 20 0.2 30 0.2 40 0.3 50 60

Explanation / Answer

(a) Cost of overbooking full-fare seats, Co = 200

Cost of underbooking full-fare seats, Cu = 450-200 = 250

Critical ratio = 1 - pd/pf = 1 - 200/450 = 0.556

Optimal protection level for full-fare seats = 10 + (40-10)*0.556 = 27

(b) z-stat = NORMSINV(0.556) = 0.1397

Optimal protection level for full-fare seats = 30+0.1397*20 = 33

(c) Construct cumulative probability table

In the comulative probability table, look for cumulative probability greater than or equal to 0.556.

The cumulative probability greater than 0.556 is 0.8. Corresponding demand is 40.

Therefore, optimal protection level for full-fare seats = 40

Demand Probability Cumulative probability 10 0.1 0.1 20 0.2 0.3 30 0.2 0.5 40 0.3 0.8 50 0.1 0.9 60 0.1 1

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