Yield Management: What Quantities of Airline Tickets to Sell at What Prices and What Times


Problem Statement

An airline is selling tickets for flights to a particular destination.[25] The flight will depart in three weeks’ time. It can use up to six planes each costing £50,000 to hire. Each plane has:

37

First Class seats

38

Business Class seats

47

Economy Class seats

Up to 10% of seats in any one category can be transferred to an adjacent category.

It wishes to decide a price for each of these seats. There will be further opportunities to update these prices after one week and two weeks. Once a customer has purchased a ticket there is no cancellation option.

For administrative simplicity three price level options are possible in each class (one of which must be chosen). The same option need not be chosen for each class. These are given in Table 24.1 for the current period (period 1) and two future periods.

Table 24.1:  

 

Option 1

Option 2

Option 3

 

First

£1200

£1000

£950

 

Business

£900

£800

£600

Period 1

Economy

£500

£300

£200

 

First

£1400

£1300

£1150

 

Business

£1100

£900

£750

Period 2

Economy

£700

£400

£350

 

First

£1500

£900

£850

 

Business

£820

£800

£500

Period 3

Economy

£480

£470

£450

 


Demand is uncertain but will be affected by price. Forecasts have been made of these demands according to a probability distribution which divides the demand levels into three scenarios for each period. The probabilities of the three scenarios in each period are:

Scenario 1

0.1

Scenario 2

0.7

Scenario 3

0.2

The forecast demands are shown in Table 24.2.

Decide price levels for the current period, how many seats to sell in each class (depending on demand), the provisional number of planes to book and provisional price levels and seats to sell in future periods in order to maximize expected yield. You should schedule to be able to meet commitments under all possible combinations of scenarios.

With hindsight (i.e. not known until the beginning of the next period) it turned out that demand in each period (depending on the price level you chose) was as shown in Table 24.3.

Use the actual demands that resulted from the prices you set in period 1 to rerun the model at the beginning of period 2 to set price levels for period 2 and provisional price levels for period 3.

Repeat this procedure with a rerun at the beginning of period 3. Give the final operational solution.

Contrast this solution to one obtained at the beginning of period 1 by pricing to maximize yield based on expected demands.

Table 24.2:  

 

Price option 1

Price option 2

Price option 3

 

First

10

15

20

Period 1

Business

20

25

35

Scenario 1

Economy

45

55

60

 

First

20

25

35

Period 1

Business

40

42

45

Scenario 2

Economy

50

52

63

 

First

45

50

60

Period 1

Business

45

46

47

Scenario 3

Economy

55

56

64

 

First

20

25

35

Period 2

Business

42

45

46

Scenario 1

Economy

50

52

60

 

First

10

40

50

Period 2

Business

50

60

80

Scenario 2

Economy

60

65

90

 

First

50

55

80

Period 2

Business

20

30

50

Scenario 3

Economy

10

40

60

 

First

30

35

40

Period 3

Business

40

50

55

Scenario 1

Economy

50

60

80

 

First

30

40

60

Period 3

Business

10

40

45

Scenario 2

Economy

50

60

70

 

First

50

70

80

Period 3

Business

40

45

60

Scenario 3

Economy

60

65

70

 


Table 24.3:  

 

Price option 1

Price option 2

Price option 3

 

First

25

30

40

 

Business

50

40

45

Period 1

Economy

50

53

65

 

First

22

45

50

 

Business

45

55

75

Period 2

Economy

50

60

80

 

First

45

60

75

 

Business

20

40

50

Period 3

Economy

55

60

75

 




[25] Reproduced with permission of John Wiley & Sons Ltd. (Williams 1999, pp. 256–258).