Forecasting as a basis for managing operational risks

Several processes in the airline industry are heavily depending on a good forecast of passenger demand.²⁹⁵ While on a strategic level, network planning builds upon projected Origin-Destination demand for various fare classes, on a tactical and operational level Yield Management requires as accurate as possible forecasts to allocate capacity units (seats) to arriving booking requests in order to maximize the overall revenue. In the following, the main applied forecast methods to cope with demand uncertainty will be presented. In most cases a combination of quantitative (mostly naïve) and qualitative forecast methods are employed.

“The term naïve may be applied to any forecast obtained solely from historical values of the variables to be forecasted.”²⁹⁶

Therefore the simplest available “forecast” method would be an unchanged projection of the last observation of a variable for future points in time. More complex methods do not only rely on a single observation in the past but do take several data points into consideration, e.g. by building a moving average of past observation values. Further advanced time-series analysis methods do also consider trends and seasonality by incorporating adjustment factors (see example below). Due to the fact that they are building upon several (additive or multiplicative) components, they are referred to as component models. An additive component is used if a trend is rather constant in absolute numbers (e.g. the number of worldwide airline passengers grows by an additional 100 Mio. passengers each year), while a multiplicative component can be used to accommodate the fact that certain periods always show a different level in proportion to a changing absolute base number (e.g. an airline always transports 1,4x as many passengers in July than in an average month).²⁹⁷

t+i = (at + i*bt) * s

with: t+i = forecasted value at = base value (e.g. last observation) i = forecasted periods bt = absolute trend adjustment factor s = multiplicative seasonality

If there is an influence of several independent (exogenous) variables onto the dependent (endogenous) variable, a multivariate forecast model should be used. To obtain valid results, the variables entering a model should have a logical, i.e. causal relationship to the forecasted variable (e.g. the presence of state holidays is assumed to positively influence the demand for flights on these days). In order to be able to forecast future values of the dependant variable, the input variables should either be already available at an earlier point of time (e.g. holidays are usually known several months or even years ahead) or at least be easier to estimate than the target values. The most prominently used multivariate forecasting method is linear regression analysis, which

295 Cf. Doganis (2002), p. 208: “Forecasting is the most critical area of airline management”

296 Chrisholm / Whitakter (1971), p. 8

297 Cf. Winters (1960), p. 327ff; Hansmann (1983), p. 47f; Schlittgen / Streitberg (1984), p. 9

assumes a linear function between the weighted input factors and the predicted variable (see example below).²⁹⁸

xt= a0 + b1y1t + b2y2t + . . . + bnynt + et

with: xt = value of dependent variable at time t a0 = (any) constant term b1, b2, bn = parameters y1, y2, yn = independent variables et = error term

By comparing the correlation between the predicted and the actual value (usually denominated by the coefficient of determination, r²) the goodness of fit of the model can be calculated, telling the researcher how much of the variance of the dependent variable is explained by the independent variables. The initial calibration of the model is done via a trial of several weight parameters with the aim of minimizing the sum of squared error terms of the entire regression function (method of least squares).²⁹⁹

To assess the quality of a forecast (or the forecast error) a range of metrics can be used, of which two widely used ones, the Mean Absolute Deviation (MAD) and the Mean Squared Deviation (MSD), will be presented in the following. While in both cases the deviations between estimator and actual value are scrutinized, with the latter more weight is given to large deviations (since the residuals are squared, large errors receive proportionally more attention than small ones). To present the forecast error as a relative measure, the mean absolute percentage error (MAPE) can be used.³⁰⁰

MAD = ∗ ∑ | − | MSD = ∗ ∑ ( − )

MAPE = ∗ ∑ | |

with: t = forecasted value (estimator) xt = actually observed value T = total number of forecasted periods t=1 = first forecasted period

High forecast accuracy is of great importance for airline revenue management. Having examined data from several high-demand flights of US airlines, Lee reports an increase of 0,5% - 3% in average revenues for every 10% increase in forecast accuracy.³⁰¹ These findings were also confirmed in a simulation study by Belobaba and Weatherford.

“The greatest impacts were observed when the fare class demand forecasts proved to be inaccurate. Demand forecasting errors of 25% for each fare class, not an outrageous magnitude in yield management practice where the demand for

298 Cf. Hansmann (1983), p. 126ff; Chrisholm / Whitakter (1971), p97

299 Cf. Schlittgen / Streitberg (1984), p. 16

300 Cf. Hansmann (1983), p. 15

301 Cf. Lee (1990), p. 255

a single fare class can be of the order of 10-20 passengers, were simulated to have negative revenue impacts of 1-2% or more on the highest demand flights.”³⁰² Two factors which have a strong influence on the forecast error are the forecasted time span as well as the spatial and temporal aggregation level of the forecast. In a survey among 160 managers from the US that were responsible for demand forecasts, Cox &

Mentzer found a strong correlation between forecast horizon, aggregation level and forecast error. This has also been confirmed by Fildes and Beard who conducted several case studies with British manufacturing companies (cf. Table 17). Although with higher MAPE-error figures, results following the same logic were also obtained in studies dealing with the airline³⁰³ or the hotel industry.³⁰⁴

Mean absolute percent errors of forecast forecast period

Aggregation level < three months < two years > two years

Product group 10% (10%) 15% (10%) 20% (15%)

Product line 11% (12%) 16% (12%) 20% (19%)

Product 16% (16%) 21% (20%) 26% (27%)

Values from a survey of US companies (Cox / Mentzer), values in brackets from a British study (Beard / Fildes).

Table 17: Influence of aggregation level & forecast period on forecast error³⁰⁵

If companies require a forecast for individual items as well as item groups, often a hierarchical forecasting process is used. Within such processes, two distinct approaches can be distinguished, namely the bottom-up as well as the top-down approach.

• In the bottom-up process, the demand for individual segments (e.g. specific Stock-Keeping Unit, a single day or a single sales entity) is forecasted and later on aggregated to a cumulative forecast of the demand for the superordinate entity.

• If the demand of forecasted products follows similar patterns, in order to reduce the time and the costs involved with individual forecasting, companies can apply a top-down approach. In this case aggregate demand is predicted and later on disaggregated on the basis of historical segment proportions to produce a so-called derived forecast for each segment.³⁰⁶

Based on these fundamental characteristics of forecasts several risk reduction strategies (e.g. postponement) have been built up which will be presented in the next section. Furthermore these characteristics also form the basis for the cost reduction and

302 Belobaba / Weatherford (2002), p. 820

303 Cf. Sa (1987), p. 81

304 Cf. Kimes (1999), p. 1106f. Having examined the group arrival forecast accuracy of hotels, Kimes found that “the MAPE averaged 40% at two months before arrival, dropped to about 30% at one month before arrival, and decreased to 10-15% on the day of arrival.”

305 Cf. Cox / Mentzer (1984), p. 33; Beard / Fildes (1992), p. 9

306 Cf. Caniato et al. (2005), p. 480

demand induction potentials that come along with the use of flexible tickets in the airline industry, which will be presented in more detail in chapter 4.