Damp trend Grey Model forecasting method for airline industry

Abstract

This paper presents a modification of the Grey Model (GM) to forecast routes passenger demand growth in the air transportation industry. Forecast methods like Holt-Winters, autoregressive models, exponential smoothing, neural network, fuzzy logic, GM model calculate very high airlines routes pax growth. For this reason, a modification has been done to the GM model to damp trend calculations as time grows. The simulation results show that the modified GM model reduces the model exponential estimations grow. It allows the GM model to forecast reasonable routes passenger demand for long lead-times forecasts. It makes this model an option to calculate airlines routes pax flow when few data points are available.

The United States domestic air transport market data are used to compare the performance of the GM model with the proposed model.

Introduction

In this paper, a new version of the Grey Model (GM) forecasting method is proposed. In this version, a damping trend factor has been included to the GM model. It forecasts reasonable airlines routes passenger (pax) growth for long lead-time.

A problem when using forecasting methods such as Holt-Winters, autoregressive models, exponential smoothing, neural network, fuzzy logic, and Grey Model (GM) is the fact that these models tend to calculate high airlines routes pax growth for long lead-time forecasting (Grubb & Mason, 2001) (Gardner and McKenzie, 1985, Gardner and McKenzie, 1988, Gardner and McKenzie, 1989). Another problem when forecasting airlines pax flow growth for long lead-time forecasting is the quantity of data points available and needed to use any of these methods. A forecasting method able to solve both problems allows estimating reasonable airlines routes pax flow growth for relatively new routes; it is very important for airlines making decisions of network planning, network management, fleet assignment, man power planning, aircraft routing, flight scheduling, revenue management, new routes and investments.

Armstrong (2006) reviewed forecasting methods. He recommended the damping trend as well established forecasting method to improve accuracy in practical applications. Despite of these improvements, Armstrong (2006) explained that a damp trend factor has been added in small number of forecasting methods. Fildes, Wei, and Ismail, (2008) and Hyndman, Koehler, Ord, and Snyder (2008) found and concluded that using a damping trend factor is favorable for forecasting exponential smoothing method.

This paper shows that forecasting pax flow between cities origin and cities destination (O–D pairs) using a GM model without a damping trend factor does not forecast reasonable data. Thus, the authors proposed to add a damping trend parameter (ς) to modify the trend component in the GM model forecasting method.

The modified GM model is proposed to estimate reasonable routes pax flow between cities/airports (O–D pairs) when having a minimum of four data points. The GM model has three main advantages. Firstly, the GM model forecasts data that have unknown parameters. Secondly, the GM model requires few data (minimum 4 data points) to approximate the behavior of unknown systems. A big advantage because there are many circumstances in which the data is not enough to perform a good forecast for long lead-times using other forecasting methods. Thirdly, the GM model has been used by other researcher, such as Hsu and Wen, 2000, Hsu and Wen, 2002, Hsu and Wen, 2003, to create data for the design of airline networks without assessing how good is the GM forecast. Hsu and Wen, 2000, Hsu and Wen, 2002, Hsu and Wen, 2003 did not prove if the GM model is an accurate forecasting method to estimate reasonable airlines routes pax growth for long lead-time. Then, this paper analyses the feasibility of using the modification of the GM model for long lead-times proposed by Carmona Benitez (2012).

In Section 2, the damping trend factor is added to the GM model to forecast reasonable long lead-time data for the airline pax industry. In Section 3, the source of data used to prove the forecasting method is presented (DOT US Consumer Report, 2005-2008). In Section 4, the results are shown for 9 extreme study cases. Finally, Section 5 concludes this chapter.