Pergamon Computers ind. Engng Vol. 33, Nos 3--4, pp. 845-848, 1997 © 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-8352/97 $17.00 + 0.00 PII: S0360-8352(97)00263-5 Prediction of Future Origin Destination Matrix of Air Passengers by Fratar and Gravity Models Rakhmat Ceha and Hiroshi Ohta Dept. of Industrial Engineering, Osaka Prefecture University, 1-1, Gakueneho, Sakai, Osaka 593, Japan Abstract This article presents the need to predict the future demand of the air traffic passengers for scheduled commercial airlines. To determine the passengers demand, we have proposed an algorithm for assigning the origin destination (OD) matrix of the passengers air traffic between different airports. In order to realize the problem, we assume two different circumstances. Firstly, we predicted the total air traffic passengers with the target year. Secondly, we distributed the air traffic passengers between airports according to geographic location using the gravity and fratar models. The effectiveness of proposed method was examined through an air transportation network in Sumatra island (in Indonesia) as a ease study. © 1997 Elsevier Science Ltd Kevwgrds: OD Matrix, Gravity Model, Fratar Model 1. Introduction The flight planning of the scheduled commercial airlines includes many sub-problems such as vehicle aasigmnent, re- scheduling in disturbed situat/on, prediction of future need and the prospective airport movement, etc. In order to solve these problems, it is necessary to understand the muses which are usually due to the trip pattern. The notion of origin destination (OD) matrix is being used by transport planners to find the trip pattern. When an OD matrix is assigned to the network, the corresponding flow pattern is automatically produced. Many attempts have already been made to identify the trip pattern. Various methods can be used to estimate the OD matrix. These methods are very different among themselves and can be divided into three catagories[1], i.e., direct sample estimation, model estimation, and estimation by traffic flows. All these existing approaches are usually used to estimate the OD matrix considering some statistical aspects of estimation, where the estimation is done for only the base year i.e., few attempts have been made for prediction of the OD matrix for the future target year. This paper proposes an algorithm to predict the future OD matrix of passengers between different airports based on the available limited data. 2. Procedure for Predicting the OD Matrix This paper presents a procedure for predicting the future OD matrix in the target year using the OD matrix of the base year, and the previous data of the economic indices. The procedure for predicting the future OD matrix consists of two stages. The first stage is to predict the total air traffic with the target year, and the second stage is to distribute the passengers between airports according to hub and spoke geographic location (i.e., provinces)J2]. In the first stage an ordinary least square model is applied to historical data. The demand of passengers is expressed as a function of the specified explanatory variables. In the second stage the gravity and frntar models[3] are used. The gravity model is used for measuring and distributing the trip generation as being directly related to the number of passengers between airports. The Fratar model is used for predicting the future OD matrix between locations. The procedure can be summarized to II steps as follows. Step O. Collecting the economic indices and the air traffic data There are two sets of inputs, namely the air traffic data and the economic indices which have been collected from the various authorities concerned. Step 1. Analysis of the economic indices Several kinds of the basic economic indices (i.e., population, total personal income, etc.) in each province are collected and analyzed to know the various economic parame- ters relating the development policy of government and also the basis for the projection of other economic indices (i.e., regional industrial development plan, tourist destination areas, etc.). Step 2. Determination o.f trip production model by each province In order to determine explanatory variables, it is necessary to carry out the correlation analysis for air traffic demand. For this purpose, several kinds of the basic economic indices from Step 1, are utilized for predicting the traffic demand. Step J. Prediction of :uture economic indices An analysis based on time series is carried out here to project/find the future economic indices in each province. 845