A Mathematical Model for Demand Distribution in An Air Transport Network

Abstract

This article describes the great distance that separates Sardinia from mainland Italy has made the island – the second largest island of the Mediterranean – a marginal and remote region. Its system of ferry links for people travelling to and from Sardinia has such long journey times (8-12 hours) that it is clearly in no way a valid alternative to air transport. It was mainly on the basis of these reasons and with a view to protecting and ensuring the mobility of Sardinian residents that Public Service Obligations (PSO) were imposed on some of the main air routes starting from 2002. Our study is set against this background. It aims to resolve one of the main critical factors that distinguish the PSO network: the shortage of flights on certain routes and the concomitant over-scheduling of others. More specifically, the insufficient scheduling of weekly flights to certain airports, such as Verona and Turin, forces a number of passengers to decide not to travel at all and another part to use connecting flights to Rome/Milan airports or to travel using more than one route, via air or ground transport, with inevitably higher transport costs. The problem was addressed by using a linear scheduling model applied to a network of nodes and arcs representing, respectively, the airports and their connecting routes, and the airport of Cagliari. The decision variables identified were the number of passengers travelling on all of the arcs and the impedance measures associated with the distance travelled by the arcs, represented by the generalized cost of transport. The objective is to determine a network structure which corresponds to the distribution of passengers on the various branches capable of minimizing the total cost. This cost was considered as a useful parameter for comparing the various network scenarios which were obtained by changing the passenger load coefficient and the number of flights. Our study demonstrates that a simple intervention, aimed at the internal reallocation of the flights on the various routes, is able to guarantee categories of users (here divided into business and non-business users) greater access to air transport services. The scenario that more than others is able to improve service efficiency, granting undeniable benefits for all users without having an impact on the costs of air carriers, particularly stands out because it: • Allows access to all network airports through direct flights; • Decongests the Rome and Milan routes