CARGO AND PASSENGERS AIR TRANSPORT IN BRAZIL: AN APPLICATION OF THE SINGLE AND MULTIPLE ASSIGNMENT P- HUB LOCATION PROBLEM

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1 CARGO AND PASSENGERS AIR TRANSPORT IN BRAZIL: AN APPLICATION OF THE SINGLE AND MULTIPLE ASSIGNMENT P- HUB LOCATION PROBLEM Rafael Mesquita Antunes de Figueiredo Catholic University of Rio de Janeiro Industrial Engineering Department, Marques de Sao Vicente Street, 225, Rio de Janeiro RJ Brazil, Tel: /Fax: Nelio Domingues Pizzolato Catholic University of Rio de Janeiro Industrial Engineering Department, Marques de Sao Vicente Street, 225, Rio de Janeiro RJ Brazil, Tel: /Fax: ABSTRACT Air transportation of cargo and passengers in Brazil has shown explosive growth rates. In 2007, in relation to 2006, demand for passengers grew approximately 12%, with companies increasing their offers of seats by 16.3%. With the trend of the Brazilian economy towards stabilization and the relative increase in the purchasing power of the population in general, combined with the increasing participation of the low cost/low fare companies, air transportation has become available to large sectors of the population. The increasing utilization of the hub-and-spoe configuration by the air companies, portrays the system s weaness. This wor will mae an application of the single and multiple assignment p-hub location problems in the Brazilian environment, taing into account cargo and passengers issues, through the concept of WLU (Wor Load Unit). Flow data concerning each airport, published by the National Agency of Civil Aviation, in 2006, will be used. KEYWORDS. Hub-and-spoe. Location. Mathematical programming. AL (Application in Logistics and Transportation) XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1099

2 1. Introduction Economic expansion in many countries around the world (mainly in those called emergents) and the spread of the globalization process has brought significant consequences for the air transport industry. Another fact that plays an important role is the entrance of the LCC (Low Cost Carriers) in the maret. These carriers have pushed the competition among themselves, and with other modes of transportation, in particular the road transportation. This type of carrier operates with a modern and standardized fleet, maing possible an efficient cost of operation and high rates of productivity. These carriers configure their networs in a point-to-point model, focusing their operations in the secondary airports and offering a nofrill service. Such policies reduce considerably the airfares and mae the air transportation service available to larger parts of the population. At the same time, some countries have been facing a serious lac of investment in infrastructure, with serious consequences to the users. In Brazil, two recent accidents, claiming the lives of more than 300 people within a year, have exposed this weaness. Given the highly complex management of all the logistics activities involved, it is a big challenge to identify the optimal investments so as to achieve a sustainable development. On the other hand, to survive in a competitive environment, the air carriers need to rethin their strategies. One of the strategies that has been presenting interesting results is the hub-andspoe model. This model tries to optimize air services and to allow the carriers to obtain good rates of cost reduction. In this case, some major airports (hubs) concentrate the flows and are fed by some minor airports, which are called spoes. This configuration maes possible gains due to economies of scale along the lins between hubs - and by the more intensive use of larger aircraft. Other associated characteristics are the increase in the frequency of flights and the decrease of the airfares. The planning management of all tass involved is not simple. The definition of the number of aircraft to serve a set of cities, the frequency of flights, the route planning, all of the demand forecasts and the management of all costs involved are difficult tass. In most of the cases, the airport infrastructure is provided by the public agencies. This infrastructure includes passenger and freight terminals, road, rail and subway access, number of runways and all the necessary technology to handle the air space control. This paper explores the expected growth rates in passenger and freight air transportation, describing the hub-and-spoe model, its main characteristics and advantages, and maes an application of a hub location model in the Brazilian maret of passenger and freight, through the concept of WLU (Wor Load Unit). The next section will provide some bacground about the passenger and freight air transportation. Section 3 will describe the mathematical model to be applied. Section 4 will analyze the results attained, while Section 5 setches some conclusions. 2. Literature Review 2.1 The Air Passenger and Freight Transport Nowadays, the air carriers around the world have been transporting more than 1.6 billion of passengers and 30 million of tons of freight per year. It is expected that the total length flown over the next 20 years will increase three times and the number of planes in operation will increase two times in the same period. The Chinese maret has been experiencing growing rates between 8 and 10% per year. A similar forecast for the United Kingdom maret identifies growing rates in the passenger maret by three times, turning from 180 million passengers transported per year to 300 million in the next 30 years (Whitelegg and Cambridge 2004). According to these authors: two ey industry statistics used to measure aviation activity, that are: Available Seat Kilometers (ASK) and Revenue Passenger Kilometers (RPK) and these are projected to increase by 2.5 times over the next 20 years from 3 trillion in 1999 to nearly 8 trillion, with a small increase in the passenger load factor (from per cent). By 2022, the total number of aircraft will nearly double and it will include a larger number of smaller, singleaisle planes used on short haul routes (Boeing, 2003). Table 1 illustrates this trend. XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1100

3 Table 1: Key Air Travel Statiscs (Airbus, 2003) - Whitelegg and Cambridge 2004 Passenger Aircraft Only / 2002 % Growth World ASKs (billion) 4,514 7,076 11, World RPKs (billion) 3,166 5,100 8, Average Flight Distance (Km) 1,437 1,414 1, Number of Aircraft 10,789 14,815 20, Number of Departures (000) 15,865 23,464 31, Seats per Departure Both segments of air passenger and air freight transport have been showing increasing rates and so is the buying power index of the population. As noticed by Lindsay (2006): Over the past 30 years, global GDP has risen 154%, and the value of world trade has grown 355%. But the value of air cargo has climbed an astonishing 1,395%. Today, 40% of the total economic value of all goods produced in the world barely comprising 1% of their total weight are shipped by air (and that goes for more than 50% of total U.S. exports, which are valued at $554 billion). All the expansion in air cargo industry has a strong relation with the environment in worldwide trade. Influenced by the import/ export flows among countries and regions, the air cargo has worldwide growth at about twice the rate of worldwide gross domestic product (GDP) growth. According to Boeing World Aircargo Forecast ( ), world airborne cargo will grow by 6,4% per year for the next 20 years. Most of this growth will occur in international marets, which will exceed 86% of total revenue ton ilometer by the year The average annual growth in freight-ton ilometers on international scheduled services during the last decade was 7,9%, (Zhang, 2003). Boeing s forecasts (2004) for the next 20 years estimates the freighter fleet to double, from 1766 to 3456 aircrafts (Gardiner et al., 2005). Increasing growth rates in air freight are supported by the emergence of globally integrated, Just in Time (JIT) production and distribution systems and the emergence of e-commerce and e- business, Zhang et al. (2004). According to these authors, companies have been trying to reduce inventories and cut down the time they tae to move products to the maret, while product life spans are also shortening.. These companies have been focusing on virtual warehousing, eeping goods in transit as a substitute for holding goods in storage. The logistics process involved must be in accordance with all the business strategic requirements, to eep high level of services. Geography of freighter aircraft services is dominated by the Pacific basin, and the regional dominance of freighter aircraft services in particular reflects the higher importance of the Pacific basin within global air freight flows (Bowen, 2004). This author claims that in the past few decades, the air freight traffic has grown faster than passenger traffic, mainly supported by the fact that the production of goods as diverse as tennis shoes and semiconductor chips has become dependent upon air freight services that lin globally dispersed supply chains. One important issue supporting the increasing rates for the air cargo flows is its adoption by a growing number of manufacturers in supply chains that place a premium on the speed and reliability of transportation. The same authors assert that, in the past, virtually all freighter aircraft were converted aircrafts, but a growing number of freighter aircrafts are assembled new, because new aircrafts are more fuel efficient and more reliable. The same authors define three principal types of carriers in freight transportation: heavy freight airlines, combination carriers and integrators. The former emphasize the transportation from airport to airport, the second focus on transportation including passenger and cargo traffic and the latter synthesize the air and ground transportation functions. The largest integrators in the world are: FedEx, UPS, TNT and DHL. There exists a trend that the proportion of cargo carried in the bellyholds will fall due to the inherent limitations with bellyhold cargo, although about 60% of airfreight is still carried in the bellyholds of passenger planes. The three most important XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1101

4 airports in the world in terms of operation of freight in 2000 were: Memphis, Hong-Kong and Los Angeles. According to Lee (2003): The demand for airfreight in the Asia-Pacific region has continued to grow steadily, and the region is forecast to account for more than 50% of world demand by Multinational enterprises and many other companies are expanding global sourcing of raw materials equipment and finished goods, in conjunction with global manufacturing and mareting. This rapid trend of globalization has increased the international material exchange, which in turn has enhanced the strategic importance of international logistics. 2.2 The Hub-and-Spoe Model With the increasing level of competitiveness observed in international marets, one successful strategy is the hub-and-spoe model. O Kelly (1998) classifies hubs as being special nodes of a networ, located in order to facilitate the linages among these nodes. The hubs are defined to be geographical points, located in a strategic manner so as to have the transportation costs minimized. Ayin (1995) remembers that the scale economies attained by the increase in the flow volume between hubs are one of the main advantages of this networ configuration. O Kelly and Bryan (1998) divide the hub-and-spoe configuration in two ways: the first one, called single allocation, the spoe nodes are allowed to be allocated to only one hub and in the second one they are allowed to be allocated to more than one hub. In both cases, hubs are completely interconnected. Huston and Buttler (2001) suggest that the decision of locating a set of hubs may influence the economic activity associated with the operation of a hub. They note that the operation of an airport hub can be a great competitive resource to low density traffic routes. They mention that the decision of locating a hub is based upon geographical and demographical characteristics of a region. According to these authors, government authorities have been showing an increasing interest in the development of hubs. Martin and Roman (2003) have studied the viability of a hub-and-spoe networ between South America and Europe. According to these authors, regarding passengers, some issues are related to the increase in the total travel time, including the connection time at a hub, extra operations of landing and taing-offs, and extra distance traveled in lins among spoe nodes. But most of the time, these are offset by the decrease in flight delays and the increase in the frequency of flights. This configuration increases the accessibility of cities and regions, and creates new opportunities in the job maret. In Europe, according to Cento et al. (2005): The development of the hub-and-spoe networ started quite some time ago in the long history of European aviation. Before liberalization, the Hub-and-Spoe networ in Europe has developed out of the former national flag carriers and too advantage of operating in a regulated industry: bilateral agreements, protected marets, and administered prices. Indeed, the former bilateral regime of air service agreements has already led to the development of hubs. Its main characteristic remains in the networ layout and topology optimization. It allows to decrease the number of all pairs of lins, n(n-1)/2, in an undirected graph, to a number of lins relatively small upon the use of hubs, as shown in the following example. In Fig. 1.a, the number of lins to connect all pairs of cities is 36. With the hub-and-spoe configuration, this number decreases to 9 arising a simpler layout and topology as in Fig. 1.b. (O Kelly and Bryan 1998). XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1102

5 a) b) F G H B E A D C Figure 1: Networ completely interconnected (1.a) and networ configured in hub-andspoe model (O Kelly and Bryan 1999 adapted) 3. The Model Application In this section, two different models will be applied: the multiple and the single assignment p-hub location problem. The former one allows a spoe point to be allocated to more than one hub and the latter allows a spoe point to be allocated to only one hub. In both cases, the hubs are fully interconnected. The application to be made in this paper locates 3 hubs for both types of assignment. The networ studied contains 25 nodes, some of the most important Brazilian airports (regarding passenger and freight movements). The database utilized here is concerned with the domestic transportation among these airports in 2006 and were published by the National Agency of Civil Aviation (ANAC). The Table 2 shows the list of airports in the study and their respective IATA codes. Table 2: List of Airports in the Study City - State Code City - State Code Rio Branco AC RBR Recife PE REC Maceio AL MCZ Curitiba PA CWB Manaus AM MAO Londrina PA LDB Salvador BA SSA Rio de Janeiro RJ GIG Fortaleza CE FOR Natal RN NAT Brasilia DF BSB Porto Velho RO PVH Goiania GO GYN Boa Vista RR BVB Sao Luiz MA SLZ Porto Alegre RS POA Belo Horizonte MG CNF Florianopolis SC FLN Uberlandia MG UDI Aracaju SE AJU Campo Grande MS CGR Guarulhos SP GRU Belem PA BEL Joao Pessoa - PA JPA Campinas SP VCP The flow data utilized taes into account the interactions for passenger and freight combined, through the concept of Wor Load Unit (WLU). According to Graham (2001), since most airports handle both passengers and freight, this suggests the use of an output measure which combines the two, such as the WLU (Wor Load Unit). The WLU originated from the airline industry and uses weight criteria for combining these two types of traffic: one WLU is equivalent to one passenger or 100 g of freight. I XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1103

6 In some Brazilian cities there exist more than one important airport operating within the metropolitan area. This is the case of Sao Paulo (which has the airports of Guarulhos GRU and Congonhas CCG), Rio de Janeiro (Galeao GIG and Santos Dumont SDU) and Belo Horizonte (Pampulha - PLU and Confins CNF). These airports (the ones in the same region/city) are very close to each other, meaning that a flight between them would not be reasonable. Then, in order to catch the total movements for a same region/city, the best airport in terms of infrastructure was ept and the other one was discarded. The methodology used to do that was to eep the location of the biggest/main airport and add the movements (in WLU) for the second biggest/main airport. For instance, GRU was considered the biggest/main airport for its region. Then, the data location of GRU (longitude and latitude) was ept with the addition of the total movements of the other airport in the region (CCG, in this case). Therefore, GRU has its original data for location and its own WLU movement plus the CCG WLU movement. The same methodology was applied for GIG and CNF. The first model is nown as the multiple assignment p-hub location problem, in which the spoe points may be allocated to more than one hub. This model was originally proposed by Campbell (1995). In this case, the number p of hubs to be located is nown and there are no capacity constraints and fixed costs. Min s.a.: Wij Ci Cm + i j m Y = m m Y p ( + α C ) X (1) mj ijm X ijm = 1, i, j (3) X Y ijm 0, i, j, (4) X Y ijm m 0, i, j, m (5) {0,1}, (2) (6) The objective function (1) sees the minimization of the total costs involved in the transportation between every origin and destination pair. The set of constraints (2) establishes that p hubs must be opened. The set of constraints (3) imposes that all the flow transported for every origin-destination pair is made using hubs and m. Constraints (4) and (5) impose that every flow moved are made through hub locations. The decision variables X determine the allocation of the spoe nodes to the hubs. The decision variable Y indicates the location of hubs. For the single assignment p-hub location problem (Sorin-Kapov et al. 1995), every spoe node must be allocated to only one hub (denoted by the set 9 of constraints). The objective function is the same as in the multiple assignment allocation model. The set of constraints (10) indicate that a spoe node can be allocated to a hub only if this point is a hub. Constraints (11) and (12) impose that a valid path only exists if an origin and a destination node are allocated to hubs. Min s.a.: Wij Ci Cm + i j m Z = p ( + α C ) X (7) mj ijm ijm (8) XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1104

7 Z i = 1, i (9) Z Z 0, i (10) m Y i X ijm Z i = 0, i, j, (11) X ijm Z jm 0, i, j, m (12) {0,1}, (13) Where: X ijm : Flow fraction transported between origin i and destination j, through hubs located in nodes and m; Y = 1, if a location is a hub; 0, otherwise; W : Flow originated at location i and destinated to location j; ij C ij : Unit cost from i to j (denoted by the distance); p : The number of hubs to be opened; α : The interhub discount factor ( 0 α 1). Z i : 1 if a spoe node in i is allocated to a hub in ; 0 otherwise. 4. Results The results obtained for the application of both models (multiple and single assignment) aiming the location of 3 hubs (p=3) have pointed out Salvador-BA, Brasilia-DF and Guarulhos- SP to act as hubs. To reflect the economies of scale achieved in the linages between hubs, a value of 0.6 was used for alpha (discount factor). The optimal solution was achieved using the optimization software AIMMS version 3.8. Table 3 shows some information about the results. Table 3: Summary of Results Model Number of Constraints Number of Variables Objective Function Multiple Assignment 31, ,651 (25 integers) 46,354,481,220 Single Assignment 31, ,276 (650 integers) 47,431,560,480 It is possible to notice that the objective function for the single assignment is 2.32% greater than the one for the multiple assignment. This is because in the multiple allocation model, the best path to be made between an origin and a destination is the shortest one. As long as the model allows a spoe node to be allocated to more than one hub, this spoe node is able to chose the lowest cost path to achieve the destination. In the single assignment allocation model, it is not necessarily allowed. Figures 2 and 3 show the allocation patterns for the multiple and single assignment p-hub location problem, respectively. The software TRANSCAD (version 4.5) was used to build the corresponding maps. For airports location, data from longitude and latitude found in ROTAER 1999 (Brazil Auxiliary Manual for Air Routes) were used and the distance matrix amongst every nodes was obtained using TRANSCAD software. XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1105

8 Figure 2: The Allocation Pattern for Multiple Assignment Allocation Model For the multiple assignment, it is possible to notice that some nodes were allocated to more than one hub which is the case of RBR, CGR, LDB, UDI and CNF (allocated to BSB and GRU) and BVB, BEL and SLZ (allocated to SSA and BSB). The other points were allocated just to one hub. It is nown from the literature that this type of model is better suited for passengers. For the single assignment allocation model, which is better suited for freight, it is interesting to note that in the interhub linages the flows are denser than in the multiple assignment. In this model, the linage between SSA and BSB is 38.8% denser than in the multiple assignment. For SSA and GRU, this value is 8.2% and for BSB and GRU it is 10.1% greater. It is easy to notice the bundling of flows is greater in the single assignment allocation model. The most congested hub lin was SSA-GRU. The second one was BSB-GRU and the third one was SSA-BSB. In the multiple assignment allocation model, the volume of flow transported in the lin SSA-GRU was 4.26 times greater than the volume of flow transported in the less congested lin SSA-BSB. For the single assignment allocation model, the same comparison was made and this value was 3.32 times greater (in regard to the most and less congested lins). XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1106

9 Figure 3: The Allocation Pattern for Single Assignment Allocation Model Another interesting issue to notice is the inflow and outflow from and to GIG. The lin between GIG-GRU (both directions) is 1.68 times greater than the most congested lin for single allocation. It reflects the importance of the city of Rio de Janeiro city for the national economy scenario as a huge pole for attracting and generating traffic for passengers and freight. 5. Conclusions In this paper an application of the multiple and single assignment p-hub location problem was made in the Brazilian air transportation environment. Both models aimed to locate 3 hubs in a networ containing 25 nodes, with some of the most important Brazilian airports. The concept of WLU (Wor Load Unit) was used in order to catch the movements for passenger and freight combined. Both applications have pointed out the same airports to act as hubs: Guarulhos-SP, Brasilia-DF and Salvador-BA. An interesting issue about the allocation patterns is that, in the single assignment the bundling of flows between hubs is greater than in the multiple assignment. Regarding the general costs, the multiple assignment has achieved a better solution. 6. Acnowledgments The first author would lie to than the tuition provided by CAPES in its doctorate sandwich program and also professor Morton O`Kelly (Department of Geography - The Ohio State University) for the research advisement and the second author would express gratitude to CNPq for partial support to this research. 7. References XLI SBPO Pesquisa Operacional na Gestão do Conhecimento Pág. 1107

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