- Email: [email protected]
Hub location in air cargo transportation: A case study
Journal of Air Transport Management 27 (2013) 1e4
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Hub location in air cargo transportation: A case study Hakan Oktal*, Asuman Ozger _ Avionics Department, Faculty of Aerospace Sciences, Anadolu University, Ikieylul Kampusu, 26470 Eskisehir, Turkey
a b s t r a c t Keywords: Air cargo transportation Hub and spoke networks Multiple hub location
This paper models constrained choices when establishing cargo hub and spoke networks. A mixed integer linear programming model is developed introducing additional constraints to the traditional model of uncapacitated multiple allocation hub location problem and empirically tested. The tests suggest that aircraft range and trip cost, runway availability and cargo traffic continuity of an airport are major factors affecting hub locations along with the costs of airline movements. 2012 Elsevier Ltd. All rights reserved.
1. Introduction
subject to
Hub systems require different network designs based upon their particular characteristics. Here we introduce the sectorial characteristics of air transportation into the traditional uncapacitated multiple allocation hub location problem (UMAHLP) and develop a new mixed integer linear programming model. In most of the studies on air transportation applications of hub location problem (HLP), little attention has been given to the value and the components of cost; and in particular direct operating cost (DOC), total operating cost (TOC), fixed and variable costs for aircraft are generally not considered in any detail or with consistency (e.g. Lin et al., 2003; Yang, 2009). Here we explore the effects of the new constraints and the sectorial characteristics of air transportation on HLP. These constraints can also be used in different fields such as road transportation, computer networks etc. The model developed, by including the new constraints, is tested using two data sets.
Our analysis involves modified Ebery et al.’s (2000) multiple allocation version of the capacitated hub location problem (the “EA Model”) by including additional constraints (the “New Model”). In both models, the capacity constraint is removed and the objective function 1 is used under the constraints 2e11 for the New Model and constraints 2e6, 10 and 11 for the EA Model.
min
i˛N
k˛N
CTik Zik þ
X
Zik ¼
X
Wij
XX k˛N l˛N
aCTkl Ykli þ
XX
# CTlj Ylji
þ
X
l˛N j˛N
Fk Hk
k
(1) * Corresponding author. Tel.: þ90 5322853572; fax: þ90 2223221619. E-mail address: [email protected] (H. Oktal). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jairtraman.2012.10.009
(2)
j
k˛N
Xiji ¼ Wij
ci; j˛N
(3)
l˛N
X
i Ykl þ
X
l˛N
i Xkj
j˛N
X
i Ylk Zik ¼ 0
ci; k˛N
(4)
l˛N
Zik Oi $Hk
ci; k˛N
(5)
Xlji Wij $Hl
ci; j; l˛N
(6)
dik $Hk S
ci; k
T$Hk Waðm;kÞ
2. The model
" X X
X
Hk RAk Hk ˛f0; 1g
(7) cm; k
ck
(9)
ck
i ; Zik 0 Xlji ; Ykl
(8)
(10) ci; j; k; l˛N
(11)
where; N is the set of nodes, Wij 0 is the flow from the origin i to the destination j for all, CTij is the unit trip cost from i to j, RAk is the appropriateness of node k to be a hub, Fk is the fixed hub cost of node k, S is the maximum link distance, T is the minimum required traffic flow of node k, Wa(m,k) is the flow of node k in time period m and a is the interhub discount factor. The decision variables used are given likewise: Hk ¼ 1 if node k is a hub and
2
H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
Table 1 The annual cargo traffics of Turkish airlines in 2006.
Table 3 UMAHLP analysis results for F27-500.
Airport name
IATA codes
Annual cargo traffic (Ton)
Analysis
Istanbul Ataturk Izmir Adnan Menderes Ankara Esenboga Adana Antalya Trabzon Dalaman Gaziantep Diyarbakir Istanbul Sabiha Gokcen Milas-Bodrum Kayseri Malatya Erhac Erzurum Van Ferit Melen Denizli Çardak Kars Elazig
IST ADB ESB ADA AYT TZX DLM GZT DIY SAW BJV ASR MLX ERZ VAN DNZ KSY EZS
31.155 12.241 8.802 5.096 3.545 1.402 439 359 327 321 265 225 223 182 148 52 47 28
1
i is flow from 0 otherwise, Zik is flow from origin i to hub k, Ykl i origin i and routed via hubs k and l and Xlj is flow from node i to node j via hub l. The objective function that minimizes the costs includes the trip and fixed hub costs. Constraints 2e4 represent the flows originating from node i. Constraint 5 prevents the directing of flows to a non-hub node. Constraint 6 blocks the flows between the nonhub nodes. Constraint 7 keeps the distances between nodes and hubs smaller than the maximum link distance. Constraint 8 assures that a node will not be designated as a hub if the traffic flow is less than a certain amount T. Constraint 9 guarantees that a node will not be designated as a hub if its capability does not meet the predefined requirements. Constraint 10 is an integer constraint and constraint 11 ensures that the decision variables related to the traffic flows will be positive. The new constraints 7e9 are included to the traditional model.
3. Data Data from the air cargo market in Turkey are used to test the model. Because airlines refrain from sharing their data, especially relating to the costs and traffic flows, for commercial reasons, trip costs, fixed hub costs (FHC) and cargo traffic statistics between airports could not be obtained from the same carrier. The data used, that we call “Turkish Air Cargo” (TAC) contains the air cargo flows, the flight distances between airports and unit trip costs and was provided by two cargo carriers. Since the transportation cost decreases with trip distance in air transportation, the trip cost is used instead of the transportation cost differentially with the similar data sets.
2 3 4 5 6 7 8 9 10
FHC (x$1000) 50 50 100 100 200 200 500 500 1000 1000
Model
Cost (x$M)
Hubs
EA Model
26.49
New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
44.54 26.80 44.69 27.38 44.99 28.72 45.89 30.24 47.06
ADA, ADB, AYT, DIY, ESB, GZT, IST, TZX ADA, ESB, TZX ADA, ADB, AYT, ESB, IST, TZX ADA, ESB, TZX ADA, ADB, AYT, ESB, IST ADA, ESB, TZX ADA, ADB, ESB, IST ADA, ESB, TZX ESB, IST ADA, ESB
The model is tested using the cargo statistics of Turkish Airlines, the largest air passenger and cargo carrier in Turkey. Its domestic air cargo for 2006 is given in Table 1. Although Turkish Airlines flew to 32 airports, air cargo was only handled at 18, with 96% of the traffic involving six located in highly industrialized cities; basically regional hubs. Table 2, shows the standard breakdown of TOC of an air carrier; we subsequently take TOC as the “trip cost”. IOC and the FOC are taken as constant for each trip because they are assumed independent of distance and flow. The most important element in the VOC is the fuel cost that depends on flight phase, aircraft speed and weight, flight level, meteorological conditions, and flight hours. Navigation fees change according to aircraft weight and flight distance, while airport fees depend on aircraft weight and airport category. The unit trip cost ($/ton) is found by dividing the trip cost by aircraft payload. In the calculation of unit trip costs for an A300-B4 and an F27-500, data for 2006 was obtained from the MNG Air Cargo Company that operates nine cargo aircraft. FHC consist of facility ownership/rental costs, equipment costs, and ground staff costs that are affected by the aircraft fleet, air cargo, salaries and the operational policies of airline and the category of hub airport. The values of FHC are increased gradually. The trip costs for F27-500s are assumed to vary between $2300 and $11,500 according to flight hours, and between $5200 and $19,000 for A300-B4s; the wide body A300-B4, the turboprop aircraft, F27-500 were the most widely used cargo aircraft in Turkey in 2006. The flight distances, times and fuel consumption between airports are calculated using the Graflight program which is also used by many airlines in their cost analyses. 4. Results The constraint of “maximum link distance (Cons.7)” in the New Model for the F27-500 and the A300-B4 at maximum take-off Table 4 UMAHLP analysis results for A300-B4.
Table 2 The elements of operating costs. Total operating cost (TOC) Indirect operating cost (IOC)
Facility Staff Marketing Administration
Direct operating cost (DOC) Fixed operating cost (FOC)
Variable operating cost (VOC)
Aircraft lease/owning Flight crew Maintenance Insurance Handling, dispatch fees
Fuel and oil Navigation fees Airport fees
Analysis
FHC (x$1000)
Model
Cost (x$M)
Hubs
1 2 3 4 5 6 7 8 9 10
50 50 100 100 200 200 500 500 1000 1000
EA Model New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
6.82 6.95 7.06 7.10 7.40 7.40 7.94 7.94 8.44 8.44
ADA, ADB, AYT, ESB, IST ADB, ESB, IST ADA, ADB, ESB, IST ADB, ESB, IST ADB, ESB, IST ADB, ESB, IST IST IST IST IST
H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
3
Fig. 1. Hub locations and allocations for F27-500.
weight (MTOW) are 700 nm and 2900 nm (Fokker, 1986; Airbus, 1991) while the maximum flight distance between Turkish airports is about 900 nm. An airport which does not have regular cargo traffic because of seasonal variations in demand may be chosen as a hub, but this can increase personnel and equipment costs. Therefore, Constraint 8 controls for the continuity of cargo traffic when assign hubs. “Appropriateness of a node to be a hub” (Constraint 9) is taken as the runway availability at an airport; take-offs and landings depend on runway availability in terms of length, width and strength. The constructing of a new runway or increasing the capacity of an existing one necessitates sizable investments. Moreover, airport designated as hub should have enough runway available to receive large cargo aircraft with high traffic densities. The requirements for runway length, width and strength are taken from the aircraft’s flight manuals, the Aerodrome Design Manual of the International Civil Aviation Organization and the Aeronautical Information Publication of Turkey. The runway availability of an airport is evaluated by comparing the requirements for A300-B4 and F27-500 under existing runway conditions. The runway length is determined by taking into account the maximum take-off/ landing weights, air temperature, elevation, runway slope and wind conditions. Eight airports in the Turkish network do not meet the requirements for A300-B4s while all airports do for the F27500. In the New Model, if an airport does not meet runway requirements of the related aircraft, RAk is taken as zero and one otherwise. To reflect the influence of aircraft type and new constraints on costs and hub locations, rather than examining the efficiency in using a single aircraft type, we assume: The cargo is transported by all cargo A300-B4s or F27-500s. Runway slope and wind conditions are ignored. Each aircraft type considered performs a minimum of 15 landings per month at an airport with a maximum payload to meet the continuity constraint.1 FHC is the same for each node.
1 The minimum cargo traffic per month of 90 tons for F27-500s and 660 tons for A300-B4s at an airport to meet the cargo traffic continuity requirement finds 12 airports for F27-500s and 15 airports for A300-B4s have no regular traffic.
The cost discount factor between hubs (a) is taken as 0.9 following Ebery et al. (2000) and Ernst and Krishnamoorthy (1998). The mixed integer linear programming model is coded by GAMS and solved by CPLEX solver. The results for the EA Model and the New Model change according to the value of FHC used are seen in Tables 3 and 4. We see that in comparing costs, number of assigned hubs and their locations, there are changes for the same FHC especially for the F27-500. An increase in the FHC naturally decreases the number of assigned hub. There are also considerable cost differences relating to the range and unit trip costs of aircraft. Adana and Ankara Esenboga airports located in the south east and the middle of Turkey are designated as the hubs for the F27-500 while a single hub, Istanbul Ataturk _ Airport, is a hub for A300-B4s. Although Istanbul Ataturk and Izmir Adnan Menderes airports are the busiest for both air passenger and cargo traffics, they have not been chosen as hubs because of the limited range of F27-500s. Within the network of airports that have the non-homogeneous cargo traffic, the use of one type aircraft with a low payload and short range, such as F27-500, considerably increases the cost in HLP. The costs of using wide body aircraft with higher payload and longer range is not affected by these limitations. The selection of Istanbul Ataturk Airport as a hub by Turkish air cargo carriers operating generally wide-body aircraft confirms our results. Istanbul Ataturk, the busiest airport in Turkey, handles half of domestic air cargo traffic. One reasons it is a hub is that this has the bi-directional cargo traffic flows with all airports in the network. Hub locations and allocations based on the last analysis of both tables for F27-500 and A300-B4 are seen in Figs. 1 and 2; hub airports are circled. The performance of the model is also tested using data from Tan and Kara (2007) and Alumur et al. (2009). The data set called the “Turkish Network” contains data on 81 nodes for cargo delivery services, and includes travel distances, time, flow, fixed link costs between the 81 cities and fixed hub costs for the node cities. We assume: The aircraft range is 700 nm (1300 km). If there is an airport in a city, RAk is set as one and zero otherwise. The value of cargo continuity is 837,000 tones per city. This value which signifies the annual average traffic per city is calculated from the “Turkish Network” data set. FHC is the same for each node.
4
H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
Fig. 2. Hub locations and allocations for A300-B4.
Table 5 UMAHLP results for network data set. Analysis
FHC (x$1000)
Model
Cost (x$M)
Hubs
Execution time (seconds)
1 2 3 4 5 6 7 8 9 10
50 50 100 100 200 200 500 500 1000 1000
EA Model New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
16.93 54.19 17.24 54.60 17.66 55.34 17.96 56.98 18.46 59.00
Adana, Ankara, Diyarbakir, Gaziantep, Istanbul, Izmir, Konya Adana, Icel, Kayseri, Konya, Kahramanmaras, Ordu, Samsun, Sivas, Tokat Adana, Ankara, Diyarabakir, Gaziantep, Istanbul, Izmir Adana, Kayseri, Konya, Kahramanmaras, Ordu, Samsun, Sivas, Tokat Gaziantep, Istanbul Adana, Kayseri, Konya, Ordu, Samsun, Sivas, Tokat Istanbul Adana, Konya, Ordu, Samsun, Tokat Istanbul Adana, Konya, Ordu, Samsun
14.087 16.022 13.042 12.808 13.541 12.948 12.231 13.837 13.214 12.808
As can be seen in Table 5, both models are solved in a few seconds with the benchmark data set of nodes. The analyses of the two data sets reveal that the new constraints included in the EA Model change the costs, the optimal number of hubs and their locations. These outcomes reveal that the hub locations and allocations in HSN especially in transportation systems depend on not only traffic flows, unit trip costs and distances but also the characteristics of related sector and vehicle type.
5. Conclusion Network design has a strategic importance for the companies. In air cargo, the selection of aircraft type and fleet planning are the central decisions that can affect the success of a company. These decisions are often linked to expensive investments. For optimality, network design and fleet planning need to be treated and updated jointly. Sector features and aircraft characteristics should be taken into account as the significant factors affecting the hub selection process especially when this requires major investment and incurs operational costs.
Acknowledgments The authors would like to thank Professor Kenneth Button and the anonymous referees for their valuable contribution to this paper. References Airbus, 1991. A300 Airplane Flight Manual. Airbus Industrie, Tolouse. Alumur, S., Kara, B.Y., Karasan, O.E., 2009. The design of single allocation incomplete hub networks. Transportation Research B 43, 936e951. Ebery, J., Krishnamoorthy, M., Ernst, A., Boland, N., 2000. The capacitated multiple allocation hub location problem: formulations and algorithms. European Journal of Operational Research 120, 614e631. Ernst, A.T., Krishnamoorthy, M., 1998. Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research 104, 100e112. Fokker, 1986. Fokker F27 Airplane Flight Manual (Chapter 1), vol. 1. Fokker Services B.V, Hoofddorp. Lin, C.C., Lin, Y.J., Lin, D.Y., 2003. The economic effects of center-to-center directs on hub-and-spoke networks for air express common carriers. Journal of Air Transport Management 9, 255e265. Tan, P.Z., Kara, B.Y., 2007. A hub covering model for cargo delivery systems. Networks 49, 28e39. Yang, T.H., 2009. Stochastic air freight hub location and flight routes planning. Applied Mathematical Modeling 33, 4424e4430.
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Hub location in air cargo transportation: A case study Hakan Oktal*, Asuman Ozger _ Avionics Department, Faculty of Aerospace Sciences, Anadolu University, Ikieylul Kampusu, 26470 Eskisehir, Turkey
a b s t r a c t Keywords: Air cargo transportation Hub and spoke networks Multiple hub location
This paper models constrained choices when establishing cargo hub and spoke networks. A mixed integer linear programming model is developed introducing additional constraints to the traditional model of uncapacitated multiple allocation hub location problem and empirically tested. The tests suggest that aircraft range and trip cost, runway availability and cargo traffic continuity of an airport are major factors affecting hub locations along with the costs of airline movements. 2012 Elsevier Ltd. All rights reserved.
1. Introduction
subject to
Hub systems require different network designs based upon their particular characteristics. Here we introduce the sectorial characteristics of air transportation into the traditional uncapacitated multiple allocation hub location problem (UMAHLP) and develop a new mixed integer linear programming model. In most of the studies on air transportation applications of hub location problem (HLP), little attention has been given to the value and the components of cost; and in particular direct operating cost (DOC), total operating cost (TOC), fixed and variable costs for aircraft are generally not considered in any detail or with consistency (e.g. Lin et al., 2003; Yang, 2009). Here we explore the effects of the new constraints and the sectorial characteristics of air transportation on HLP. These constraints can also be used in different fields such as road transportation, computer networks etc. The model developed, by including the new constraints, is tested using two data sets.
Our analysis involves modified Ebery et al.’s (2000) multiple allocation version of the capacitated hub location problem (the “EA Model”) by including additional constraints (the “New Model”). In both models, the capacity constraint is removed and the objective function 1 is used under the constraints 2e11 for the New Model and constraints 2e6, 10 and 11 for the EA Model.
min
i˛N
k˛N
CTik Zik þ
X
Zik ¼
X
Wij
XX k˛N l˛N
aCTkl Ykli þ
XX
# CTlj Ylji
þ
X
l˛N j˛N
Fk Hk
k
(1) * Corresponding author. Tel.: þ90 5322853572; fax: þ90 2223221619. E-mail address: [email protected] (H. Oktal). 0969-6997/$ e see front matter 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jairtraman.2012.10.009
(2)
j
k˛N
Xiji ¼ Wij
ci; j˛N
(3)
l˛N
X
i Ykl þ
X
l˛N
i Xkj
j˛N
X
i Ylk Zik ¼ 0
ci; k˛N
(4)
l˛N
Zik Oi $Hk
ci; k˛N
(5)
Xlji Wij $Hl
ci; j; l˛N
(6)
dik $Hk S
ci; k
T$Hk Waðm;kÞ
2. The model
" X X
X
Hk RAk Hk ˛f0; 1g
(7) cm; k
ck
(9)
ck
i ; Zik 0 Xlji ; Ykl
(8)
(10) ci; j; k; l˛N
(11)
where; N is the set of nodes, Wij 0 is the flow from the origin i to the destination j for all, CTij is the unit trip cost from i to j, RAk is the appropriateness of node k to be a hub, Fk is the fixed hub cost of node k, S is the maximum link distance, T is the minimum required traffic flow of node k, Wa(m,k) is the flow of node k in time period m and a is the interhub discount factor. The decision variables used are given likewise: Hk ¼ 1 if node k is a hub and
2
H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
Table 1 The annual cargo traffics of Turkish airlines in 2006.
Table 3 UMAHLP analysis results for F27-500.
Airport name
IATA codes
Annual cargo traffic (Ton)
Analysis
Istanbul Ataturk Izmir Adnan Menderes Ankara Esenboga Adana Antalya Trabzon Dalaman Gaziantep Diyarbakir Istanbul Sabiha Gokcen Milas-Bodrum Kayseri Malatya Erhac Erzurum Van Ferit Melen Denizli Çardak Kars Elazig
IST ADB ESB ADA AYT TZX DLM GZT DIY SAW BJV ASR MLX ERZ VAN DNZ KSY EZS
31.155 12.241 8.802 5.096 3.545 1.402 439 359 327 321 265 225 223 182 148 52 47 28
1
i is flow from 0 otherwise, Zik is flow from origin i to hub k, Ykl i origin i and routed via hubs k and l and Xlj is flow from node i to node j via hub l. The objective function that minimizes the costs includes the trip and fixed hub costs. Constraints 2e4 represent the flows originating from node i. Constraint 5 prevents the directing of flows to a non-hub node. Constraint 6 blocks the flows between the nonhub nodes. Constraint 7 keeps the distances between nodes and hubs smaller than the maximum link distance. Constraint 8 assures that a node will not be designated as a hub if the traffic flow is less than a certain amount T. Constraint 9 guarantees that a node will not be designated as a hub if its capability does not meet the predefined requirements. Constraint 10 is an integer constraint and constraint 11 ensures that the decision variables related to the traffic flows will be positive. The new constraints 7e9 are included to the traditional model.
3. Data Data from the air cargo market in Turkey are used to test the model. Because airlines refrain from sharing their data, especially relating to the costs and traffic flows, for commercial reasons, trip costs, fixed hub costs (FHC) and cargo traffic statistics between airports could not be obtained from the same carrier. The data used, that we call “Turkish Air Cargo” (TAC) contains the air cargo flows, the flight distances between airports and unit trip costs and was provided by two cargo carriers. Since the transportation cost decreases with trip distance in air transportation, the trip cost is used instead of the transportation cost differentially with the similar data sets.
2 3 4 5 6 7 8 9 10
FHC (x$1000) 50 50 100 100 200 200 500 500 1000 1000
Model
Cost (x$M)
Hubs
EA Model
26.49
New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
44.54 26.80 44.69 27.38 44.99 28.72 45.89 30.24 47.06
ADA, ADB, AYT, DIY, ESB, GZT, IST, TZX ADA, ESB, TZX ADA, ADB, AYT, ESB, IST, TZX ADA, ESB, TZX ADA, ADB, AYT, ESB, IST ADA, ESB, TZX ADA, ADB, ESB, IST ADA, ESB, TZX ESB, IST ADA, ESB
The model is tested using the cargo statistics of Turkish Airlines, the largest air passenger and cargo carrier in Turkey. Its domestic air cargo for 2006 is given in Table 1. Although Turkish Airlines flew to 32 airports, air cargo was only handled at 18, with 96% of the traffic involving six located in highly industrialized cities; basically regional hubs. Table 2, shows the standard breakdown of TOC of an air carrier; we subsequently take TOC as the “trip cost”. IOC and the FOC are taken as constant for each trip because they are assumed independent of distance and flow. The most important element in the VOC is the fuel cost that depends on flight phase, aircraft speed and weight, flight level, meteorological conditions, and flight hours. Navigation fees change according to aircraft weight and flight distance, while airport fees depend on aircraft weight and airport category. The unit trip cost ($/ton) is found by dividing the trip cost by aircraft payload. In the calculation of unit trip costs for an A300-B4 and an F27-500, data for 2006 was obtained from the MNG Air Cargo Company that operates nine cargo aircraft. FHC consist of facility ownership/rental costs, equipment costs, and ground staff costs that are affected by the aircraft fleet, air cargo, salaries and the operational policies of airline and the category of hub airport. The values of FHC are increased gradually. The trip costs for F27-500s are assumed to vary between $2300 and $11,500 according to flight hours, and between $5200 and $19,000 for A300-B4s; the wide body A300-B4, the turboprop aircraft, F27-500 were the most widely used cargo aircraft in Turkey in 2006. The flight distances, times and fuel consumption between airports are calculated using the Graflight program which is also used by many airlines in their cost analyses. 4. Results The constraint of “maximum link distance (Cons.7)” in the New Model for the F27-500 and the A300-B4 at maximum take-off Table 4 UMAHLP analysis results for A300-B4.
Table 2 The elements of operating costs. Total operating cost (TOC) Indirect operating cost (IOC)
Facility Staff Marketing Administration
Direct operating cost (DOC) Fixed operating cost (FOC)
Variable operating cost (VOC)
Aircraft lease/owning Flight crew Maintenance Insurance Handling, dispatch fees
Fuel and oil Navigation fees Airport fees
Analysis
FHC (x$1000)
Model
Cost (x$M)
Hubs
1 2 3 4 5 6 7 8 9 10
50 50 100 100 200 200 500 500 1000 1000
EA Model New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
6.82 6.95 7.06 7.10 7.40 7.40 7.94 7.94 8.44 8.44
ADA, ADB, AYT, ESB, IST ADB, ESB, IST ADA, ADB, ESB, IST ADB, ESB, IST ADB, ESB, IST ADB, ESB, IST IST IST IST IST
H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
3
Fig. 1. Hub locations and allocations for F27-500.
weight (MTOW) are 700 nm and 2900 nm (Fokker, 1986; Airbus, 1991) while the maximum flight distance between Turkish airports is about 900 nm. An airport which does not have regular cargo traffic because of seasonal variations in demand may be chosen as a hub, but this can increase personnel and equipment costs. Therefore, Constraint 8 controls for the continuity of cargo traffic when assign hubs. “Appropriateness of a node to be a hub” (Constraint 9) is taken as the runway availability at an airport; take-offs and landings depend on runway availability in terms of length, width and strength. The constructing of a new runway or increasing the capacity of an existing one necessitates sizable investments. Moreover, airport designated as hub should have enough runway available to receive large cargo aircraft with high traffic densities. The requirements for runway length, width and strength are taken from the aircraft’s flight manuals, the Aerodrome Design Manual of the International Civil Aviation Organization and the Aeronautical Information Publication of Turkey. The runway availability of an airport is evaluated by comparing the requirements for A300-B4 and F27-500 under existing runway conditions. The runway length is determined by taking into account the maximum take-off/ landing weights, air temperature, elevation, runway slope and wind conditions. Eight airports in the Turkish network do not meet the requirements for A300-B4s while all airports do for the F27500. In the New Model, if an airport does not meet runway requirements of the related aircraft, RAk is taken as zero and one otherwise. To reflect the influence of aircraft type and new constraints on costs and hub locations, rather than examining the efficiency in using a single aircraft type, we assume: The cargo is transported by all cargo A300-B4s or F27-500s. Runway slope and wind conditions are ignored. Each aircraft type considered performs a minimum of 15 landings per month at an airport with a maximum payload to meet the continuity constraint.1 FHC is the same for each node.
1 The minimum cargo traffic per month of 90 tons for F27-500s and 660 tons for A300-B4s at an airport to meet the cargo traffic continuity requirement finds 12 airports for F27-500s and 15 airports for A300-B4s have no regular traffic.
The cost discount factor between hubs (a) is taken as 0.9 following Ebery et al. (2000) and Ernst and Krishnamoorthy (1998). The mixed integer linear programming model is coded by GAMS and solved by CPLEX solver. The results for the EA Model and the New Model change according to the value of FHC used are seen in Tables 3 and 4. We see that in comparing costs, number of assigned hubs and their locations, there are changes for the same FHC especially for the F27-500. An increase in the FHC naturally decreases the number of assigned hub. There are also considerable cost differences relating to the range and unit trip costs of aircraft. Adana and Ankara Esenboga airports located in the south east and the middle of Turkey are designated as the hubs for the F27-500 while a single hub, Istanbul Ataturk _ Airport, is a hub for A300-B4s. Although Istanbul Ataturk and Izmir Adnan Menderes airports are the busiest for both air passenger and cargo traffics, they have not been chosen as hubs because of the limited range of F27-500s. Within the network of airports that have the non-homogeneous cargo traffic, the use of one type aircraft with a low payload and short range, such as F27-500, considerably increases the cost in HLP. The costs of using wide body aircraft with higher payload and longer range is not affected by these limitations. The selection of Istanbul Ataturk Airport as a hub by Turkish air cargo carriers operating generally wide-body aircraft confirms our results. Istanbul Ataturk, the busiest airport in Turkey, handles half of domestic air cargo traffic. One reasons it is a hub is that this has the bi-directional cargo traffic flows with all airports in the network. Hub locations and allocations based on the last analysis of both tables for F27-500 and A300-B4 are seen in Figs. 1 and 2; hub airports are circled. The performance of the model is also tested using data from Tan and Kara (2007) and Alumur et al. (2009). The data set called the “Turkish Network” contains data on 81 nodes for cargo delivery services, and includes travel distances, time, flow, fixed link costs between the 81 cities and fixed hub costs for the node cities. We assume: The aircraft range is 700 nm (1300 km). If there is an airport in a city, RAk is set as one and zero otherwise. The value of cargo continuity is 837,000 tones per city. This value which signifies the annual average traffic per city is calculated from the “Turkish Network” data set. FHC is the same for each node.
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H. Oktal, A. Ozger / Journal of Air Transport Management 27 (2013) 1e4
Fig. 2. Hub locations and allocations for A300-B4.
Table 5 UMAHLP results for network data set. Analysis
FHC (x$1000)
Model
Cost (x$M)
Hubs
Execution time (seconds)
1 2 3 4 5 6 7 8 9 10
50 50 100 100 200 200 500 500 1000 1000
EA Model New Model EA Model New Model EA Model New Model EA Model New Model EA Model New Model
16.93 54.19 17.24 54.60 17.66 55.34 17.96 56.98 18.46 59.00
Adana, Ankara, Diyarbakir, Gaziantep, Istanbul, Izmir, Konya Adana, Icel, Kayseri, Konya, Kahramanmaras, Ordu, Samsun, Sivas, Tokat Adana, Ankara, Diyarabakir, Gaziantep, Istanbul, Izmir Adana, Kayseri, Konya, Kahramanmaras, Ordu, Samsun, Sivas, Tokat Gaziantep, Istanbul Adana, Kayseri, Konya, Ordu, Samsun, Sivas, Tokat Istanbul Adana, Konya, Ordu, Samsun, Tokat Istanbul Adana, Konya, Ordu, Samsun
14.087 16.022 13.042 12.808 13.541 12.948 12.231 13.837 13.214 12.808
As can be seen in Table 5, both models are solved in a few seconds with the benchmark data set of nodes. The analyses of the two data sets reveal that the new constraints included in the EA Model change the costs, the optimal number of hubs and their locations. These outcomes reveal that the hub locations and allocations in HSN especially in transportation systems depend on not only traffic flows, unit trip costs and distances but also the characteristics of related sector and vehicle type.
5. Conclusion Network design has a strategic importance for the companies. In air cargo, the selection of aircraft type and fleet planning are the central decisions that can affect the success of a company. These decisions are often linked to expensive investments. For optimality, network design and fleet planning need to be treated and updated jointly. Sector features and aircraft characteristics should be taken into account as the significant factors affecting the hub selection process especially when this requires major investment and incurs operational costs.
Acknowledgments The authors would like to thank Professor Kenneth Button and the anonymous referees for their valuable contribution to this paper. References Airbus, 1991. A300 Airplane Flight Manual. Airbus Industrie, Tolouse. Alumur, S., Kara, B.Y., Karasan, O.E., 2009. The design of single allocation incomplete hub networks. Transportation Research B 43, 936e951. Ebery, J., Krishnamoorthy, M., Ernst, A., Boland, N., 2000. The capacitated multiple allocation hub location problem: formulations and algorithms. European Journal of Operational Research 120, 614e631. Ernst, A.T., Krishnamoorthy, M., 1998. Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research 104, 100e112. Fokker, 1986. Fokker F27 Airplane Flight Manual (Chapter 1), vol. 1. Fokker Services B.V, Hoofddorp. Lin, C.C., Lin, Y.J., Lin, D.Y., 2003. The economic effects of center-to-center directs on hub-and-spoke networks for air express common carriers. Journal of Air Transport Management 9, 255e265. Tan, P.Z., Kara, B.Y., 2007. A hub covering model for cargo delivery systems. Networks 49, 28e39. Yang, T.H., 2009. Stochastic air freight hub location and flight routes planning. Applied Mathematical Modeling 33, 4424e4430.