An innovative approach for integrated airline network and aircraft family optimization

CJA 1432 20 November 2019 Chinese Journal of Aeronautics, (2019), xxx(xx): xxx–xxx

No. of Pages 30

1

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics [email protected] www.sciencedirect.com

3

4

An innovative approach for integrated airline network and aircraft family optimization

6

Jose´ ALEXANDRE, T.G. FREGNANI, Bento S. DE MATTOS, Jose´ A. HERNANDES

7

Department of Aeronautical Engineering, Technological Institute of Aeronautics, 12228-900 Sao Jose dos Campos, Brazil

8

Received 31 October 2018; revised 22 October 2019; accepted 22 October 2019

5

9

11 12

KEYWORDS

13

Air transport; Aircraft design; Airline economics; Airline network optimization; Multidisciplinary design optimization

14 15 16 17 18 19

20

Abstract The determination of optimal aerial transport networks and their associated flight frequencies is crucial for the strategic planning of airlines, as well as for carrying out market research, to establish target markets, and for aircraft and crew rostering. In addition, optimum airplane types for the selected networks are crucial to improve revenue and to provide reduced operating costs. The present study proposes an innovative approach to determine the optimal aerial transport network simultaneously with the determination of the optimum fleet for that network, composed of three types of airplanes (network and vehicle integrated design). The network profit is maximized. The passenger’s demands between the airports are determined via a gravitational model. An embedded linear programming solution is responsible for obtaining potential optimal network configurations. The optimum fleet combination is determined from a database of candidate aircraft designs via genetic algorithm. A truly realistic airplane representation is made possible thanks to accurate surrogate models for engine and aerodynamics is adopted. An accurate engine deck encompassing a compression map and an innovative engine weight calculation besides an aerodynamical artificial neural network module enable a high degree of accuracy for the mission analysis. The proposed methodology is applied to obtain the optimum network comprised of twenty main Brazilian airports and corresponding fleet. Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

E-mail address: [email protected] (B.S. DE MATTOS) Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

1. Introduction

21

The need for reduction of operational cost is widely agreed by the commercial air transportation industry. Indeed, the segment is characterized by low operational margins. As per recent studies,1 since the 19800 s the average world airlines profit margin has demonstrated a narrow variation, from 4% to 3%. Optimization methods have been widely applied to reduce operational costs, such as fuel-efficient flight paths,

22

https://doi.org/10.1016/j.cja.2019.10.004 1000-9361 Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

23 24 25 26 27 28

CJA 1432 20 November 2019

2

No. of Pages 30

J. ALEXANDRE et al.

Nomenclature a0 (m/s) Speed of sound at sea level on standard atmosphere ADj (min) Arrival delay at airport j ANN Artificial neural network B City pair combined buying power index Bi Buying power index related to the city of the i-th airport BPR Engine by-pass ratio b Passenger capacity bk Passenger capacity of k-th aircraft CARGO (kg) Total cargo loaded onboard C City pair airport catchment area product Ci (km2) City pair airport catchment related to the i-th airport CD Drag coefficient ck ($/n mile) Average direct operational cost of k-th aircraft at design range Cfix ($/n mile) Fixed component component of direct operational cost (crew, oil, fuel and insurance) Cmaint ($) Maintenance (labor and material) component of the direct operational cost Cdepr ($) Depreciation (airframe, engines and avionics) component of the direct operational cost Cfee ($) Fees (Navigation, Airport and Register) component of the direct operational cost Cfin ($) Financial (airframe and engine leasing) component of the direct operational cost CL Lift coefficient CLmax Maximum lift coefficient at undeflected flap/gear up airplane configuration D (N) Total aircraft drag De (m) Engine fan diameter DDi (min) Departure delay at i-th airport dij (n mile) Distance from i-th to j-th airport DOC ($/n mile) Direct operational cost DOCijk ($/n mile) Direct operational cost from i-th to j-th airport DU (h) Average daily aircraft utilization eTIT (K) Engine turbine inlet temperature fij Daily demand from airport i-th to j-th airport FF (kg/s) Engines total fuel flow FOB (kg) Total fuel on board FPR Engine fan pressure ratio g (m/s2) Gravity acceleration G Combined city pair Gross Domestic Product GDPi ($) Gross Domestic Product related to the city of the i-th airport hMAXBUFFET (ft) Maximum pressure altitude limited by buffet margin Hp (ft) Pressure altitude HT Horizontal tail ID ($/min) Average inflight delay cost k1 Total operational costs to direct operational costs ratio k2 Total revenue to ticket revenue ratio

L (N) Airplane lift force LATi (°) Latitude of the origin airport LAtj (°) Latitude of the destination airport LFref Reference Load Factor LONi (°) Longitude of the origin airport LONj (°) Longitude of the destination airport LW (kg) Landing weight Ma Number of Mach MAXFUEL(kg) Maximum fuel capacity MDO Multi-disciplinary design and optimization MLW (kg) Maximum landing weight MOGA Multiobjective genetic algorithm MTOW (kg) Maximum takeoff weight MZFW (kg) Maximum zero fuel weight Nacftk Total number of k-th aircraft NAND Nested analysis design NDOC ($/ n mile) Total air transport network’s direct operational cost NP ($/(passenger n mile)) Total network profit OEW (kg) Operational Empty Weight OPR Engi e overall pressure ratio p ($) Average ticket price P City pair population product Pi City pair population related to the city of the i-th airport PAX Passenger or Passengers PAXWT (kg) Total passenger’s weight including baggage PAYLOAD (kg) Total payload carried by the aircraft SAND Simultaneous analysis and design Tnet (N) Net engine thrust Tij (min) Trip time spent between i-th and j-th airports TBij (min) Block time spent between i-th and j-th airports TIT (min) Average taxi in time TOT (min) Average taxi out time TAT (min) Average turnaround time TOF (kg) Takeoff fuel (fuel on board at beginning of takeoff run) TOW (kg) Takeoff weight V (m/s) True airspeed VT Vertical tail W (kg) Airplane weight Wf (kg) Total fuel burned from origin to destination airport Wfapproach (kg) Total fuel burned on approach phase Wfalternate (kg) Total fuel burned from destination to alternate airport Wfcontingency (kg) Contingency fuel Wfholding (kg) Fuel for the holding flight phase Wftaxi (kg) Taxi fuel Xiltj Fraction of the passenger’s demand flow fij from origin i to destination j Yijk Number of type-k airplane linking i-th to j-th city (route frequency) Β (°C/ft) Temperature/altitude drop ratio at troposphere (°0.00 1982 °C/ft) dmax Atmospheric pessure ratio (actual static pressure/standard sea level pressure) at maximum altitude

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization

c(rad) Flight path angle Ʌ Wing Sweep Angle at 25% chord DISA (°C) Temperature deviation from standard temperature

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

optimum slot allocation and turnaround time reduction.2 They can already be applied in the airline’s operational planning process, which is divided into three major blocks, as shown in Fig. 13. The first block is called Schedule Generation (or Flight Definition). There, route allocation is determined according to the estimated or actual demand among city pairs, taking into consideration airport constraints, such as operational hours or infrastructure issues. Afterwards, the amount of frequencies for each city pair is determined based on the capacity of the selected aircraft type followed by the generation of the airline’s flight schedule. In this block, the objective function is normally set to market revenue maximization.4,5 The second block is related to fleet assignment and there the sequence of scheduled flights of each type of aircraft is determined. In this process, the best aircraft is assigned to each scheduled flight with the objective to maximize profit at selected routes, considering maintenance and aircraft performance constraints. In Block 2, the objective function is usually established to maximize profit.6 After network and type of airplanes are determined, the last block is related to crew assignment, where crew members are allocated to each flight, complying with labor regulations and technical constraints, on a rostering/pairing scheme. In this block, the objective function is normally set to cost minimization.4,7 The independence of the blocks shown in Fig. 1 is worth mentioning, where costs and revenues are related to each step in the airline planning cycle.7 Because of this, some models are built to solve the problem in a single step, where the minimization of costs or maximization of revenues are set as objective function.3 However, the unified model to optimize the entire process leads to large-scale problems, sometimes involving non-linear programming algorithms8 and therefore significant computational power may be required for the complete solution. The selection of the aircraft fleet types suited to the network is most of the times performed prior to the optimization of Block 1, which is a significant factor that influences the flight frequencies. The determination of the optimal flight network and associated frequencies is a key step for airlines to elaborate their strategic planning, from market determination to aircraft and crew rostering. An optimal solution for this block facilitates the solution for the others. Furthermore, if in this optimization, the optimum aircraft types could be associated with the assigned network, the goal for maximum revenue and/or minimum operational costs would be even further improved. In other words, the network optimization is normally carried out separately from the aircraft optimization in the airline planning process.

Fig. 1

u

3

Acceleration factor function

Some aspects related to the conceptual design of commercial transport airplanes shall be mentioned at this point. Typically, this design phase is carried out by aircraft manufacturers (and frequently be the academia) through optimization of averaged direct operational cost in each set of stage lengths (or ranges), carefully chosen by the project team. Considerations about the suitability of the product into a realistic airline network are usually not given. In order to capture more realistic design scenarios, a common approach is to conduct surveys with airlines to incorporate their requirements into the project. Airline representatives are usually allocated into an aircraft development program council in order to provide regular feedbacks on design reviews. However different airlines present different requirements for their fleets, highly influenced by their business model and operational profile, sometimes not explicit to this kind of committee for strategic reasons. Because of this, families of aircraft types (derived from a single model) are offered to customers, in order to provide a range of solutions for different airline profiles and business models. Until the 19900 s, the tools used for the aircraft conceptual design were limited by computational power. Simplistic models were developed in several aeronautical disciplines, and therefore this led to lower fidelity of the disciplines. Because of that, aircraft designers most of the times restricted mission requirements and performed optimizations focused on subsystems, ignoring the high degree of dependency that exists between airplane and network, resulting in a sub-optimization of system functionalities. With the increase of the computational power, the aircraft conceptual design process is nowadays carried out by manufacturers using Multidisciplinary Design Optimization (MDO) frameworks. A great deal of computational analysis is required to obtain optimum configurations to satisfy many objectives and design constraints. Disciplines such as aerodynamics, propulsion, flight mechanics, structures and aeroelasticity, among others, are frequently considered in the optimization framework to obtain more realistic geometries of flight vehicles in addition to mission analysis into the network. Because of the increased complexity of such kind of methodology, significant efforts of computational analysis are required to obtain optimum configurations that satisfy many objectives and design constraints. Disciplines such as aerodynamics, propulsion, flight mechanics, structures and aeroelasticity, among others, are frequently considered in the optimization framework to obtain more realistic geometries of flight vehicles and, recently, the addition of flight profile

Typical operational planning process of airlines.3

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122

CJA 1432 20 November 2019

No. of Pages 30

4 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178

J. ALEXANDRE et al.

and mission analysis. Nowadays, many design variables (and types) may be employed, and advanced optimization algorithms enable that complex models of the aeronautical disciplines be considered. Empirical formulae like the Class-I and -II methodologies proposed by Torenbeek9 and Loftin10 for drag and weight estimation are still extensively used for modeling because they provide faster results.11 However, surrogate techniques have been increasingly adopted to model the physics with enough precision, at the same time reducing the computational time of complex and heavy calculations in MDO frameworks.12 Genetic Algorithms (GA) have been successfully employed and they are suitable for complex multi-disciplinary problems involving different types of design variables and efficiency on converging to the global minima, although not mathematically proven.13 Besides, GAs can handle complex design frameworks, since they do not require function derivatives and can deal with different types of design variables and constraints.14 In order to produce realistic results, the airplane representation used in design framework is considerably more complex and sophisticated than that utilized by many authors. For instance, the airplane is modeled with CAD surfaces inside the optimization platform, which allows to easily calculate areas, angles and dimensions. In comparison, Taylor and De Week15 or Bower and Kroo16 ran optimizations with only a single objective cost function and adopted just three aircraft design parameters (range, lift-to-drag ratio, and cruise speed), associated to simplistic frameworks with few disciplines. The present work considers over 60 parameters to generate an airplane. Furthermore, the inclusion of the network in airplane design frameworks with realistic performance calculations is highly desirable. Some of the design variables and constraints considered in the airplane generation are: (1) Geometric variables: front fuselage, tailcone, fuselage cross-section shape and dimensions, wing planform characteristics and wing airfoil geometries, wing structural sizing, vertical and horizontal tail characteristics, winglets, and landing gear sizing. (2) Topology: engine location, wing location, number of engines, engine positioning to avoid hot exhaust gases hitting flaps and fan debris reaching fuel tanks, wing structure layout, seating abreast, number of aisles, main and nose landing gear location and sizing to comply with engine clearances from ground, and tail configuration. (3) Propulsion: engine by-pass ratio, overall pressure ratio, fan pressure ratio, turbine inlet temperature, and fan diameter. (4) Environmental constraints: noise footprint and engine emissions. (5) Certification and performance requirements: 2nd segment climb, rate of climb, cruise speed, initial cruise altitude, time to climb, landing climb, takeoff climb, wing spanwise location where stall starts, landing and takeoff field lengths, flap settings, and fuel storage.

179 180 181 182

For the calculation of tail surface areas, the iterative process is employed according to the procedure described in Ref.17. Engine integration is performed considering the con-

straints mentioned before. Landing gear is designed according to constraints and guidelines furnished by Torenbeek.18 Considering that a complex network approach was adopted,19 the main indicators reflecting the statistical features of air transport network structure are included in the framework such as degree of a node, average degree, average path length, density and clustering coefficient.20 Airport characteristics in the aerial network are included in the mission profile computation, such as, for instance, noise level constraints for operating airplanes, runway length, elevation, magnetic declination, and environmental conditions. In summary, there is a need for integrated design where both aircraft or family of aircraft and air transport networks are simultaneously optimized. For realistic results, it is mandatory detailed representation of the airplane with accurate and concise mission performance calculations, which must consider operational characteristics of airlines in their aerial network.

183

1.1. Literature review

200

The Airline Deregulation Act, enacted in late 1978 by the North American government, presented a set of economic and operational measures tailored to lower the level of control on airfares, routes and stimulate the entry of new airlines into the aviation market. Consequently, the power of civil aviation regulators over fares was eliminated, and market forces were established for the first time in the history of airline industry. Ever since, this model has been quickly replicated in other countries as a form to support the growing passenger demands worldwide. Because of free competition between airlines, huband-spoke networks have evolved as the minimum cost configuration for Legacy Airlines while fully connected networks have become the emerging solution for the low-cost carriers in their competition for growing markets. Since then, boosted by these industry trends, various research initiatives were conducted on network optimization techniques with the objective to maximize profit for airlines. Akhuja et al.21 performed a detailed study about applications for network optimization problems in several fields of operational research, including the ones related to transportation. His study addressed cost minimization using linear programming models. Campbell22 performed another study presenting an integer programming formulation for four types of hub-allocation problems, featuring discrete hub centers and models. Aykin23 studied hub location and routing, proposing an interactive method to solve both problems separately. Jaillet et al.24 introduced an innovative flow-based linear model for designing networks presenting minimum cost and their associated frequencies, considering local demands. The proposed model can predict the occurrence of hubs if they reveal to be cost effective. A detailed study regarding network types and schedules was performed by Lederer and Nambimadom,19 where analytic expressions for passengers and airline costs were derived for several network types. Parametric studies were conducted to evaluate the effect of distances, demands and frequencies on profit with the aim of profit optimization.23 Evans et al.25 proposed a model for network optimization considering flight scheduling and constraints on airport capacity. Complementing these studies, Dong20 developed metrics to evaluate efficiency of the transport networks featuring any

201

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303

kind of topology. More recently, Caetano and Gualda7 have proposed a solution for joint route assignment and fleet scheduling using a simplified linear program model. In another study,3 both authors described the so-called transport momentum methodology as a proxy for operational costs that are tailored for solving fleet assignment problems encompassing scheduling. Passenger demand is an important input to be considered in the network optimization process. Gravitational models became popular to determine passenger demand in air transportation mainly because of their simplicity and forecast capacity using historical econometric variables related to the cities involved and time-geometric parameters. In this kind of model, a simple multivariable log-linear regression is enough to determine the associated coefficients with relatively good accuracy. Grosche et al.26, for example, proposed a complete model considering population, catchment area, buying power index, gross domestic income, time to travel and distance between city pairs, using data from 28 European airports for calibration. Doganis1 proposed a different approach, estimating the passenger demand of airports considering airfares, frequency and scheduled traffic. Wojahn27 determined the characteristics of the optimum airline networks using gravity models. In his work, the demand and cost conditions of an airline have been identified as one of the main determinants of network topology. Few studies integrate aircraft design characteristics and performance to realistic mission analysis for each city pair considered. The research on integration of entire airline networks with aircraft design variables started to be developed in the last ten years and has only been possible with the increase of computational power and development of robust optimization solvers which are capable of handling multivariable, multiobjective functions and are submitted to non-linear constraints. Recent studies show that the direct coupling of aircraft design and airline fleet-route allocation frequently uses Mixed-Integer, Non-Linear Programming (MINLP) formulation, a suitable solution via a decomposition approach.28,29 It is worth mentioning that most of the researches are until now directed to the identification of aircraft characteristics that reduce direct operational costs. Although many researches have been conducted on airline network optimization problems, especially on route and tail assignment, few studies integrated aircraft design characteristics and performance to realistic mission analysis for each city pair considered.15,16 The research on integration of entire airline networks with aircraft design variables started to be developed in the last fifteen years and was enabled with the increase of computational power and development of robust optimization solvers which are capable of handling multivariable, multi-objective functions and are submitted to non-linear constraints.12,30 The inclusion of network and mission analysis modules into the aircraft MDO framework is a complex task since it involves several operational variables and is extremely dependent on aircraft performance related disciplines and nonlinear equations. In fact, initial studies show that the direct coupling of aircraft design and airline fleet-route allocation frequently uses mixed-integer and nonlinear programming formulations and requires diverse types of design variables, constraints and disciplines. This would require a decomposition approach, using disciplines sub-optimizations, in order to facilitate the resolution of such framework.28,29 Some key

5

studies on this approach are mentioned in the following paragraphs. Roth and Crossley31 proposed the use of genetic algorithms, combined with a gradient based method, for aircraft design optimization in specific mission profiles. Isikveren32 expanded this concept including range optimization and computing fuel consumption with semi-empirical formulations. Cavalcanti et al.33 proposed a multi-objective optimization of wing planform carried out by the minimization of the block time and block fuel for a given mission. Cabral et al.34 proposed a design framework to optimize families of aircraft for a given mission profile using genetic algorithms. Taylor and De Week15 presented, for the first time, the benefits of optimizing an air transportation network concurrently with the vehicle design. This study focused exclusively on the design of an air transportation network for overnight package delivery on two turn-around hub configurations connecting seven U.S. cities. By concurrently optimizing both the vehicle, with a simplified model based on Breguet Range equation, and the network for a few selected cities with fixed demand, it was possible to obtain a ten percent improvement of operational costs over the one obtained by optimizing only the network design when using a set of pre-defined aircraft. This was accomplished by embedding a linear programming solver in the perturbation step of simulated annealing algorithm to solve the substantial number of linear constraints imposed by the capacity and demand requirements of the network. Afterwards, Mane et al.35 conducted a research proposing to split aircraft design and airline allocation problems, on a systemof-systems approach. The aircraft design block first optimized a new aircraft for a specified design mission range and payload. The designed aircraft along with the existing set in fleet were allocated to the route network via a MINLP problem. This study also compared the decomposition approach with the one solving the coupled problem as an MINLP problem using algorithms like genetic algorithms and branch and bound. Bower and Kroo16 developed a methodology for aircraft design considering demands of a given aerial network. In their design approach, the objectives are the minimization of direct operating costs and airplane emissions (CO2 and NOx). For this purpose, a hierarchical decomposition was used with discipline-specific optimization algorithms using simplistic models. A modified version of a multi-objective genetic algorithm is implemented in the system level aircraft design subspaces. Results were presented for a test problem that involved designing a single-aisle commercial airplane for a route network consisting of four cities and eight route segments, using eighteen design variables. Nusawardhana and Crossley29 proposed a mathematical formulation to solve simultaneously the aircraft design and fleet dynamic allocation problem, indeed a ‘‘tail assignment” task, using a two-level evaluation, at system and subsystem levels, for the airline side problems. Siqueira et al.36 built an MDO framework to select the optimum conceptual aircraft design for an existing scheduled (fixed) airline network. Braun et al.37 demonstrated the evaluation of future aircraft optimizing network and fleet assignment at the same time. The effect that selection of aircraft configurations and decisions concerning capture of target markets have on tradeoffs between risk in serving demand itineraries and expected profit was addressed by Davendralingam and Crossley in their concurrent engineering optimization framework.38. A scenario

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365

CJA 1432 20 November 2019

6

415

involving six airports is solved to validate their methodology. In preliminary studies,39 the authors investigated the impact of aircraft configurations choices on moves to capture target markets, measuring how it impacts demand of itineraries and evaluating associated economic risks. Hwang and Marins40 presented a method for simultaneous design and mission allocation optimization, with surrogate modules for aerodynamics, propulsion within a mission analysis tool. They used a gradient-based optimization technique. A three-route problem was run with a single aircraft configuration for validation purposes. They obtained a 200% to 400% profit increase when compared with a standard airliner. Extending this work, Hwang and Martins40 expanded the analysis for a 128-route framework, considering a parallel computing technique. Later, Hwang and Martins41 integrated the above methods on a concurrent optimization encompassing aircraft design, mission profiles, and the allocation of aircraft to routes in an airline network. To enable the solution of this complex approach, a gradient-based optimization approach was adopted with a parallel computational framework, which boosted the computation of derivatives in the multidisciplinary analysis. A surrogate model for Computational Fluid Dynamics (CFD) analysis is retrained in each optimization iteration given the new set of shape design variables. The resulting optimization problem contains over 6000 design variables and 23,000 constraints, and it is solved in approximately 10 hours on a machine with 128 processors. The optimization revealed a 27% increase in airline profit when the allocation-missiondesign optimization was compared to allocation only optimization. Afterwards, Roy et al.42 proposed the aircraft allocation optimization into this framework, introducing a Mixed Integer Non-Linear Problem (MINLP) to the problem, increasing the complexity of the solution search. In a preliminary study, the authors proposed a framework based on the so-called ‘‘efficient global optimization”, a special gradient-based algorithm which is applied in the design space, to solve this problem.43 Finally, Roy et al.44 studied the inclusion operational and revenue management variables (such as fare, booking limits, demand and aircraft count constraints), using a genetic algorithm as heuristic method combined with a branch-and-bond method (gradient-based), in a monolithic approach for network optimization. This approach solves a 11-route problem, providing significant improvements on airlines’ objectives using a standard single-aisle aircraft. It is worth mentioning that all above researches directed the optimization frameworks considering the minimization of global network operational costs or profit, in single objective functions. No study was conducted considering multi-objective approaches.

416

2. Objective and contributions

366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414

417 418 419 420 421 422

The present work proposes a methodology to determine the optimal aerial transport network simultaneously with the optimum fleet for this network, which is composed of three airplane types (typical airline classification for fleet purchase). The major contributions of the present research are outlined as follows:

No. of Pages 30

J. ALEXANDRE et al. (1) The optimization simulations deliver optimal fleets of airliners jointly with their related optimum aerial network, for given passenger demands calculated via gravitational model. By utilizing this tool, an airline can easily evaluate the economic impact of the introduction of new aircraft types on its network. (2) The use of databases of airplanes with their characteristics defined by over 60 design parameters. Optimal fleet is obtained by optimization runs resorting to databases, ensuring in this way faster convergence of the optimization process, permitting the aircraft selection to be optimized simultaneously to the network. The database is comprised of from 50-seat to 180-seat airliners. Among others, different motorizations, tail configurations, wing planform parameters, seating abreast, and container type for cargo compartments were considered to design the airplanes, even for those similar in passenger capacity. There are airplanes in the database that are very close to the existing ones like the medium-capacity Boeing 737–700 and the small capacity Embraer ERJ-140 twinjet. (3) Curfews and operational constraints due to noise levels and engine emissions can be measured in both airplane design and aerial network connections. (4) The design parameters used enable to represent the airplanes in the database in the finest detail. This, in conjunction with accurate aerodynamic, stability and control, and performance calculations, leads to precise mission analysis and guarantees very realistic airplane configurations. The level of detail, for instance, considers engine positioning in order to avoid hot exhaust gases hitting flaps and fan debris reaching fuel tanks. Aircraft in the database are designed according to the following requirements: (A) Adherence to FAR 25 requirements: climb rate at 2nd segment, missed approach, takeoff field length, landing field length, takeoff and landing climb, climb rate at service ceiling. (B) Able to cruise at desired Mach number. (C) Adequate fuel storage for specified missions at maximum takeoff mass. (D) Calculation of noise signatures at ICAO certification points: sideline, approach, and takeoff.45 (E) Innovative method for turbofan engine weight: coupling with engine deck program guarantees accurate weight calculation. (F) Tail surfaces are designed to comply with stability and control requirements. Typically, most works employ simpler formulations, like the tail volume coefficient. (G) Landing gear sizing and positioning with tires being designed to withstand speed and load requirements. Objectives of tire dimensioning are minimum size and minimum weight for the nose and main landing gear, respectively. (H) An artificial neural network system is employed to calculate the aerodynamic characteristics of the airplane configurations, based on full potential formulation with viscous correction.46 The use of the ANN enables a high degree of accuracy and

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization 483 484 485 486

fidelity for the calculation of aerodynamics coefficients. This, in turn, cares for performance calculations with high level of accuracy in the conceptual design.

487 488 489 490 491 492 493 494 495 496 497 498 499

(5) Optimal airplane fleets are obtained considering maximization of network profit and minimization of Direct Operational Cost (DOC). A genetic algorithm is then used, and the results are analyzed in a multi-objective context, presenting a Pareto-type analysis of network profit versus DOC. (6) The determination of the optimum network considers a two-stop route model and three airplane types composing the airline fleet. This is solved in a sub-procedure for obtaining the network with maximum profit, instead of the conventional minimum DOC approach. The number of airplanes that compose a fleet can be easily modified.

500

501

502 503 504 505 506 507 508 509

510 511 512 513 514 515 516 517 518

7

the aerodynamic and propulsion sub-modules to determine the necessary fuel flow and drag for the trajectory calculations. Before running the network optimizer module, this module calculates the DOC for each aircraft for the related range. This module is also used by the network analysis module to determine the fuel burn, trip time and DOC of each sector of the optimized network. (3) Network optimizer. In this module, the optimum networks related to three airplane types are determined simultaneously based on airport and econometric information (retrieved from a database), aircraft maximum passenger capacity, aircraft design range and associated DOC. This represents as secondary local optimization step inside the global optimization cycle (see Fig. 2). (4) Network analysis. In this module, fuel burn, trip time and DOC for all sectors are calculated and integrated to calculate the total Network Profit (NP) and Network Direct Operational Cost (NDOC).

3. Methodology

519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538

The design optimization framework of the present work, shown in Fig. 2, is intended to find out optimal aircraft fleets, composed of three aircraft types, and corresponding networks, which maximize the total Network Profit (NP), satisfying given city-pair passenger demands. The modeFrontierÒ package is employed as integrating platform. Four MATLABÒ-coded modules are part of the optimization framework, which are described as follows: (1) Aircraft data loader. Retrieves required data related to the three selected airplanes (engine location and parameters, weights, fuel capacity, noise signature, passenger accommodation, fuselage dimensions, range, and others). (2) Mission performance. Calculates the fuel burn, trip time, and DOC for a mission between origin and destination airports. In addition, it also provides takeoff weight and environmental conditions. This module calls

Fig. 2

The aircraft databases were built according to three ranges of passenger capacity. The first one considers airplanes with capacity ranging from 44 to 80 seats and is comprised of 13 individuals. The database 2 hosts airplanes transporting between 81 and 95 passengers and it has 16 configurations. Finally, the third database has 22 types of airplanes featuring between 91 and 110 seats. Thus, there are 4576 potential aircraft combinations to be explored in the design space. Design ranges for the airplanes of the three databases are defined at the point of maximum passenger capacity considering takeoff with Maximum Takeoff Weight (MTOW), varying from 1000 to 2500 nautical mile. Each aircraft in the databases is represented by 46 parameters associated to airframe, propulsion and certification characteristics as listed in Tables 1–5. The aircraft database is generated through random variation of most of parameters within a specific interval, as listed in the tables. It is noticeable that some of them are kept fixed to simplify the calculations in some modules (for example, Horizontal/Vertical tails parameters (see Table 3) are kept fixed in this study with the objective to simplify the tail sizing computations).

Airplane/network integrated optimization framework.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558

CJA 1432 20 November 2019

No. of Pages 30

8

J. ALEXANDRE et al. Table 1

Airframe parameters – Fuselage.

Table 4

Parameter

Characteristic/Value

Parameter

Range or value

Passenger cabin external width

Calculated to fulfill clearances, ditching, container type, and other cabin parameters Calculated to fulfill clearances, ditching, container type, and other cabin parameters Based on seat arrangement, emergency exits, galley and toilet areas From 44 to156

De (m) BPR FPR OPR eTIT (K) Number of engines

1.14–1.40 4.80–6.20 1.39–1.85 22.00–32.00 1290–1380 2

Passenger cabin external height Fuselage length

Airplane PAX capacity at 32 inch pitch, single class Number of aisles Seating abreast PAX cabin crew Cabin aisle width (m) Cabin height (m) Seat width (m)

Table 5 1 3–6 1 + 1 for every 50 PAX 0.50 2.00 0.46

Table 2

Range or value

Wing reference area (m2) Wing aspect ratio Wing taper ratio Wing sweepback angle at quarter chord (°) CLmax of clean wing configuration Location of break station (fraction of semispan) Wing mean aerodynamic chord (m) Wing wetted area (m2) Incidence angle at wing root (°) Incidence angle at break station (°) Incidence angle at wingtip (°) Airfoil relative thickness (root, break, and tip stations) (%)

50–124 7.5–9.2 0.25–0.45 20–32 1.50–1.70 0.32–0.39 4.11–3.27 258.5–113.15 2 0–0.5 0.5 to 3.5 (12.88, 10.55, 9.82)

561

Airframe parameters of HT and VT.

Parameter

Value

HT aspect ratio HT reference area (m2) HT sweep angle (°) HT taper ratio

4.35 Defined by stability and controllability criteria

VT VT VT VT (°)

560

Airframe parameters – Wings.

Parameter

Table 3

aspect ratio area (m2) taper ratio sweep angle

Certification parameters.

Parameter

Range or value

Operational empty weight (kg)

18540–26187 (see Fig. 3) 30467–44349 (see Fig. 3) 37475–27383 (see Fig. 3) 29980–21906 4886–10162 41,000 0.82/340 1000–2500 2200

Maximum takeoff weight (kg) Maximum landing weight (kg)

Note: 1 inch = 24.5 mm.

559

Powerplant parameters.

Wing sweepback angle +5o Typically, 0.435 but for ‘‘T”-tail configurations it will depend on the VT tip chord 1.20 Defined by stability and controllability criteria 0.50 41

During the database generation, MTOW, Maximum Landing Weight (MLW) and Operational Empty Weight (OEW) of each aircraft are calculated through an iterative process as

Maximum zero fuel weight (kg) Maximum fuel capacity (kg) Maximum certified altitude (ft) Maximum cruise speed (Ma/CAS) (kt) Design range (n mile) Reference takeoff field length (MTOW, ISA, sea level) (m) Reference landing field length (MLW, ISA, sea level) (m)

1500

Note: 1 ft = 0.3048 m; 1 kt = 1.852 km/h.

illustrated in Fig. 3. In this calculation, weight of pylons, fuselage, empennage, systems, landing gear and engines are calculated separately using empirical formulas.9,47 The wing weight is calculated by sizing the wingbox to withstand aerodynamic loads calculated with a full potential code in some few maneuvers in the flight envelope; the secondary structure is estimated by empirical methods. All these weights are considered for the determination of the Operational Empty Weight (OEW). With the weight of each component, it is also possible to obtain the Center of Gravity (CG) of the aircraft and its variation with fuel consumption and different payloads. The MTOW and MLW are then estimated interactively using the mission analysis module and the calculated OEW for the given design range.45 The network optimizer module generates the design variables (X1, X2, and X3). These continuous variables are numbers varying from 0 to 1, representing the airplane address in each of the three databases. After the aircraft are chosen, the aircraft loader module reads the aircraft and engine characteristics, which are used as input for the mission performance module. The only constraint enforced at this point is that of passenger capacity differentiation by five seats among the three airplanes. This ensures that similar aircraft in capacities are not selected, promoting more diversity in solutions. This module provides to the network optimizer NDOC and NP values. The multi-objective MOGA-II algorithm48 is chosen as optimization engine thanks to its robustness and ability to handle global minima or maxima inside a complex design space built with many variables. This first-generation evolutionary algo-

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization

Fig. 3

Flowchart of airplane calculation including key mass figures.

611

rithm is designed to use inherent genetic operators (crossover, mutation and selection) combined with parenting elitism, which means that it always favors individuals with better fitness values than its parents. The algorithm was set to run 20 generations, with 50% probability of crossover, 5% probability of selection and 1% probability of mutation. The uniform Latin hypercube sampling method14 is used to generate the starting points for the GA optimization. In this study, 20 individuals are initially created to compose the starting population of the process. It is worth mentioning that for everyone in the GA population, given by the triplet (X1, X2, and X3), an optimum network is found in a secondary optimization task, where a linear programming problem is exactly determined with appropriate LP solver.49 The linear programming model has for objective to determine the configuration presenting the maximum profit, based on the calculated demands, aircraft characteristics, passenger capacity and design range. Extended explanations related to the implementation of each module and sub-modules shown in Fig. 2, are provided in next sections.

612

3.1. Network optimizer

613

Provided the airplane triplet (X1, X2, and X3) is known, the optimum network, including the necessary frequencies, is solved in a secondary optimization process using a linear programming algorithm. The aircraft allocation (tail assignment and schedule for each frequency) is not considered in the present framework and will be considered in future versions. The airline networks are optimized considering operations within a certain geographical area or a certain market share. For this, it

591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610

614 615 616 617 618 619 620

9

is necessary that passenger demand among airports, average ticket price, aircraft fleet capacity, range, and operational costs be known. Then, an optimized network can be drawn up considering the profit maximization. In this context, the profit is maximum if all passengers’ potential demand is fulfilled for each city pair, allocating the necessary frequencies for each aircraft type. Also, it is assumed that the airline allows passengers to buy tickets for maximum two stops between origin and destination, meaning that three types of services are possible: (A) non-stop flights, (B) one-stop connecting flight and (C) twostop connecting flights. In fact, this is a common policy practiced by the Brazilian domestic airlines nowadays. The optimization algorithm in this module is derived from the Linear Programming Model (LPM) proposed by Sun and Smith11 for generic network determination considering passengers fractional flow. A MATLABÒ code was developed to set up and solve this problem using the LPM solver available for this application. The mathematical formulation of the problem is presented in the next paragraphs. Let Xiltj be the fraction of the passenger’s demand flow fij from origin i to destination j, served by a two-stop connecting flight through cities l and t, Yijk the number of aircraft type k used in the route from city i to j, p the average fare per passenger ($), ck the average operational cost ($/n mile) at design range, bk the passenger capacity of aircraft k, LFref the reference load factor, and dij the distance between origin and destination airports. The following integer linear programming model is proposed: XX ck dij max k1 p  k2 ð1Þ LFref bk i¼j k subject to

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649

651 652

CJA 1432 20 November 2019

No. of Pages 30

10

J. ALEXANDRE et al.

653

fij þ

X

fit Xijt þ ftj Xij  fij Xitj

t–i;j

þ

X

708



flj Xltij þ fit Xijlt  fij Xiltj

W dc L þ  ¼ Wcosc g dt



655 656 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 685

X

LFref bk Yijk

for

alli– j

ð2Þ

k

X t–i;j

Xitj þ

X

Xiltj  1 for

alli–j

ð3Þ

where Xitj, Xiiltj are positive and Yjk integer positive for all i – j The average operational costs (ck) for each aircraft fleet, necessary for the optimization, correspond to the direct operational costs related to the design range mission. The objective function Eq. (1) is set to maximize the network profit, based on the difference between the average fare (p) and the average cost per passenger. Constraint inequality (2) states that the fractional flow on route ij cannot exceed the total capacity of the aircraft assigned, while constraint Constraint (3) ensures that the passenger flow from a direct flight from i to j is nonnegative. It is assumed that 50% of all passenger demand from i to j are derived from direct flights (Xij and Xji), 30% distributed equally among all one-stop flights (Xijt, Xtij and Xitj) and 20% distributed equally among two-stop flights (Xltij, Xijlt and Xiltj). Passengers potential demand between origin and destination (fij) is determined via gravitational model, based on city pair distance and econometric parameters. Let P be the city pair population product (P = Pi‧Pj), C the city pair airport catchment area product (C = Ci‧Cj), B the city pair combined buying power index (B = Bi + Bj), G the city pair GDP product (G = GDPi‧GDPj) and dij the reference distance of the city pair. The following passenger demand model is proposed as follows: fij ¼ K0 P C B K2

K3

GK4 dKij 5

ð4Þ

690

In Eq. (4), the exponents K0, K1, K2, K3, K4 and K5 are calibration constants, determined by log-linear regression. They may be easily calculated using the public econometric data available (Pi, Ci, Bi and GDPi often published by economic agencies).

691

3.2. Mission performance

692

This module is the most important part of the optimization cycle since it is where all calculations necessary to determine trip fuel (Wf) and trip time (T) are performed. These variables are essential to compute Direct Operational Cost (DOC) for each route (arc) determined by the network optimization module. Inputs from the aerodynamics (CD) and propulsion (net thrust – Tnet and fuel flow – FF) sub-modules are necessary for solving the mass point equations at time integration steps, for given performance state (weight and environmental conditions at altitude) and operational flight profile constraints. The vertical flight path is constructed numerically integrating the following set of equations of motion50 regarding the variables V, c and Hp:

686 687 688 689

693 694 695 696 697 698 699 700 701 702 703 704 705 707

dHp ¼ Vsinc dt

Tnet  D ¼ Wsin

cþ

W dV  g dt

ð5Þ

ð7Þ

In steady state and at small flight path angles c (absolute value < 5°, typical for commercial airplanes), Eqs. (5) and (6) lead to:

l;t–i;j

K1

710 711

i;t–i;j



ð6Þ

tan c ¼

Tnet W



CD CL

ð8Þ

1 þ fac

713 714 715 716 717

719 720

2W CL ¼ qSV2

ð9Þ

where fac, is the so-called acceleration factor, is defined according to vehicle’s speed and altitude as follows:50 For constant Mach number below tropopause: fac ¼ 0:1332Ma2

283:15  bHp 283:15  bHp þ DISA

ð10aÞ

For constant M number above tropopause: fac ¼ 0

ð10bÞ

For constant Calibrated Airspeed (CAS) below tropopause:   283:15  bHp ð10cÞ fac ¼ 0:7Ma2 /  0:1902 283:15  bHp þ DISA

722 723 724 725 726 728 729 730 732 733 734 736 737

 For constant Calibrated Airspeed (CAS) above tropopause:

738

739 740

fac ¼ 0:7Ma

ð10dÞ

2

with /¼

742 743 744

2 3:5

ð1 þ 0:2Ma Þ

1

0:7Ma2 ð1 þ 0:2Ma2 Þ2:5

ð11Þ

In addition, the total fuel consumption is calculated as the resulting integration of the fuel flow (obtained from the propulsion sub-module) along all flight path according to Z t Wf ¼ FF dt ð12Þ 0

746 747 748 749 750 752

Environmental conditions (pressure, density and temperature) at each integration point, which steps are evaluated every one second along the trajectory, are calculated as per the International Standard Atmosphere isentropic model.51 Zero wind, standard atmospheric pressure and 10 °C ISA deviation from standard temperature are assumed in this study. Tropopause lower pressure altitude limit is assumed fixed at 11 km pressure altitude. The mission profile computation considers a realistic jet transport airliner operational profile as shown in Fig. 4, according to the following segments:

753

(1) Segment A (Climb to 10,000 ft (1 ft = 0.3048 m)). From pressure altitude of 1500 ft above the elevation of the most used runway for takeoff the aircraft climbs maintaining maximum climb thrust and constant calibrated

763

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

754 755 756 757 758 759 760 761 762

764 765 766

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization

Fig. 4

767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797

11

Mission profile.

airspeed of 250 knots (1 knots = 0.5144 m/s) (respecting Air Traffic Control speed restriction rules52 until a pressure altitude of 10,000 ft. Fuel and time quantity allowances are added to computations representing the aircraft maneuvering necessary for takeoff run, lift off and gear/flap configuration changes. (2) Segment B (Climb with constant CAS). At 10,000 ft pressure altitude the aircraft then accelerates in a levelled segment to a calibrated airspeed of 280 knots and then climbs at maximum thrust maintaining this speed until the Mach-Crossover Altitude or Cruise Altitude, whichever is lower. The Mach-Crossover Altitude is the pressure altitude where the number of Mach reaches the prescribed climb cruise Mach number. (3) Segment C (Climb with constant Mach to cruise altitude). From the Mach-Crossover Altitude the aircraft climbs at maximum thrust with constant number of Mach (calculated cruise Mach number) to the selected cruise altitude. (4) Segment D (Cruise at optimum altitude and Mach number). The cruise altitude corresponds to the optimum cruise altitude adjusted to the suitable flight level as per the Reduced Vertical Separation Minima (RVSM) air traffic rules.53 To select the correct flight level, the average magnetic course between origin and destination airports is computed according to hypersine geodesic formulae.54 The optimum cruise altitude is calculated as the minimum of: maximum certified ceiling (fixed as 41,000 ft in this study), maximum specific range altitude (considering the selected cruise speed and takeoff weight), maximum altitude where the residual rate of

climb is 300 ft/min, and the maximum altitude where a 30% margin to stall is achieved. The latest considers stall at 40° bank angle in clean configuration and is calculated according to ICAO50

798 799 800 801

802 803

dmax ¼

W 2  S CLmax cosðuÞMa2

  0:1908 hMAXBUFFET ¼ 44330 1  dmax below tropopause

ð13Þ

805 806

ð14aÞ

808 809

hMAXBUFFET ¼ 11000 þ 152:8462DISA  6341:58lnð4:4771dmax Þ above tropopause ð14bÞ

811

The cruise segment is performed at constant number of Mach that is derived from the maximum Ma CCDL .

812

(5) Segment E (Descent with Constant Mach to MachCrossover Altitude). From top of descent, the aircraft descents at idle thrust with cruise Mach number to the Mach-Crossover Altitude, where a calibrated airspeed of 310 knots is reached. (6) Segment F (Descent with Constant CAS to 10,000 ft). From the Mach-Crossover Altitude, a constant calibrated airspeed of 310 knots is maintained in the descent flight at idle thrust to 10,000 ft pressure altitude where the airplane is decelerated in leveled flight to a calibrated airspeed of 250 knots.

814

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

813

815 816 817 818 819 820 821 822 823 824

CJA 1432 20 November 2019

No. of Pages 30

12 825 826 827 828 829 830 831 832 833

J. ALEXANDRE et al. (7) Segment G (Descent to 1500 ft). From 10,000 ft pressure altitude, constant calibrated airspeed of 250 knots is maintained in the descent flight at idle thrust to 1500 ft pressure altitude above the landing runway elevation where the airplane initiates the approach and landing phase. Fuel and time quantity allowances are added to computations representing the aircraft maneuvering necessary for approach, gear/flap configuration changes and landing.

834 835 836 837 838

839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858

The total Fuel On Board (FOB) is determined considering the minimum fuel required to comply with Brazilian regulations (RBAC 121.64555) for jet transport aircraft, representing the sum of the following quantities: (1) Fuel necessary to fly from origin to destination airport (Wf) considering the operational profile described before. (2) The fuel required to fly from destination to alternate (or diversion) airport considering the given operational profile. In this study, the alternate airport is chosen as the closest airport from the destination airport in the network, considering that all airports in the company network have the capacity available and handling infrastructure to absorb the demand (WfAlternate). (3) Fuel burn related to 10% of the trip time determined in (1) to be used as contingency for route deviations and adverse weather conditions (WfContingency). (4) Consideration of 30 min holding at 1500 ft height over the alternate airport elevation at suitable holding speed. In this study, the holding speed is selected as the maximum L/D speed or 1.3 g margin to stall speed (ensuring a protection of 44° maximum bank angle to stall) in clean configuration, whichever is higher, considering weight estimated at the alternate airport.

TOW < MLW þ Wf

ð22Þ

893 895

FOB < MAXFUEL

ð23Þ

896 898

The trip fuel and time determination routine were elaborated considering that aircraft departs with a certain Takeoff Weight (TOW) at the departure airport. The airplane trajectory is the top combination of the climb, cruise and descent flight phases. An interactive algorithm is implemented to determine top of descent point as shown in Fig. 5. The algorithm starts computing the top of descent over the destination airport, computing all cruise phase up to there. Then the descent distance is determined from this point and subtracted from the cruise phase, determining a new top of descent. A new computation cycle is then computed from this point, determining a new descent distance. The process is repeated until the difference between the descent points on subsequent runs is less than 0.5n mile. In addition, it is necessary to adjust the TOW, also through an iterative process, considering payload-range envelope checks (MZFW, MLW, MAXFUEL and MTOW) as shown in Fig. 6. In this cycle, the alternate fuel calculation (Wfalternate) is computed considering the TOW as estimated landing weight minus a go-around fuel allowance at the destination airport. € The Direct Operational Cost (DOC) computation is also performed in the mission performance module and provided as output to the computation of the total network DOC. In this process, the single mission DOC is determined using empirical formulae expressed as function of Maximum Takeoff Weight (MTOW), trip time(T), trip fuel (Wf) and crew number.47 Five types of cost components are calculated to compose the DOC in each sector and added according to DOC ¼ Cfix þ Cmaint þ Cdepr þ Cfee þ Cfin

ð24Þ

899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 929

3.3. Mission analysis

930

In this module, the key results related to all air transport networks and all fleets of airplanes are aggregated. The computations of total Network Profit (NP) and total network DOC (NDOC) are done via Eqs. (25) and (26), as function of route frequencies (Yijk), departure and arrival delays (DDi and ADj), average delay cost per minute (ID), sector distance (dij), aircraft passenger capacity (bk) and average ticket price (p) as follows:

931

859 860 861 862 863 864 865 866 868 869 871

Considering the statements above, Eqs. (15)–(19) are used in the mission performance calculation algorithm with the objective to determine trip fuel (Wf). They consider all elements necessary to determine the takeoff weight (empty weight, fuel on board and payload) and landing weight at each sector56: TOW ¼ OEW þ FOB þ PAYLOAD

ð15Þ

TOF ¼ Wf þ Wfalternate þ Wfcontingency þ Wfholding

ð16Þ

872 874

FOB ¼ TOF þ Wftaxi

ð17Þ

875 877

PAULOAD ¼ b  PAXWT  LFref þ CARGO

ð18Þ

878 880 881 882 883 884 885 886 887 889 890 892

LW ¼ TOW  Wf  Wfapproach

ð19Þ

In addition, payload-range diagram related limitations shall be respected when considering mission performance calculations.56 Eqs. (20)–(22) show the takeoff weight constraint equations related to maximum takeoff weight, maximum zero fuel weight, maximum landing weight and maximum fuel capacity:56 TOW < MTOW TOW < MZFW þ FOB

NDOC ¼

3 X N X n X k¼1

933 934 935 936 937 938 939

  Yijk DOCijk þ IDðDDi þ ADj Þ for j–i

J¼1

ð25Þ

941 942

NDOC NP ¼ k1 P3 PN PN  k2 P3 PN PN for j–i k¼1 i¼1 j¼1 dij k¼1 i¼1 j¼1 bk LFref Yijk p

ð26Þ

944

In addition, the fleet size required in each aircraft type k may be estimated as function of sector block time (TBij) and average Daily Utilization (DU) according to:

945

TBijk ¼ Tijk þ TOT þ TIT þ DDi þ ADj for j–i

ð20Þ ð21Þ

i¼1

932

PN PN Nacftk ¼ int

i¼1

j¼1 TBijk

DU

ð27Þ

!

946 947 948 950 951

for j–i

ð28Þ

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

953

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization

Fig. 5

954

955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980

13

Flight profile workflow for calculation of trip fuel and time.

3.4. Propulsion This routine is responsible for computing the Fuel Flow (FF) and = Net Thrust (Tnet) necessary for performance calculations at the flight phases. It is based on the thermodynamic model proposed by Thomas57 on turbofan engine operations. The program code is adapted from open source code (EngineSim application) developed by NASA Glenn Research Center,58 improved by Mattos et al.45 The output parameters from the computation are FF, Mach number, ISA deviation, compressor pressure ratio, fan pressure ratio, fan diameter, turbine inlet temperature, and throttle position. The classical one-dimensional thermodynamics modeling is the basis of the calculation procedure embedded in the code. Two calculation steps are built in the module: (A) the design step where all engine characteristics are raised at a given design point (cruise Mach number, cruise altitude and 95% throttle setting) and (B) the analysis step, where it is possible to calculate the engine thrust and fuel flow rate from the geometric characteristics obtained in the design step. In this sub-module, the engine weight, used in the component weight estimation process shown in Fig. 3, is also computed. Most of the engine weight estimation methods used in academy59 are derived from empirical formulae,60,10 based on data from first- and secondgeneration jet engines. Such methods may not be applicable to the current generation of engines, which are much different in design, applicable to the aircraft used in the proposed optimization framework. Thus, a new method for turbofan engines

weight estimation was elaborated and applied to the design of airplanes in the present work. Eq. (29) shows the kind of parametrization and variables considered to model the turbofan engine weight. !b !c !d !e    a f BPR OPR Tnet eDiam le FF WE ¼ T1       Tnet BPR FF OPR le eDiam BPR OPR Tnet De le FF þ T2            þ T3 BPR OPR Tnet De le FF ð29Þ

981

The coefficients and exponents of Eq. (29) are obtained by optimization using a genetic algorithm with the minimization of mean square error in regard to known engines.61 These engines belong to a database comprised of over 25 engines with considerable thrust variation among them, covering a large variety of turbofan designs.62 Table 6 shows the coefficients and parameters obtained with the optimization process. Table 7 shows the average parameters used for normalization. Table 8 contains weight estimation errors for some known turbofan engines. The maximum error obtained was 6.48%, which is considered very good for the scope of this study.

988

3.5. Aerodynamics

999

The aerodynamics module computes the total drag (CD), lift, and moment coefficients that are required for performance calculations at many points within the mission profile. A surro-

1000

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

982 983 984 985

987

989 990 991 992 993 994 995 996 997 998

1001 1002

CJA 1432 20 November 2019

No. of Pages 30

14

J. ALEXANDRE et al.

Fig. 6

Table 6

Obtained exponents and coefficients for Eq. (29).

Coefficient/Exponent T1 T2 T3 a b c d e f

1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018

Complete mission calculation algorithm.

Value 2587.2461 50.1920 154.6179 0.1965 0.0718 1.0435 0.2493 0.3444 0.1455

gate model based on artificial neural network is employed for the estimation of aerodynamics coefficients and it is extensively described by Secco and Mattos.46 Among many architectures that were evaluated, the multilayer feed-forward ANN was found to be best suited for non-linear problems with dozens of variables as is the present case. This type of network can approximate any function to any desired degree of accuracy, provided it has enough neurons in the hidden layers. Regarding estimation of drag coefficient, three dedicated ANNs were designed to estimate the three drag components, zero-lift, induced, and wave drag. This resulted in considerably more accuracy than the approach of employing a single ANN for the drag estimation task. Approximately 110,000 different wing configurations were employed for training and validation purposes. For the generation of the database of this size, a full potential aerodynamic

Table 7 Parameter 

Parameters used for normalization in Eq. (29). Value

BPR

4.6911

OPR

25.4000





De (m) le (m)

1.7906

Tnet (kN)

3.3276 148.1217

FF (kg/s)

464.7333





code was used. The potential module is coupled with an integral boundary layer program that calculates the viscous effects at prescribed stations along wingspan. The accuracy of drag estimation by the ANN system proved to be outstanding, recording an average error of 3 drag counts in high-Mach regimes when compared with the results from the full potential code. This is typically the error obtained with flight test data and those from large subsonic wind tunnels. If the flow is subsonic over the entire airplane surface, the average estimation error of the ANN lies below 0.1 drag counts. Input for the computations are wing geometric parameters such as aspect ratio, leading-edge sweepback angle, taper ratio, incidences, dihedral angles, location of the trailing-edge break station as well as airfoil parameters from three wing stations. An additional 3% on total CD is applied to consider miscellaneous drag. Induced drag is adjusted for the presence of winglets as per the study of De Mattos et al.63

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization Table 8 Mass error estimation for some known engines.

1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065

Engine

Deviation (%)

CF6-50C JT8D-219 GE CF-34-10A R&R RB211-535C Trent 800–875 Williams FJ-44 Pratt & Whitney PW2040 GE-90/77B R&R Tay 620

2.55 0.74 6.48 0.97 3.12 4.29 0.44 0.31 2.65

A verification of the accuracy and capability of the ANN estimation of the drag divergence is shown in Fig. 7. Two airplane configurations were selected from the database for further analysis (not part of the ANN training set) presenting different drag behavior over Mach number. Fig. 7 shows that the delay of the drag divergence with the increase of the wing sweep angle was correctly captured by the drag-predictor ANN for the two configurations. In addition, an airliner with 93.5 m2 wing reference area, designated ITA107, was also chosen to evaluate the accuracy of the designed ANNs in predicting drag and lift coefficients. Wing geometric characteristics and flight condition information are given in Table 9. The three-view of the airplane are shown in Fig. 8. The coordinates of the three basic airfoils used in the wing definition of the airplane under consideration were read from files. Airfoils of the root, break, and tip stations present a maximum relative thickness of 12.3%, 12.3%, and 10.9%, respectively. There is then a need for an optimization problem to fit Sobieczky polynomials to these geometries. This was carried out with the fsolve optimization tool from MATLABÒ. Fig. 9 shows the original wing airfoil geometries and polynomial fittings. Some small discrepancies exist between the original and calculated geometry of the tip airfoil (vertical and horizontal dimensions are normalized regarding the mean aerodynamic chord of each airfoil). Table 10 shows a comparison between the ANN and CFD results. The overall drag differs by one drag count only. The wave drag coefficient recorded the highest difference between the neural network and the full potential code, which was of

Table 9

Characteristics of ITA107 airliner.

Parameter

Value

Incidence angle at root station (o) Incidence angle at break station (o) Incidence angle at tip station (o) Wing reference area (m2) Wing aspect ratio Wing taper ratio Quarter-chord wing sweepback angle (o) Maximum Operating Mach number Service ceiling (ft) Break station location (fraction of semispan)

2 0 2 93.5 8.43 0.235 17.5 0.77 35,000 0.39

Fig. 8

Three-view of airliner considered for a test case.

Fig. 9

Fig. 7 Comparison between ANN overall drag predictions and CFD results for two airplanes with different wing sweepback angles (Altitude = 10.5 km, a = 1o.).

15

Wing airfoils of ITA107.

three drag counts. The ANN drag estimation provided average error of 3 drag counts when compared with the full potential code results. At the Mach number of 0.77 and 1° angle of attack, the streamlines on the wing upper side as calculated by the full potential code indicate attached flow close to the fuselage and at the wingtip. However, there is a separation region close to the trailing edge along a great portion of semis-

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1066 1067 1068 1069 1070 1071 1072

CJA 1432 20 November 2019

No. of Pages 30

16

J. ALEXANDRE et al.

1097

pan, caused by shock waves. It is observed that in some wing parts the flow experiences a reattachment to wing surface and suffers another separation. This is indeed a complex flow pattern, which was well captured by the ANN prediction. This example is an excellent boost for the ANNs designed in the present work. Despite the complexity of the airflow at the cruise condition over the test case airliner, ANNs could predict the drag coefficients. High-lift systems have a major influence on the sizing, economics, and safety of transport airplanes. Although high-lift systems are complex and costly, they are a necessity to allow airplanes to take off and landing on runways of acceptable length without penalizing the cruise efficiency significantly.64 Several analytical methods that both account for stall effects and enable the prediction of the maximum lift coefficient were discussed and a trade-off between the methods was conducted.65 From this trade-off, it was found that both the pressure difference rule and the so-called ‘‘critical section” are good option in terms of accuracy and versatility. The critical section method was incorporated in the present design framework. The XFOIL panel code66 for determining an airfoil’s maximum lift coefficient for a set of wing sections was combined with a wing-fuselage full potential code with viscous corrections for the estimation of maximum lift coefficient of the clean-wing configuration.67

1098

4. Case study

1099

The case study determines the optimum air transport network within a wide operational area in Brazil covered by its twenty major airports. Distances dij (used in the network optimization module) and true headings Hij (used in the mission analysis module) between city pairs are determined via haversine formula for loxodromic routes,68 according to   LATj  LATi a ¼ sin2 2   LONj  LONi ð30Þ þ cosðLONi ÞcosðLONj Þsin2 2

1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096

1100 1101 1102 1103 1104 1105

1107

1110

rffiffiffiffiffiffiffiffiffiffiffi a c ¼ 2arctan 1a

ð31Þ

1111 1113

dij ¼ 1:03Rc

ð32Þ

1108

 hij ¼ arctan

1114 1115 1116 1117 1118 1119 1120 1121 1122

Table 10 Predicted and calculated coefficient values by ANN and full potential code. Predicted coefficient (counts)

ANN

Full potential code

Deviation

CD0 CD ind CD wave CD CL

65 55 69 189 0.367

66 56 66 188 0.382

1,5% 1,8% 4,5% 0,53% 3,9%

is assumed that the airline operating this network has 20% of passenger market share and does not actuate in the cargo segment. Table A5 (see Appendix A) shows the estimated daily passenger demand, considering this share. The proposed demand model (see Eq. (4)) was calibrated using the city pair demands data related to the 20 busiest Brazilian routes in 2014, 2015 and 2016, extracted from the Brazilian Civil Aviation Authority (ANAC) statistical reports.70 A log-linear regression model was applied to calibrate the exponents for the proposed equation. Values obtained were: K0 = 3.5770, K1 = 0.4157, K2 = 0.0388, K3 = 0.1643 and K4 = 0.1331. The Pearson coefficient associated with this regression was 0.63, which was considered reasonable for air transportation analysis. Average delays at each airport are considered by the model proposed by Newell71 as function of runway configuration and capacity: for departure delays, which occur on ground, 10 minutes for airports with two or more active runways (for SBGR, SBGL and SBBR) and 5 minutes for airports with 1 active runway (for SBCT, SBPA and SBSV). Arrival delays, associated with terminal holdings and cruise speed reductions, are assumed to be 5 minutes at airports with two or more active runways and 3 minutes for airports with one active runway. Airline operational parameters assumed in this study are listed in Table 11. Also, the revenue to ticket price ratio (k1) and cost to DOC ratio (k2) are assumed as 1.1 and 1.3 respectively. A reference airplane was selected for comparative analysis (see Fig. 10). It is a two-engine airliner featuring underwing engine configuration and it can accommodate 76 passengers in a single class at 32 inch seat pitch. It is designed for a range of 2000n mile, carrying full passenger load and cruising at 35,000 ft at Mach 0.78. The main configuration characteristics are shown in Table 12.

 sinðLONj  LONi ÞcosðLATi Þ 180  cosðLATi ÞsinðLONj Þ  sinðLONi ÞcosðLATj ÞcosðLONj  LONi Þ p

where R is earth’s average radius, assumed as 3458 n mile A bias of 3% is applied on all great circle distances to accommodate airway-route differences. Tables A1 and A2 (see Appendix A) show the calculated route distances and true headings between airports. The airport data used in the mission analysis computations was extracted from the Brazilian Aeronautical Information Publication (AIP).69 Tables A3 and A4 (see Appendix A) show the airport data and associated city econometric parameters used in the gravitational model. It

1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155

ð33Þ

5. Results and discussion

1156

Exactly 528 generations were part of the simulation carried out with the genetic algorithm MOGA-II already implemented in modeFrontierÒ. Fig. 11 shows the feasible individuals from the optimization run and the resulting Network Profit (NP) as function of Network DOC (NDOC). Individuals that maximize NP with the lowest possible NDOC are marked in green

1157

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1158 1159 1160 1161 1162

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization Table 11

1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187

Airline operation parameters.

Table 12

17

Baseline airplane characteristics.

Parameter

Value

Parameter

Value

Average daily aircraft utilization (h) Average turnaround time (min) Takeoff and initial climb out fuel allowance (kg) Takeoff and initial climb out time allowance (min) Approach and landing fuel allowance (kg) Approach and landing time allowance (min) Go around fuel allowance (kg) Go around time allowance (min) Average taxi out time (from gate to runway threshold) Average taxi in time (from runway exit to gate) Total passenger weight (including baggage) Average ticket price ($) Average inflight delay cost ($/min) Fuel cost (US$/kg) Total operational costs/direct operational costs ratio k2 Total revenue/ ticket revenue ratio k1 Average captain annual salary ($) Average first officer annual salary ($) Average flight attendant annual salary ($)

12 30 200 3 100 2 200 3 10 5 110 200 20 1.7 1.3 1.1 100,000 85,000 65,000

MTOW (kg) OEW (kg) MZFW (kg) MLW (kg) Fuel Capacity (kg) Passenger Capacity (single class) Seating arrangement Fuselage length (m) Fuselage width (m) Fuselage height (m) Wing area (m2) Wing aspect ratio Wing taper ratio Wing sweepback angle (°) Engine Fan Diameter (m) Engine bypass ratio Engine Inlet Turbine Temperature (K)

38,790 21,800 31,500 34,100 8428 78 4 seats/1 aisle per row 31.68 2.89 3.29 72.72 8.6 0.44 23.5 1.30 5.00 1240

in a Pareto-type front presentation. The unfeasible individuals, marked in yellow cross, correspond to the designs where aircraft selected in different groups have close passenger’s capacity (within 5 units range) and therefore are not considered in the analysis. Table 13 shows relevant characteristics of the 11 individuals in the front resulted from the optimization task. Main network and aircraft design characteristics are displayed for reference (MTOW, wing area, aspect ratio, engine by-pass ratio and engine fan diameter). Table 14 presents the main statistics of the Pareto-type front, showing the variation of each fleet when compared with the baseline aircraft. It is noticeable that average aircraft selected in the three fleets present significantly lower ranges than the baseline, which suggests that the last one may not be the optimal design for the region in study. The Pearson’s correlation matrix is shown in Fig. 12 considering the design variables related to the Group 1 fleet and objective functions. The correlation coefficient, shown on each cell of the matrix, is a measure of the linear correlation between two pairs variables in the whole dataset, calculated as the covariance of the two variables in all designs divided by the product of their standard deviations. It ranges between +1 and 1, where 1 is total positive linear correlation (red color cells), 0 is no linear correlation, and 1 is total negative linear correlation (blue color cells).

Fig. 10

Fig. 11

Pareto-type front and dominated individuals.

As expected, the higher positive values for MTOW are registered by wing area, design range, and number of passengers. Concerning the main objective function, it is noticeable that network profit presents the strongest negative dependency on range and positive dependency on number of passengers, meaning that the model captured the payload-range tradeoff as determinant characteristics on the airline profit. On the Network DOC side, the strongest positive dependencies are found in the variables related to the increase of the weight (therefore

Reference airplane illustration.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1188 1189 1190 1191 1192 1193 1194 1195 1196

CJA 1432 20 November 2019

No. of Pages 30

18

J. ALEXANDRE et al.

Table 13 Design ID

PAX

Design Range (n mile)

MTOW (kg)

Wing Area (m2)

Wing AR

De (m)

BPR

Number of connected arcs

Network DOC ($/n mile)

Network profit (105$/pax n mile)

Reference airplane

78

2000

38,790

72.72

8.6

1.42

5.00

498

9.95

5.45

24

AC1 AC2 AC3 AC1 AC2 AC3 AC1

71 81 91 71 84 91 70

1107 1115 1079 1107 1014 1079 1048

31,488 34,837 36,830 31,488 34,885 36,830 30,467

85.77 72.34 97.09 85.77 79.85 97.09 82.22

7.6 7.6 8.2 7.6 8.7 8.2 7.7

1.31 1.34 1.28 1.31 1.36 1.28 1.25

5.61 4.80 5.54 5.61 4.93 5.54 5.73

164 158 178 164 172 178 165

8.82

5.95

8.71

5.66

8.68 min NDOC

5.70

AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3 AC1 AC2 AC3

84 91 72 85 92 72 84 91 70 82 91 70 81 91 77 85 91 72 82 91 72 84 93 72 84 91

1014 1079 1111 1293 1216 1111 1014 1079 1048 1136 1079 1111 1130 1079 1462 1293 1079 1111 1133 1187 1111 1133 1187 1111 1133 1079

34,885 36,830 30,671 38,070 37,146 31,237 34,885 36,830 30,467 35,711 36,830 30,671 37,059 36,830 34,497 38,070 36,070 31,327 36,659 36,864 31,237 36,659 35,864 31,327 36,659 36,830

79.85 97.09 81.15 78.88 91.66 81.15 79.85 97.09 82.22 95.36 97.09 81.15 100.00 97.09 83.27 78.88 97.09 81.15 95.36 97.09 81.15 92.02 85.85 81.15 92.02 97.09

8.7 9.2 7.7 8.3 8.2 7.7 8.7 8.2 7.7 8.2 8.2 7.7 9.0 8.2 7.6 8.3 8.2 7.7 8.2 8.2 7.7 8.0 7.8 7.7 8.0 8.2

1.36 1.28 1.23 1.40 1.24 1.36 1.36 1.28 1.25 1.30 1.28 1.23 1.27 1.28 1.32 1.40 1.28 1.23 1.30 1.28 1.36 1.35 1.28 1.36 1.35 1.28

4.93 5.54 5.10 4.97 5.11 5,0.32 4.93 5.54 5.73 4.91 5.54 5.10 5.48 5.54 5.44 4.97 5.54 5.10 4.91 5.54 5.32 5.77 4.80 5.32 5.77 5.54

172 178 164 160 178 164 172 178 165 162 178 164 158 178 164 160 178 164 162 178 164 160 177 164 160 178

8.94

6.05

8.71

5.73

8.76

5.80

8.83

6.02

9.13

6.22 max NP

8.77

5.95

8.91

6.06

8.86

6.04

128

168

224

238

239

240

276

288

302

303

Table 14

1197 1198 1199

Individuals selected in Pareto-type front resulted from optimization task.

Pareto-type front statistics.

Aircraft & Network

Seat capacity

Design range (n mile)

MTOW (kg)

Wing area (m2)

Wing AR

De (m)

BPR

Network number of connected arcs

Network density

Baseline Aircraft 1 Average Std deviation 95% 2 Average Std deviation 95% 3 Average Std deviation 95%

78 72 2 75 83 2 86 91 1 92

2000 1133 119 1328 1128 102 1296 1104 52 1189

38,790 31,391 1038 33,097 35,841 1240 37,880 36,855 84 36,994

72.72 82.69 1.85 85.74 84.03 9.00 98.84 95.90 3.23 101.22

8.6 7.7 0.1 7.9 8.4 0.4 9.1 8.2 0.1 8.4

1.42 1.30 0.05 1.39 1.34 0.04 1.40 1.28 0.00 1.28

5.00 5.41 0.26 5.83 5.06 0.31 5.57 5.42 0.26 5.85

164 164 1 165 164 6 173 178 0 178

0.43 0.43 0.00 0.43 0.43 0.01 0.45 0.47 0.00 0.47

increase of fuel consumption) such as MTOW, number of passengers and wing area. These observations are also applicable to Groups 1 and 2 fleets.

The Pareto-type front data shows two remarkable design extremes: maximum network profit (design #276, 6.22  105 $/ pax nautical mile) and minimum network DOC (design

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1200 1201 1202

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization

Fig. 12

1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233

19

Correlation matrix of analysis variables (Pearson analysis).

#168, 8.68 $/n mile). Figs. 13 and 14 show the resulting routes from the maximum network profit and minimum network DOC for the three fleets respectively. It may be noticed that the aircraft with lower capacities presented similar route structures in both scenarios. This may be verified on Tables B1–B3 and Tables B4–B7 (see Appendix B) where the resulting frequencies, assigned for each aircraft type on each route, are shown for maximum network profit and minimum network DOC scenarios. Tables B4 and B8 show the common citypair connections for the three fleets in these scenarios (where one means the existing connection and zero means no connection). In both tables, it may be observed that 154 city-pair connections (40.5% of the total possible) are shared among the three fleets. The optimization results related to the minimum network DOC scenario are shown in Table C1 (Appendix C). It can be verified that the best aircraft fleets resulted in design ranges (1462 n mile, 1293 n mile and 1079 n mile respectively) lower than the maximum sector distance possible (POA-MAO/ MAO-POA, 1746 n mile). In this scenario, the maximum connected route distance obtained is 1285 n mile, related to the POA-SSA/SSA-POA sectors. This means that the optimum aircraft selected from the database are the ones in which fuel capacity is just enough to accomplish the missions in their related networks. This is the point where DOC minimization objective achieves maximum influence on the optimization process and seeks to not sacrifice fuel consumption (therefore lowering the DOC) on the trade for the incremental number of passenger’s, whose consequence is always the increase structural weights with the fuselage size increase. The reduction of fuel capacity (and therefore maximum range) seems to be

Fig. 13

the strategy resulted in by the algorithm to hold the structural weight growth as consequence of the increasing number of passengers. In fact, it is observed that all three fleets resulted in lower MTOWs than the baseline aircraft, even though carrying more passengers on fleets #2 and #3. Because of these range limits, to reach the north/northeast cities, the consequent settlement of hub at SSA is identified as a natural accumulator of departures and arrivals. As net effect, it is observed that the total network DOC obtained was 12.8% lower than and the total fleet size was 19.8% higher than the one related to the baseline aircraft. In addition, the cost per passenger dropped by 10.5%, due to increased number of passengers transported in the network. Results for maximum network profit design scenario are shown in Table C2 (see Appendix C). In this case, the DOC minimization objective also led the effect of reduced design ranges to this extreme, not connecting routes longer than 1079 n mile. As in the minimum DOC extreme, a hub in SSA is also identified to cope with the range limitations of the fleets. However, in this extreme, the influence of profit maximization has a strong push on the optimization process, leading the increase of aircraft capacity for fleets #2 and #3 to #85 and #91 respectively (remaining below the 130-seat boundary). In this case, to accommodate more passengers in the cabin, aircraft designs with wider fuselages are obtained providing 5 and 6 seat row configurations. The net result recorded a relative increase of OEW and slight reduction of design range when compared with the DOC minimization. Network profit in this scenario is increased by 14.2% regarding the baseline aircraft network, also bringing a significant reduction of about 8.2% on DOC. For both extremes, con-

Routes obtained from maximum network profit.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264

CJA 1432 20 November 2019

No. of Pages 30

20

J. ALEXANDRE et al.

Fig. 14

Routes obtained from minimum network DOC.

1289

sidering that the trip profit is also dependent on DOC, a slight increase on wing areas and wing sweep angle were observed, revealing a trend from the algorithm to improve the specific range. Engines also slightly increased bypass ratios (reaching a maximum of 5.5), to minimize fuel consumption and decrease DOC. In addition, the cost per passenger dropped by 10.6%, due to increased number of passengers transported in the network. It is worth mentioning that in all fleets the wing aspect ratio relays within reasonable boundaries (between 7.6 and 9.2) in the Pareto front designs. In fact, for this class of regional airplanes, with passenger capacity topping 130 seats and maximum 2000 n mile range, no high-tech concept such as extremely flexible wings or truss-braced configurations seems to be necessary. It is also noticeable that most of wing sweepback angles produced are higher than in the baseline aircraft (23.5), suggesting that the average cruise speed, related to maximum Ma‧CL/CD condition, is faster than the one related to the last one (approximately Mach 0.78). This means that a flight time minimization component, embedded in the DOC optimization, might be pushing the results instead of minimization of fuel consumption. This is a consistent result since all aircraft have the same wing airfoils (including the baseline one) and, at higher speeds, a way to minimize the wave drag is to increase the sweepback angle.

1290

6. Conclusions

1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288

1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306

An innovative design optimization framework for designing optimal aircraft fleets, composed of three aircraft types, and corresponding networks were presented. The framework maximizes the total Network Profit (NP), satisfying given city-pair passenger demands. A test case was run for a Brazilian aerial network connecting 20 cities. The goal is to provide an enhanced tool for decision makers to assist in several aspects, such as redesign aerial networks and to properly purchase airplanes tailored to their networks. Optimal airline network covering a certain geographical area integrated with the best suited fleet composed of three airplane types can be determined. Passenger demands among the twenty main Brazilian airports were assigned by a gravitational model. Highly detailed and realistic airplanes are selected from three databases. A genetic algorithm cares for the maximiza-

tion of network profit and minimization of its associated direct operating cost. In the calculation process, for a triplet of aircraft, the optimum network is determined in a secondary optimization process using linear programming. The optimum networks present the highest profit complying with calculated passenger demands, aircraft characteristics, airplane capacity and range. A complete mission performance algorithm was designed and is applied with the objective to evaluate fuel burn and time for each sector, essential parameters for the network DOC calculation. An accurate ANN system is employed for the estimation of aerodynamics characteristics, enabling faster simulation times and realistic mission performance calculations. During the optimization process, the aerodynamic and propulsion characteristics of the selected aircraft are driven towards the best specific range, considering the optimized air transport network. The classical approach on aircraft design frequently considers only the minimization of DOC for a mission. In the present study, it becomes evident that the network profit can be considered a suitable candidate as design objective, if the associated NDOC is contemplated in the analysis, as is the case enabled here by the Pareto-type front presented. In fact, profit is an economic parameter that has been used in the air transport industry as measurement of airline efficiency and has special significance for decisions focusing on financing rather than DOC. However, its maximization leads to bigger aircraft, with increased seat capacities, as can be verified in the Pareto-type front solutions, which may bring other non-operational finance impacts for the airlines, such as increase of inventory costs and airport infrastructure and compatibility issues. The optimization framework effectiveness was ascertained by analyzing the two extremes solutions of the Pareto-type front. These solutions present 14.2% increase on the network profit and 12.8% reduction on network DOC, when compared with that of the baseline aircraft (78 passengers, twin regional jet transport, 2000 n mile design range). Finally, we suggest future research be conducted on the network optimization considering a larger number of airports and contemplating a more diverse aircraft database. Noise and emissions constraints for some airports can be enforced without much difficulty. The cruise profile can be improved considering, for instance, step cruise and air traffic control constraints.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization 1350

21

Appendix A. Network Data

1351

Table A1

Network route distances (n mile).

Departure Arrival Airport (j) Airport (i) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI

SSA VIX

AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

0 918 719 964 675 1145 1228 455 817 948 809 1492 120 333 1428 220 821 680 142 605

142 946 603 823 534 1004 1087 565 677 807 690 1462 261 472 1285 361 680 734 0 469

Table A2

Network route true headings -Hij (°).

918 0 896 1380 1161 1494 1626 632 1362 1369 944 723 928 863 1777 933 1369 273 946 1268

719 896 0 486 330 602 731 941 509 476 90 1083 831 985 893 920 517 851 603 525

964 1380 486 0 291 184 271 1320 200 16 457 1504 1084 1289 466 1184 203 1309 823 421

675 1161 330 291 0 470 560 1034 201 275 360 1413 794 998 757 895 208 1054 534 218

1145 1494 602 184 470 0 137 1486 375 200 550 1534 1264 1467 297 1365 376 1449 1004 602

1228 1626 731 271 560 137 0 1591 422 287 684 1668 1347 1556 202 1447 421 1572 1087 654

455 632 941 1320 1034 1486 1591 0 1210 1305 1026 1329 393 242 1782 349 1215 360 565 1025

817 1362 509 200 201 375 422 1210 0 188 517 1584 933 1149 624 1034 8 1252 677 232

948 1369 476 16 275 200 287 1305 188 0 450 1500 1068 1273 482 1168 191 1296 807 406

809 944 90 457 360 550 684 1026 517 450 0 1068 920 1075 834 1010 524 920 690 570

1492 723 1083 1504 1413 1534 1668 1329 1584 1500 1068 0 1543 1539 1746 1578 1592 977 1462 1598

120 928 831 1084 794 1264 1347 393 933 1068 920 1543 0 225 1547 101 937 673 261 717

333 863 985 1289 998 1467 1556 242 1149 1273 1075 1539 225 0 1754 138 1152 591 472 937

1428 1777 893 466 757 297 202 1782 624 482 834 1746 1547 1754 0 1648 623 1743 1285 856

220 933 920 1184 895 1365 1447 349 1034 1168 1010 1578 101 138 1648 0 1037 668 361 816

821 1369 517 203 208 376 421 1215 8 191 524 1592 937 1152 623 1037 0 1259 680 233

680 273 851 1309 1054 1449 1572 360 1252 1296 920 977 673 591 1743 668 1259 0 734 1119

605 1268 525 421 218 602 654 1025 232 406 570 1598 717 937 856 816 233 1119 469 0

Departure Arrival Airport (j) Airport (i) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI

SSA VIX

AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

235.5 160.4 95.1 59.3 61.7 61.5 54.9 200.8 48.1 59.2 93.0 134.4 238.5 225.8 56.6 237.7 47.5 172.3 0.0 37.6

0.0 151.8 88.0 59.0 60.5 60.9 55.1 190.7 49.5 58.8 87.0 128.9 242.9 221.9 56.6 239.4 49.0 161.6 55.8 41.9

330.5 0.0 17.3 14.7 5.9 20.2 18.2 303.3 5.9 14.2 21.8 98.6 322.5 308.9 22.6 316.9 5.8 305.3 339.1 357.0

265.5 197.4 0.0 11.0 334.9 26.1 21.4 237.3 347.2 9.5 77.9 154.8 261.5 251.3 30.1 259.0 347.1 215.1 272.7 321.4

236.1 195.1 191.4 0.0 232.0 69.8 41.8 221.3 275.2 241.2 180.9 166.0 236.0 231.6 50.9 236.1 277.2 206.2 236.7 260.6

238.7 186.7 156.1 53.0 0.0 59.7 47.5 219.1 8.8 52.5 141.8 155.3 238.6 232.4 51.8 238.4 7.9 199.6 240.1 301.6

237.1 200.0 205.7 248.8 237.7 0.0 2.7 223.7 261.6 248.0 198.2 172.1 236.7 232.7 38.5 236.7 262.8 210.3 237.9 256.1

231.2 198.1 201.2 221.0 225.7 182.9 0.0 219.8 242.5 221.9 194.9 172.6 231.3 228.1 61.3 231.7 243.5 207.4 231.3 243.9

10.5 123.8 58.9 43.3 40.2 46.4 42.6 0.0 35.2 43.0 60.4 110.1 355.9 324.5 44.9 342.3 34.9 122.5 20.7 28.1

227.7 187.0 168.8 96.6 189.1 84.1 64.8 214.1 0.0 99.3 158.6 159.4 228.8 225.2 64.5 229.6 344.8 197.9 226.6 248.6

236.0 194.6 190.0 61.2 231.5 69.2 42.8 221.1 278.0 0.0 179.1 165.4 236.0 231.5 51.2 236.1 280.1 205.7 236.6 261.4

264.1 201.7 257.6 0.0 320.2 18.2 14.6 238.5 336.6 358.2 0.0 159.2 260.5 251.3 25.0 258.3 336.7 218.4 270.2 312.7

306.0 278.1 332.8 342.8 332.1 349.3 349.5 288.8 335.6 342.2 337.3 0.0 301.5 293.5 355.5 298.6 335.6 285.0 311.3 327.7

63.1 143.8 84.2 59.1 60.6 60.8 55.4 176.2 50.9 59.0 83.6 124.1 0.0 210.5 56.7 234.2 50.5 150.9 59.0 45.1

42.2 129.8 73.7 54.6 54.4 56.5 52.1 144.7 47.2 54.4 74.0 115.5 30.6 0.0 53.6 14.2 46.9 131.7 46.3 42.0

231.5 201.9 208.8 228.8 228.8 217.6 240.1 221.2 241.0 229.1 204.3 178.1 231.4 228.5 0.0 231.7 241.6 210.3 231.8 242.1

59.7 138.0 81.7 59.4 60.5 60.9 55.9 162.6 51.9 59.2 81.4 121.1 54.4 194.2 57.1 0.0 51.5 142.7 58.3 46.9

227.2 186.9 168.7 98.6 188.2 85.2 65.8 213.8 164.9 101.4 158.7 159.5 228.4 224.9 65.2 229.2 0.0 197.7 226.0 246.7

340.7 125.4 35.7 26.7 19.6 31.5 28.6 302.1 17.6 26.3 39.3 105.8 330.0 311.0 32.3 321.9 17.4 0.0 351.5 8.7

221.1 178.6 143.8 83.0 122.8 79.5 67.3 207.8 69.7 83.7 135.5 151.8 224.0 220.9 66.8 225.6 67.8 189.5 217.0 0.0

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

22 Table A3

J. ALEXANDRE et al. Airport data.

Airport code (IATA)

Airport location/name

Reference latitude (°)

Reference longitude (°)

Reference elevation (ft)

Magnetic variation (°)

Average departure delay (min)

Average arrival delay (min)

AJU BEL BSB

Aracaju/Santa Maria Bele´m/Val de Caes Intl Brası´ lia/Jucelino Kubitscheck Intl Sao Paulo/Congonhas Belo Horizonte/Confins Intl Curitiba/Afonso Pena Intl Floriano´polis/Hercı´ lio Luz Intl Fortaleza/Pinto Martins Rio de Janeiro/Tom Jobim (Galea˜o) Intl Sa˜o Paulo/Andre´ Franco Montoro (Guarulhos) Intl Goiaˆnia/Santa Genoveva Eduardo Gomes/Manaus Intl Maceio´/Zumbi dos Palmares Natal/Sa˜o Gonc¸alo do Amarante Intl Porto Alegre/Salgado Filho Intl Recife/Guararapes Intl Rio de Janeiro/Santos Dumont Sa˜o Luiz/Marechal Cunha Machado Intl Salvador/Antoˆnio Carlos Magalha˜es Intl Vito´ria/Goiabeiras

10.9840 1.3793 15.8635

37.0703 48.4763 47.9276

23 54 3497

23 19 20

2 3 10

2 3 5

23.6267 19.6338 25.5285 27.6705

46.6554 43.9689 49.1758 48.5472

2631 2715 2988 20

20 21 18 17

3 3 5 2

3 3 5 2

3.7763 22.8089

38.5326 43.2436

82 28

21 21

2 10

2 5

23.4321

46.4695

2459

20

10

5

16.6320 3.0386 9.5108 5.9114

49.2207 60.0497 35.7917 35.2477

2450 264 387 169

19 14 22 22

2 2 2 2

2 2 2 2

29.9944

51.1714

11

15

3

3

8.1268 22.9105

34.9230 43.1631

33 11

23 21

2 3

2 3

2.5854

44.2341

178

20

2

2

12.9110

38.3310

64

23

2

2

20.2581

40.2864

11

23

2

2

CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

Table A4

Econometric data.

Airport Location/Name

Population (2016)

Catchment Radius (km)

Buying Power Index (2016)

GDP 2016 (106 BRL)

Aracaju/Santa Maria Bele´m/Val de Caes Intl Brası´ lia/Jucelino Kubitscheck Intl Sao Paulo/Congonhas Belo Horizonte/Confins Intl Curitiba/Afonso Pena Intl Floriano´polis/Hercı´ lio Luz Intl Fortaleza/Pinto Martins Rio de Janeiro/Tom Jobim (Galea˜o) Intl Sa˜o Paulo/Andre´ Franco Montoro (Guarulhos) Intl Goiaˆnia/Santa Genoveva Eduardo Gomes/Manaus Intl Maceio´/Zumbi dos Palmares Natal/Sa˜o Gonc¸alo do Amarante Intl Porto Alegre/Salgado Filho Intl Recife/Guararapes Intl Rio de Janeiro/Santos Dumont Sa˜o Luiz/Marechal Cunha Machado Intl Salvador/Antoˆnio Carlos Magalha˜es Intl Vito´ria/Goiabeiras

641,523 1,446,042 2,977,216 12,038,175 2,523,794 1,893,997 477,798 2,609,716 6,498,837 12,038,175

100 200 100 20 200 100 100 100 100 100

36.00 20.00 37.65 36.68 30.85 43.74 34.58 36.00 33.68 36.68

14,893,787 28,706,165 197,432,059 628,064,882 87,656,760 78,892,229 17,328,527 56,728,828 299,849,795 628,064,882

1,021,709 2,094,391 1,021,709 877,662 1,481,019 1,625,583 6,498,837 1,091,868 2,938,092 363,140

100 200 100 100 100 100 20 100 100 100

37.00 20.00 36.00 36.00 41.31 36.38 33.68 25 24.94 30

46,094,735 67,572,523 18,302,279 19,076,030 63,990,644 50,688,395 299,849,795 26,326,087 56,624,041 23,370,919

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization Table A5

23

Estimated passengers demand per day (20% Market share).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

1352

0 324 420 723 385 464 302 450 524 637 345 351 307 328 434 343 594 321 347 220

324 0 411 718 383 465 295 444 525 633 333 278 381 352 429 394 596 256 401 223

420 411 0 834 443 537 357 627 623 734 325 427 503 479 514 525 707 420 533 273

723 718 834 0 720 760 517 1084 910 0 668 736 861 822 781 898 1033 734 917 438

385 383 443 720 0 485 318 586 507 631 362 398 462 444 468 484 577 393 477 222

464 465 537 760 485 0 297 691 622 678 429 473 551 524 458 574 705 473 600 290

302 295 357 517 318 297 0 450 407 460 286 300 359 341 284 374 460 303 384 188

450 444 627 1084 586 691 450 0 795 955 512 496 517 452 642 525 901 425 599 339

524 525 623 910 507 622 407 795 0 796 504 543 626 600 604 654 0 537 658 299

637 633 734 0 631 678 460 955 796 0 588 649 759 724 692 791 904 647 808 385

345 333 325 668 362 429 286 512 504 588 0 343 411 392 412 429 572 342 438 223

351 278 427 736 398 473 300 496 543 649 343 0 413 385 434 428 616 307 431 233

307 381 503 861 462 551 359 517 626 759 411 413 0 365 514 363 710 376 441 263

328 352 479 822 444 524 341 452 600 724 392 385 365 0 487 353 680 345 445 255

434 429 514 781 468 458 284 642 604 692 412 434 514 487 0 534 684 439 560 275

343 394 525 898 484 574 374 525 654 791 429 428 363 353 534 0 742 388 475 277

594 596 707 1033 577 705 460 901 0 904 572 616 710 680 684 742 0 609 746 339

321 256 420 734 393 473 303 425 537 647 342 307 376 345 439 388 609 0 407 229

347 401 533 917 477 600 384 599 658 808 438 431 441 445 560 475 746 407 0 271

220 223 273 438 222 290 188 339 299 385 223 233 263 255 275 277 339 229 271 0

Appendix B. Network frequencies (after optimization)

Table B1

Maximum network profit – frequencies per sector (Fleet#1–77 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 3 BEL 0 0 0 0 0 BSB 3 0 0 5 3 CGH 0 0 5 0 5 CNF 3 0 3 5 0 CWB 0 0 4 5 3 FLN 0 0 3 4 2 FOR 3 3 0 0 0 GIG 0 0 4 5 3 GRU 0 0 5 0 4 GYN 0 0 0 4 3 MAO 0 2 0 0 0 MCZ 2 0 0 0 0 NAT 2 0 0 0 0 POA 0 0 0 5 3 REC 3 0 0 0 0 SDU 0 0 4 5 4 SLI 2 2 0 0 0 SSA 3 0 4 0 3 VIX 2 0 2 3 2 IDENTIFIED HUBS: CGH/SDU/SSA

0 0 4 5 3 0 2 0 4 4 3 0 0 0 3 0 4 0 0 2

0 0 3 4 2 2 0 0 3 3 2 0 0 0 2 0 3 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 4 3 0 4 0 3 4 0

0 0 4 5 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

0 0 5 0 4 4 3 0 5 0 4 0 0 0 4 0 5 0 0 3

0 0 0 4 3 3 2 0 3 4 0 0 0 0 0 0 4 0 3 2

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 0 0 0 4 0 0 0 0 0 3 0 3 0 3 3 2

2 0 0 0 0 0 0 3 0 0 0 0 3 0 0 3 0 3 3 0

0 0 0 5 3 3 2 0 4 4 0 0 0 0 0 0 4 0 0 0

3 0 0 0 0 0 0 4 0 0 0 0 3 3 0 0 0 3 3 0

0 0 4 5 4 4 3 0 0 5 4 0 0 0 4 0 0 0 5 3

2 2 0 0 0 0 0 3 0 0 0 0 3 3 0 3 0 0 3 0

3 0 4 0 3 0 0 4 4 0 3 0 3 3 0 3 5 3 0 2

2 0 2 3 2 2 0 0 2 3 2 0 2 0 0 0 3 0 2 0

1353

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

24 Table B2

J. ALEXANDRE et al. Maximum network profit – frequencies per sector (Fleet#2–85 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 3 BEL 0 0 0 0 0 BSB 3 0 0 5 3 CGH 0 0 5 0 4 CNF 3 0 3 4 0 CWB 0 0 3 4 3 FLN 0 0 2 3 2 FOR 3 3 0 0 0 GIG 0 0 4 5 3 GRU 0 0 4 0 4 GYN 0 0 0 4 2 MAO 0 2 0 0 0 MCZ 2 0 0 0 3 NAT 2 0 0 0 0 POA 0 0 0 4 3 REC 2 0 0 0 0 SDU 0 0 4 5 3 SLI 2 2 0 0 0 SSA 2 0 3 0 3 VIX 0 0 2 3 0 IDENTIFIED HUBS: CGH//GIG/SDU

Table B3

0 0 3 4 3 0 2 0 4 4 3 0 0 0 3 0 4 0 0 2

0 0 2 3 2 2 0 0 3 3 2 0 0 0 2 0 3 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 4 0

0 0 4 5 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

0 0 4 0 4 4 3 0 5 0 4 0 0 0 4 0 5 0 0 3

0 0 0 4 2 3 2 0 3 4 0 0 0 0 0 0 3 0 3 0

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 3 0 0 3 0 0 0 0 0 2 0 2 0 2 3 2

2 0 0 0 0 0 0 3 0 0 0 0 2 0 0 2 0 2 3 0

0 0 0 4 3 3 2 0 4 4 0 0 0 0 0 0 4 0 0 0

2 0 0 0 0 0 0 3 0 0 0 0 2 2 0 0 0 3 3 0

0 0 4 5 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

2 2 0 0 0 0 0 3 0 0 0 0 2 2 0 3 0 0 3 0

2 0 3 0 3 0 0 4 4 0 3 0 3 3 0 3 4 3 0 2

0 0 2 3 0 2 0 0 2 3 0 0 2 0 0 0 2 0 2 0

Maximum network profit – frequencies per sector (Fleet#3–91 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 2 BEL 0 0 0 0 0 BSB 3 0 0 4 3 CGH 0 0 4 0 4 CNF 2 0 3 4 0 CWB 0 0 3 4 3 FLN 0 0 2 3 2 FOR 3 3 0 0 0 GIG 3 0 3 5 3 GRU 0 0 4 0 4 GYN 2 0 0 4 2 MAO 0 2 0 0 0 MCZ 2 0 3 0 3 NAT 2 2 0 0 0 POA 0 0 0 4 3 REC 2 0 0 0 0 SDU 3 0 4 5 3 SLI 2 0 3 0 0 SSA 2 0 3 5 3 VIX 0 0 2 3 0 IDENTIFIED HUBS: SSA/CGH/SDU

0 0 3 4 3 0 2 0 3 4 3 0 0 0 3 0 4 0 0 2

0 0 2 3 2 2 0 0 2 3 2 0 0 0 2 0 3 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 3 0

3 0 3 5 3 3 2 0 0 4 3 0 0 0 3 0 0 0 4 2

0 0 4 0 3 4 3 0 4 0 3 0 0 0 4 0 5 0 4 2

2 0 0 4 2 3 2 0 3 3 0 0 0 0 3 0 3 0 3 0

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 3 0 3 0 0 3 0 0 0 0 0 2 0 2 0 2 3 0

2 2 0 0 0 0 0 3 0 0 0 0 2 0 0 2 0 2 3 0

0 0 0 4 3 3 2 0 3 4 2 0 0 0 0 0 4 0 0 2

2 0 0 0 0 0 0 3 0 0 0 0 2 2 0 0 0 2 3 2

3 0 4 5 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

2 0 3 0 0 0 0 3 0 0 0 0 2 2 0 2 0 0 2 0

2 0 3 5 3 0 0 3 4 4 3 0 3 3 0 3 4 2 0 2

0 0 2 3 0 2 0 0 2 2 0 0 0 0 2 2 2 0 2 0

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization Table B4

25

Maximum network profit – common connections of 3 fleets.

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

Table B5

0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0

0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0

1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1

0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1

1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0

0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1

0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0

1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0

0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1

0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1

0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0

1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0

0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0

1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0

0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1

1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0

1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1

0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0

Minimum network DOC – frequencies per sector (Fleet#1–70 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 3 BEL 0 0 0 0 0 BSB 3 0 0 6 3 CGH 0 0 6 0 5 CNF 3 0 3 5 0 CWB 0 0 4 6 4 FLN 0 0 3 4 3 FOR 3 3 0 0 0 GIG 0 0 4 6 4 GRU 0 0 5 0 5 GYN 0 0 0 5 3 MAO 0 2 0 0 0 MCZ 3 0 0 0 0 NAT 3 0 0 0 0 POA 0 0 0 6 4 REC 3 0 0 0 0 SDU 0 0 5 6 4 SLI 3 2 0 0 0 SSA 3 0 4 0 4 VIX 2 0 2 3 2 IDENTIFIED HUBS: CGH/SDU/CNF

0 0 4 6 4 0 3 0 4 5 3 0 0 0 4 0 5 0 0 2

0 0 3 4 3 3 0 0 3 4 2 0 0 0 2 0 4 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 4 3 0 4 0 3 4 0

0 0 4 6 4 4 3 0 0 6 4 0 0 0 4 0 0 0 5 3

0 0 5 0 4 5 4 0 6 0 4 0 0 0 5 0 6 0 0 3

0 0 0 5 3 3 2 0 4 4 0 0 0 0 0 0 4 0 3 2

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 0 0 0 0 0 0 4 0 0 0 0 0 3 0 3 0 3 3 2

3 0 0 0 0 0 0 4 0 0 0 0 3 0 0 3 0 3 3 0

0 0 0 6 4 4 2 0 4 5 0 0 0 0 0 0 5 0 0 0

3 0 0 0 0 0 0 4 0 0 0 0 3 3 0 0 0 3 4 0

0 0 5 6 4 5 3 0 0 6 4 0 0 0 5 0 0 0 5 3

3 2 0 0 0 0 0 3 0 0 0 0 3 3 0 3 0 0 3 0

3 0 4 0 4 0 0 4 5 0 3 0 3 3 0 4 5 3 0 2

2 0 2 3 2 2 2 0 3 3 2 0 2 0 0 0 3 0 2 0

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

26 Table B6

J. ALEXANDRE et al. Minimum network DOC – Frequencies per sector (Fleet #2–84 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 3 BEL 0 0 0 0 0 BSB 3 0 0 5 3 CGH 0 0 5 0 4 CNF 3 0 3 4 0 CWB 0 0 3 4 3 FLN 0 0 2 3 2 FOR 3 3 0 0 0 GIG 3 0 4 5 3 GRU 0 0 4 0 4 GYN 2 0 0 4 2 MAO 0 2 0 0 0 MCZ 2 0 0 0 3 NAT 2 0 0 0 0 POA 0 0 0 5 3 REC 2 0 0 0 0 SDU 4 0 4 6 4 SLI 2 2 0 0 0 SSA 2 0 3 5 3 VIX 0 0 2 3 0 IDENTIFIED HUBS: SSA/CGH/SDU

Table B7

0 0 3 4 3 0 2 0 4 4 3 0 0 0 3 0 4 0 0 2

0 0 2 3 2 2 0 0 3 3 2 0 0 0 2 0 3 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 4 0

3 0 4 5 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

0 0 4 0 4 4 3 0 5 0 4 0 0 0 4 0 5 0 5 3

2 0 0 4 2 3 2 0 3 4 0 0 0 0 0 0 3 0 3 0

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 3 0 0 3 0 0 0 0 0 2 0 3 0 3 3 2

2 0 0 0 0 0 0 3 0 0 0 0 2 0 0 2 0 2 3 0

0 0 0 5 3 3 2 0 4 4 0 0 0 0 0 0 4 0 0 0

2 0 0 0 0 0 0 3 0 0 0 0 3 2 0 0 0 3 3 2

4 0 4 6 4 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

2 2 0 0 0 0 0 3 0 0 0 0 3 2 0 3 0 0 3 0

2 0 3 5 3 0 0 4 4 5 3 0 3 3 0 3 4 3 0 2

0 0 2 3 0 2 0 0 2 3 0 0 2 0 0 2 2 0 2 0

Minimum network DOC – frequencies per sector (Fleet #3–91 seats).

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU 0 0 3 0 2 BEL 0 0 0 0 0 BSB 3 0 0 4 3 CGH 0 0 4 0 4 CNF 2 0 3 4 0 CWB 0 0 3 4 3 FLN 0 0 2 3 2 FOR 3 3 0 0 0 GIG 3 0 3 5 3 GRU 0 0 4 0 4 GYN 2 0 0 4 2 MAO 0 2 0 0 0 MCZ 2 0 3 0 3 NAT 2 2 0 0 0 POA 0 0 0 4 3 REC 2 0 0 0 0 SDU 3 0 4 6 3 SLI 2 0 3 0 0 SSA 2 0 3 5 3 VIX 0 0 2 3 0 IDENTIFIED HUBS: SSA/CGH/SDU

0 0 3 4 3 0 2 0 3 4 3 0 0 0 3 0 4 0 0 2

0 0 2 3 2 2 0 0 2 3 2 0 0 0 2 0 3 0 0 0

3 3 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 3 0

3 0 3 5 3 3 2 0 0 4 3 0 0 0 3 0 0 0 4 2

0 0 4 0 3 4 3 0 4 0 3 0 0 0 4 0 5 0 4 2

2 0 0 4 2 3 2 0 3 3 0 0 0 0 3 0 3 0 3 0

0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 3 0 3 0 0 3 0 0 0 0 0 2 0 2 0 2 3 0

2 2 0 0 0 0 0 3 0 0 0 0 2 0 0 2 0 2 3 0

0 0 0 4 3 3 2 0 3 4 2 0 0 0 0 0 4 0 0 2

2 0 0 0 0 0 0 3 0 0 0 0 2 2 0 0 0 2 3 2

3 0 4 6 3 4 3 0 0 5 3 0 0 0 4 0 0 0 4 2

2 0 3 0 0 0 0 3 0 0 0 0 2 2 0 2 0 0 2 0

2 0 3 5 3 0 0 3 4 4 3 0 3 3 0 3 4 2 0 2

0 0 2 3 0 2 0 0 2 2 0 0 0 0 2 2 2 0 2 0

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization Table B8

27

Minimum Network DOC – Common connections of 3 fleets.

Dep Apt (i) Arrival Airport (j) AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX AJU BEL BSB CGH CNF CWB FLN FOR GIG GRU GYN MAO MCZ NAT POA REC SDU SLI SSA VIX

1354

0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0

0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0

1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1

0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1

1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0

0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1

0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0

1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0

0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1

0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1

0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0

1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0

0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0

1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0

0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1

1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0

1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1

0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0

Appendix C. Final optimization results

1355

Table C1

Results for minimum network DOC scenario.

Parameter

Baseline Aircraft

Fleet #1

Fleet#2

Fleet #3

Total

Difference from baseline (%)

Distance flown (n mile) Number of passengers TOTAL COST (US$) COST PER PASSENGER (US$) TOTAL REVENUE (US$) TOTAL PROFIT (US$) Network DOC ($/n mile) Network Profit (105US$/pax. n mile) Estimated number of aircraft Design Range (n mile) MTOW (kg) OEW (kg) Fuel Capacity (kg) Passenger Capacity Seat Configuration Fuselage length (m) Wing area (m2) Wing aspect ratio Wing taper ratio Wing sweepback angle (o) Engine fan diameter (m) Engine by-pass ratio

612,442 90,459 7924657.95 87.60 10945539.00 3020881.05 9.95 5.45 111 2000 38,790 21,800 8428 78 2–2 31.68 72.72 8.6 0.44 23.5 1.42 5.00

252340.01 33,544 2699819.69 80.49 4058824.00 1359004.31 8.23 16.05 45 1048 30,467 18,971 6953 70 2–3 26.81 88.22 7.65 0.35 24.9 1.56 5.73

248464.32 36,304 2855227.35 78.65 4392784.00 1537556.65 8.84 17.03 44 1014 34,885 21,334 5756 84 3–3 27.26 79.85 8.7 0.42 20.0 1.36 4.93

247017.66 37,845 2882815.39 76.17 4579245.00 1696429.61 8.98 18.14 44 1079 36,830 22,418 8941 91 2–3 28.57 97.09 8.21 0.33 26.4 1.28 5.54

747821.98 107,693 8437862.43 78.35 13030853.00 4,592,991 8.68 5.70 133

22.1 19.1 6.5 10.5 19.1 52.0 12.8 4.6 19.8

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

CJA 1432 20 November 2019

No. of Pages 30

28 Table C2

J. ALEXANDRE et al. Results for maximum network profit scenario.

Parameter

Baseline Aircraft

Fleet #1

Fleet#2

Fleet #3

Total

Difference from baseline (%)

Distance flown (n mile) Number of passengers TOTAL COST (US$) COST PER PASSENGER (US$) TOTAL REVENUE (US$) TOTAL PROFIT (US$) Network DOC (US$/n mile) Network Profit (105 US$/pax. n mile). Estimated number of aircraft Design Range (n mile) MTOW (kg) OEW (kg) Fuel Capacity (kg) Passenger Capacity Seat Configuration Fuselage length (m) Wing area (m2) Wing aspect ratio Wing taper ratio Wing sweepback angle (o) Engine fan diameter (m) Engine by-pass ratio

612,442 90,459 7924657.95 87.60 10945539.00 3020881.05 9.95 5.45 111 2,000 38,790 21,800 8428 78 2–2 31.68 72.72 8.6 0.44 23.5 1.42 5.00

228,626 33,132 2654193.15 80.11 4008972.00 1354778.85 8.93 17.88 41 1462 34,497 20,560 6817 77 2–3 28.07 83.27 7.6 0.39 20.46 1.32 5.44

210,900 33,184 2612693.07 78.73 4015264.00 1402570.93 9.53 20.041 40 1293 38,070 23,048 6308 85 2–2 30.51 78.88 8.3 0.33 27.89 1.40 4.97

246,611 37,699 2876383.61 76.30 4561579.00 1685195.39 8.97 18.126 39 1079 36,830 22,418 8940 91 2–3 28.57 97.09 8.2 0.33 26.44 1.28 5.54

686137.02 104015.00 8143269.83 78.29 12585815.00 4442545.17 9.13 6.22 120

12.0 15.0 2.8 10.6 15.0 47.1 8.2 14.2 8.1

1356

References

1357

1. Doganis PR. Flying off course IV: airline economics and marketing. London: Routledge; 2009. 2. Medau JC. Allocation of aircraft to flights considering aircraft operational, maintenance and performance restrictions. Sao Paulo (Brazil): University of Sao Paulo; 2017. 3. Caetano DJ, Gualda NDF. A flight schedule and fleet assignment model. 12th World Conference on Transport Research. Portugal: Lisboa; 2010. 4. Klabian D. Large-scale models in the airline industry. New York: Springer; 2014. 5. Rabetanety A, Calmet J, Schoen C. Airline schedule planning integrated flight schedule design and product line design[dessertation]. Karlsruhe: University of Karlsruhe; 2006. 6. Hane CA, Barnhart C, Johnson EL, Marsten RE, Nemhauser GL, Sigismondi G, et al. The fleet assignment problem: solving a largescale integer program. Math Program 1995;70(1–3):211–32. 7. Caetano DJ, Gualda NDF. An exact model for airline flight network optimization based on transport momentum and load factor. Transportes 2017;25(4):14–26. 8. Gurkan H, Gureal S. Altuk MS An integrated approach for airline scheduling, aircraft fleeting and routing with cruise speed control. Transp Res 2016;68:38–57. 9. Torenbeek E. Advanced aircraft design. New York: Wiley & Sons; 2013. 10. Loftin LK. Subsonic aircraft: Evolution and the matching of size to performance. Washington, D.C.: NASA; 1980. p. 441. 11. Sun YC, Smith HK. Supersonic business jet conceptual design in a multidisciplinary design analysis optimization environment. 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston: AIAA; 2018. 12. Lambe AB, Martins JRRA. Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes. Struct Multidiscip Optim 2012;2 (46):273–84.

1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390

13. Coello ACC, Lamont GB, Van Veldhuizen DA. Evolutionary algorithms for solving multi-objective problems. New York: Springer; 2007. 14. McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from computer code. Technometrics 2000;55–61. 15. Taylor C, De Week OL. Integrated transportation network design optimization47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2006 May 1-4; Newport. RI. Reston: AIAA; 2006. p. 1–16. 16. Bower GC, Kroo IM. Multiobjective aircraft optimization for minimum cost and emissions over specific route networksThe 26th Congress of ICAS and 8th AIAA ATIO, 2008 Sep 14-19; Anchorage, USA. Reston: AIAA; 2008. p. 1–23. 17. Mattos BS, Secco NR. An airplane calculator featuring a highfidelity methodology for tailplane sizing. J Aerosp Technol Manage 2013;5:371–86. 18. Torenbeek T. Synthesis of subsonic airplane design. Delft: Delft University Press; 1976. 19. Lederer PJ, Nambimandom RS. Airline network design. Oper Res 1999;46(6):785–804. 20. Dong B. Reliability analysis for aviation airline network based on complex network. J Aerosp Technol Manage 2014;6(2):193–201. 21. Akhuja R, Magnanti TL, Orlin JB, Reddy MR. Handbooks of operations research and management science. India: Kanpur; 1995. p. 1–83. 22. Campbell JF. Integer programming formulations of discrete hub location programming. Eur J Oper Res 1994;72(2):387–405. 23. Aykin T. The hub location and routing problem. Eur J Oper Res 1993;83(1):200–19. 24. Jaillet P, Song G, Yu G. Airline network design and hub allocation problems. Location Science 1996;4(3):195–212. 25. Evans AD, Schafer A, Dray L. Modelling airline network routing and scheduling under airport capacity constraints26th congress of international council of the aeronautical science, 2008 Sep 14-19; Anchorage, USA. Reston: AIAA; 2008. p. 1–13.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426

CJA 1432 20 November 2019

No. of Pages 30

An innovative approach for integrated airline network and aircraft family optimization 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493

26. Grosche T, Rothlauf F, Heinzl A. Gravity models for airlines passenger volume estimation. J Air Transport Manage 2007;13 (4):175–83. 27. Wojahn OW. Airline network structure and the gravity model. Transp Res Part E 2001;37(4):267–79. 28. Crossley W, Mane M. System of systems inspired aircraft sizing applied to commercial aircraft/airline problems. AIAA 5th Aviation, Technology, Integration, and Operations Conference (ATIO); 2005 Sep 26-28; Arlington, USA. Reston: AIAA; 2005. p. 1–12. 29. Nusawardhana N, Crossley W. Concurrent aircraft design and variable resource allocation in large scale fleet networks. 9th AIAA Aviation Technology, Integration, and Operations Conference (ATIO); 2009 Sep 21-23; Hilton Head, USA. Reston: AIAA; 2009.p.1-11. 30. Davedralingam N, Crossley W. Concurrent aircraft design and network design incorporating passenger demand models9th AIAA Aiation Technology, Integration, and Operations Conference (ATIO), 2009 Sep 21-23; Hilton Head, USA. Reston: AIAA; 2009. p. 1–10. 31. Roth, GL, Crossley WA. Commercial transport aircraft conceptual design using a genetic algorithm-based approach. 7th AIAA/ USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, multidisciplinary analysis optimization conferences; Reston: AIAA; 1998.p.1-12. 32. Isikveren AT. Quasi-analytical modelling and optimisation techniques for transport aircraft design[dissertation]. Stockholm: Royal Stockholm of Technology (KTH); 2002. 33. Cavalcanti J, Mattos BS, Paglione P. Optimal conceptual design of transport aircraft11th AIAA/ISSMO multidisciplinary analysis and optimization conference, 2006 Sep 6-8; Portsmouth, USA. Reston: AIAA; 2006. p. 1–22. 34. Cabral LV, Paglione P, De Matos BS. Multi-objective design optimization framework for conceptual design of families of aircrafts44th AIAA aerospace sciences meeting, 2006 Jan 9-12; Reno, USA. Reston: AIAA; 2006. p. 1–12. 35. Mane M, Crossley WA, Nusawardhana A. Systems-of-systems inspired aircraft sizing and airline resource allocation via decomposition. J Aircraft 2007;44(4):1222–35. 36. Siqueira LP, Loureiro V, Mattos BS.The suited airliner for an existing airline network. 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Structures, Structural Dynamics, and Materials and Co-located Conferences; 2009 May 4-7; Palm Springs, USA. Reston: AIAA; 2009. 1–23. 37. Braun M, Wicke K, Koch A. Analysis of natural laminar flow aircraft based on airline network design and fleet assignment. 11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference; 2011 Sep 20-22; Virginia Beach, USA. Reston: AIAA; 2011.p.1-13. 38. Davendralingam N, Crossley W. Robust Approach for concurrent aircraft design and airline network design. J Aircraft 2014;51 (6):1773–83. 39. Davendralingam N, Crossley W. Robust optimization of aircraft design and airline network design incorporating econometric trends. 11th AIAA Aviation Technology, Integration, and Operations Conference (ATIO); 2011 Sep 20-22; Virginia Beach, USA. Reston: AIAA; 2011. 1–10. 40. Hwang JT, Martins JR. Datals parallel allocation-mission optimization of a 128-route network. 16th AIAA/ISSMO multidisciplinary analysis and optimization conference; 2015 Jun 22-26; Dallas, USA. Reston: AIAA; 2015. 1–11. 41. Hwang JT. Martins JR. Allocation-mission-design optimization of next-generation aircraft using a parallel computational framework. 57th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference; 2016 Jan 4-8; San Diego, USA. Reston: AIAA; 2016.p.1-20.

29

42. Roy S, Moore K, Hwang JT, Gray JS, Crossley WA, Martins A. A mixed integer efficient global optimization algorithm for the simultaneous aircraft allocation-mission-design problem58th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2017 Jan 9-13; Grapevine, USA. Reston: AIAA; 2017. p. 1–18. 43. Roy S, Crossley WA. An EGO-like optimization framework for simultaneous aircraft design and airline allocation. 57th AIAA/ ASCE/AHS/ASC structures, structural dynamics, and materials conference; 2016 Jan 4-8; San Diego, USA. Reston: AIAA; 2016. p.1-10. 44. Roy S, Crossley WA, Moore KT, Gray JS, Martins A.Next generation aircraft design considering airline operations and economics. 2018 AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference; 2018 Jan 8-12; Kissimmee, USA. Reston: AIAA; 2018.p.1-16. 45. Mattos BS, Fregnani JATG, Magalha˜es Paulo CS. Conceptual design of green transport airplane. Book Series: Frontiers in Aerospace Science – Vol 3. Sharjah (UAE): Bentham Books Sciences Publishers; 2018. 46. Secco NR, Mattos BS. Artificial neural networks applied to airplane design. 53rd AIAA aerospace sciences meeting; 2015 Jan 5-9; Kissimmee, USA. Reston: AIAA; 2015.p.1-28. 47. Kundu AK. Aircraft Design. Cambridge: Cambridge University Press; 2010. 48. Fonseca CM, Fleming P J. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Forrest S, editor. Proceedings of the Fifth International Conference; San Mateo (CA): Morgan Kaufmann; 1993.p.1-8. 49. Zang Y. Solving large-scale linear programs by interior-point methods under MATLAB environment. Optim Methods Software 1995;10(1):1–31. 50. The Boeing Company. Jet transport performance methods. Seattle, USA: Boeing Commercial Aircraft; 1998. 51. International Civil Aviation Organization (ICAO). Manual of the ICAO standard atmosphere. Montreal: ICAO; 1993. Document No.: Doc.7488/3. 52. International Civil Aviation Organization (ICAO). Annex 11 to the convention on international civil aviation – air traffic services. Montreal: ICAO; 2001. 53. International Civil Aviation Organization (ICAO). Manual of Implementation of a 300m (1000ft) vertical Separation Minimum between FL290 and FL410. Montreal: ICAO; 2002. Document No.: Doc 9574. 54. Vicenty T. Direct and inverse solutions of geodesic on the ellipsoid with application of nested equations. Empire Survey Review 1975;23:88–93. 55. Brazilian Civil Aviation Agency (ANAC). Brazilian civil aviation regulations #121 – operating requirements: domestic, supplemental and flag operations. Brası´ lia: ANAC; 2010. 56. Fregnani G, Tavares JA, Carlos M, Ribeiro CA. A fuel tankering model applied to a domestic airline network. J Adv Transp 2011;47 (4):386–98. 57. Thomas B. An interactive educational tool for turbojet engines. AIAA 31st joint propulsion conference exhibit. AIAA: Reston; 1995. 58. NASA. NASA Glenn Research Center. EngineSim Version1.8a. [Internet] 2016. [Cited 2018 Jan 30]; Available from: https:// www.grc.nasa.gov/WWW/K-12/airplane/enginesim.html. 59. Colmenares QR. Techno-economic and environment risk assessment of innovative propulsion systems for short-range civil aircraft [dissertation]. Cranfield: Cranfield University; 2009. 60. Daniel R. Aircraft design: A conceptual approach. Reston: AIAA; 2012. 61. MathWorks. Genetic algorithm: Find global minima for highly nonlinear problems. [Internet]. 2017 Dec. Available from: https:// www.mathworks.com/discovery/genetic-algorithm.html.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560

CJA 1432 20 November 2019

30 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575

62. Jane’s. Jane’s aero engines. [Internet]. 2017 Dec. Available from: https://janes.ihs.com/. 63. De Mattos BS, Macedo AP, Silva Filho Da DH. Considerations about winglet design. 21st AIAA applied aerodynamics conference; 2003 Jun 23-26. Orlando, USA. Reston: AIAA;2003. p.1-11. 64. Van Dam CP. The aerodynamic design of multi-element high-lift systems. Prog Aerosp Sci 2002;38(2):101–44. 65. Singh B. A medium-fidelity method for rapid maximum lift estimation[dissertation]. Delft: Delft University; 2017. 66. Drela M. XFOIL – subsonic airfoil development system [Internet]. 2018 Oct. Available from: http://web.mit.edu/drela/Public/web/ xfoil/. 67. De Mattos BS. Numerical design of transonic wings and wing profiles using the AF2 algorithm to solve the full potential equation PhD Thesis.. Stuttgart: Universita¨t Stuttgart 1995.

No. of Pages 30

J. ALEXANDRE et al. 68. Robusto CC. The cosine-harvesine formula. The Americal Mathematical Monthly 1957;64:30–40. 69. Brazilian Airspace Control Department. Aeronautical Information Publication (AIP) – AGA Part. Rio de Janeiro: Institute of Aeronautical Cartography; 2016. 70. Brazilian Civil Aviation Agency (ANAC). Air Transport Yearbook. [Online] National Civil Aviation Agency (ANAC) 2014, 2015 and 2016. [cited: January 30th 2018]; Available from: http:// www.anac.gov.br/assuntos/dados-e-estatisticas/mercado-de-transporte-aereo/anuario-do-transporte-aereo/dados-do-anuario-dotransporte-aereo. 71. Newell GF. Airport capacity and delays. Transp Sci 1979;13 (3):201–41.

Please cite this article in press as: ALEXANDRE J et al. An innovative approach for integrated airline network and aircraft family optimization, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.10.004

1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589