Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad Sustaiable Developmet Approaches Sama Sorouri Ghareaghaj 1, Rami Sadeghia *2, Reza Tavakkoli-Moghaddam 3, Ahmad Makui 4 Abstract Received: 15. 08. 2017 20. 05. 2018 I each time period, the passegers demad for each route is fiite ad airlies compete for earig more profits. The complex competitio amog airlies causes some problems, such as complicatig flight plaig ad icreasig empty seats for some routes. These problems icrease air pollutio ad fuel cosumptio. To solve these problems, this research studies the cooperatio of the airlies with game theory ad sustaiable developmet app.roaches. To ivestigate the issue, the three steps are suggested as itroducig the compoets of the multi-attribute game theory to the multi-objective model, modelig multi-objective formulatio with a sustaiable developmet app.roach, ad solvig the model by a multiobjective method. Pay-off fuctios are to maximize the profit of airlies, miimize the total differece amog the No.s of flier passegers ad their demad o all routes ad all flight times, ad miimize empty seats. All the above-metioed objectives preset ecoomic, social, ad evirometal aspects of sustaiable developmet. The results of the airlie cooperatio model are compared with the iformatio about o-cooperatio collected from airlies i the curret form. The cooperatio of airlies ca improve the objective fuctios ad the sustaiable developmet app.roach. This research ca be used to help airlies i idetifyig the role of cooperatio i air trasportatio. Keywords: Airlie; multi-objective model; cooperatio; game theory; sustaiable developmet. Correspodig author E-mail: sadeghia@pu.ac.ir 1 Ph.D. Studet, Departmet of Idustrial Egieerig, Payame Noor Uiversity, Tehra, Ira. 2 Associate Professor, Departmet of Idustrial Egieerig, Payame Noor Uiversity, Tehra, Ira. 3. Professor, School of Idustrial Egieerig, College of Egieerig, Uiversity of Tehra, Tehra, Ira. 4 Professor, School of Idustrial Egieerig, Ira Uiversity of Sciece ad Techology, Tehra, Ira. 367 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... 1. Itroductio Air trasportatio should be reliable, effective, ad safe. At the begiig of the air trasportatio market, airlies begi servig cliets i differet routes. A icrease i trasportatio causes problems, such as traffic cogestio, air pollutio ad trasportatio cost. Also, developmet of air trasportatio presets ew challeges related to the aviatio ad airlies. Airlies play a crucial role i reducig costs ad attractig passegers. Nowadays, airlies compete for providig better services to passegers ad earig more profits. There are a lot of defiitios of sustaiability; however, they are scattered i differet sources of iformatio. There are ot fully defied i literature priciples of sustaiable developmet of public trasport systems [Patlis, 2017]. The sustaiable developmet app.roach seeks to strike a balace amog ecoomic, evirometal, ad social factors (amely, sustaiability) i preset ad future. It also fids solutios to reduce complicatios from differet sectios. Furthermore, the cooperatio of the airlies ca affect ecoomic, evirometal, ad social factors, so a sustaiable developmet app.roach is studied i this research. The cocept of sustaiable developmet is a kid of effort to compoud the growig cocepts i the field of evirometal issues alog with social ad ecoomic issues. I this research, cooperatio meas promotig ecoomic ad atioal market share agreemet o joit exploitatio of opp.ortuities for airlies ad does ot mea participatio i stock owership or mergers. This meas that airlies coordiate with each other i flight schedulig for commo iterests ad atioal iterests of idepedet orgaizatios. The goal of this research is to evaluate airlies cooperatio ad sustaiable developmet app.roaches to solve the problems facig airlies ad aviatio. This research ca be used to help airlies idetify the role of cooperatio i the iterests i air trasportatio as a competitive strategy. I each time period, the passegers demad for each route are fiite ad this makes it harder for airlies to compete. There are studies that focus o maximizig the profit or flight frequecy for airlies; however, there was o attetio to the ew eeds ad sustaiable developmet app.roach i the aviatio idustry. Hase itroduced the air competitio expaded i hub situatios with the o-cooperatio game to maximize the profit amog airlies, i which a o-cooperatio game developed airlies were able to choose their frequecy [Hase, 1990]. Takebayashi ad Kaafai developed a model to simulate cotemporary competitio betwee the etwork ad poit-to-poit (PP.) carriers i air trasportatio markets [Takebayashi ad Kaafai, 2005]. They itroduced the multi-level competitio to optimize the No. of passegers uder the etwork service quality. The equilibrium i the air trasportatio idustry seeks to evaluate the most profitable hub ad spoke etwork for a airlie to survive i a deregulated eviromet. Adler preseted a iteger liear programmig model to geerate the potetial etworks i the first stage of the game [Adler, 2001]. I the secod stage, a o-liear programmig model maximizes profits for each airlie, based o the etworks chose by all participats. The variables of the model icluded the frequecy ad airplae size. Adler ad Smilowitz preseted a solutio for optimizig the maximum profit ad etwork desig by a game theoretic for aalyzig cooperatio of airlies [Adler ad Smilowitz, 2007]. The result of the Uited States ad Europea airlie shows that some of the cooperatio ca be more successful tha the others. Wei ad Hase used the game theory to aalyze airlies based o the size of aircrafts ad their service frequecy i moopoly markets [Wei ad Hase, 2007]. Zito, Salvoa, ad Fro itroduced a model was surveyed to maximize profit i a o-cooperatio i two modes: moopoly ad equilibrium markets for that how airlies make decisios i a competitive eviromet based o fare ad frequecy of services [Zito, Salvoa ad Fro, 2011]. They developed a multi-objective mixediteger liear programmig (MILP) model for Iteratioal Joural of Trasportatio Egieerig, 368
Sama Sorouri Ghareaghaj, Rami Sadeghia, Reza Tavakkoli-Moghaddam, Ahmad Makui supp.ly chai plaig by usig the game theory o a cooperatio mode. Zamarripaa et al. developed three attributes (total cost, delays ad patroage costs for competitiveess issues) by differet optimizatios, i which the results of a case study were compared with both cooperatio ad o-cooperatio scearios [Zamarripaa et al. 2012]. Kimms ad Demet determied the strategies to improve system performace by takig a sufficiet profit for each parter i the game theory, i which fair allocatio of icome is importat to log-term cooperatio parters [Kimms ad Demet, 2012]. They showed that icome could be calculated eve for large etworks of cooperatio effectively. Aggarwal, Cha, ad Tiwari itroduced a attitude to improve the aviatio with the itroductio of cost-effective ad better services for airlies [Aggarwal, Cha, ad Tiwari, 2013]. Service family selectio was shared by usig the game coalitio. I this case, a group of services was plaed for reachig mass customizatio. Shiao ad Hwag studied the competitio of iteratioal air cargo carriers i two stages: 1) decisio to or ot to eter i the Asia geeral air cargo markets, ad 2) profit optimizatio [Shiao ad Hwag, 2013]. They cocluded a profit equilibrium poit with the waitig period, cargo Volume, ad demad. The sharig reveues amog airlies ad airports should be checked. Saraswati ad Haaoka recogized the reveue sharig for the maximum beefit [Saraswati ad Haaoka, 2014]. They ivestigated several airlies ad airports i the cooperative mode. The results showed that airports would prefer to share the profit to improve their reveue. Evas ad Schafer foud the Nash equilibrium betwee competitor airlies by simulatio, i which each airlie has its ow beefits ad they tried to gai market share (split passegers) [Evas ad Schafer, 2014]. The validity of this model for a group of 22 etwork airports i 14 states i the USA. The passeger demad, fares, flight delays, CO 2 ad NOx gas system disposal were simulated ad estimated i the Chicago O'Hare airport. Ricardo et al. used the game theory i the allocatio of profit betwee the players [Ricardo et al. 2015, Grauberger ad Kimms, 2014]. These results show that the output of cooperative modes is higher tha a o-cooperative mode. Dae Ko itroduced competitio betwee a low-cost carrier ad full-service carrier airlies i fares, flight frequecy, ad a No. of flights o specific routes for maximizig the profit [Dae Ko, 2016]. I a supp.ly chai, schedulig plays a sigificat role i coordiatig ad cooperatio. Beheshtiia ad Ghasemi cosidered a itegratio of supp.lier ad vehicle schedulig problems for trasportig raw materials from the supp.liers to some maufacturig ceters [Beheshtiia ad Ghasemi, 2017]. The aim is to miimize the total tardiess of all assiged orders to the supp.liers ad miimize the total travelled distace of the vehicles. A ew meta-heuristic algorithm, amely multiple league champioship algorithm (MLCA), is proposed to solve this problem ad compared with two differet algorithms. The results prove that the proposed algorithm has better performace. Some studies have focused o evirometal protectio ad ecoomic iterests i air trasportatio idirectly to maitai the sustaiable developmet i the aviatio idustry [Lu, 2011. Hagma et al. 2015 ad Tasi et al. 2014]. Pagoi ad Psaraki studied the carbo emissios, cost, ad air fares i the aviatio idustry by a game theory app.roach to obtai the maximum profit [Pagoi ad Psaraki, 2016]. Kilkis ad Kilkis modeled ie airports based o their sustaiable ratig idicators ad itroduced the idex ad dimesios. Some aviatio idicators are eergy cosumptio per passeger, emissios dimesios, air pollutio idicators, fossil fuels i aviatio ad sharig public trasportatio, ad biological protectio [Kilkis ad Kilkis, 2015]. A sustaiable developmet app.roach has bee used for airlie cooperatio because may idicators of sustaiable developmet related to the airlie s operatio. Sustaiable developmet has bee the objective of may fields, icludig the tourism ad trasportatio sector. However, a major part of this airlie idustry deals with may egative 369 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... impacts, such as air pollutio, oise, CO 2 emissio, ad labor practice. Saremi, Hosseii-Motlagh ad Sadjadi app.lied a MILP model for cosiderig cotaier demads, ad CO 2 emissios o Islamic Republic of Ira Shipp.ig Lies (IRISL), i which the results showed the ievitable ifluece of the fuel price ad primary ivetory level of the cost of the ships [Saremi, Hosseii-Motlagh ad Sadjadi, 2016]. Ghater Samai et al. proposed a two-echelo biobjective model uder the assumptio of characteristics, icludig multi-commodity, simultaeous pickup ad delivery ad soft time widows [Ghater Samai et al. 2016]. The objective fuctios were to miimize the trasportatio/locatio costs ad fuel costs, respectively. The proposed model used a robust app.roach for the ucertaity i customers demads. The results imply to decreased costs. Tsui, Yue, ad Fug survey a hub aviatio ad added to that kowledge to empirically ivestigate Hog Kog s eight major tourist source markets [Tsui, Yue, ad Fug, 2017]. The fidigs of this study suggested that the icreased air trasport capacity of foreig coutries ad Hog Kog to Chia, trade Volumes betwee Chia ad its tradig parters, air trasport costs, ad the global fiacial crisis are the key factors i affectig the No. of visitors to Chia by air passig through Hog Kog as their preferred stopover. Majidi et al. proposed a mixed-iteger oliear programmig model to miimize the cost of fuel cosumptio ad greehouse gas (GHG) emissios of vehicles i vehicle routig problem with simultaeous pickup ad delivery ad time widows [Majidi et al. 2017]. The results idicated that the proposed solutio method was the capability of fidig high quality solutios i most istaces. Abdoli Aghaei et al. used a road map model, modified digital logic (MDL) ad expert s viewpoits for developig the aircraft desig ad maufacturig idustry [Abdoli Aghaei et al. 2015]. This roadmap was a foresight tool, ad its goal ad app.licatio was to decrease the risk of a ivestmet, aircraft desig ad maufacturig idustry. Daesh Asgari, Haeri ad Jafari itroduced a ew app.roach to the selectio of a right efficiecy idicator i order to help maagers ad decisio makers i the trasportatio idustry to recogize right idices for performace improvemet by the balaced scorecard ad data evelopmet aalysis models [Daesh Asgari, Haeri ad Jafari, 2017]. The research questios to address this issue are as follows. Does airlie cooperatio affect o their profits? Does airlie cooperatio affect o reductio of the total capacity flight? Does airlie cooperatio, respod to the passegers demad at differet times? Does airlie cooperatio affect o the sustaiable developmet? Airlie s maagers should strive to icrease the efficiecy i a maagemet system ad reduce costs as much as possible. Airlies should fid solutios to flight schedulig, ad for this purpose, they should cosider some facilities ad strategies. Thus, airlies face issues such as high costs, may No.s of flight frequecy ad omissio of small airlie compaies. These compaies have to prevet the problems ad solve them with accurate ad practical solutios. If the airlies do ot cooperate, the capacity of the flights is goig to be much more tha the passeger demads ad the empty seats will icrease. The cotributios of research to address this issue are as follows: the cooperative game theory, a sustaiable app.roach used to solve abovemetioed problems ad a balace betwee supp.ly ad demad. I this research, three steps are itroduced to address these issues: (1) itroducig the compoets of a multi-attribute game to the multi-objective model, (2) multiobjective modelig by a sustaiable developmet app.roach, (3) solvig a multi-objective model by a developed method. Suggestio process ca be used for airlies i other similar cases. This problem is modeled by a multi-attribute game theory ad solved by usig Ligo software. To validate this model, the results were compared with the o-cooperatio mode. Iteratioal Joural of Trasportatio Egieerig, 370
Sama Sorouri Ghareaghaj, Rami Sadeghia, Reza Tavakkoli-Moghaddam, Ahmad Makui Table 1. Comparig this research with the existig literature Author Game theory CO2 emissio Sustaiable Aviatio Further details Hase * * No-cooperatio, choosig their frequecy, maximizig the profit, airlie Takebayashi * Optimizig the No. of passegers i trasportatio Adler * * Frequecy ad airplae size, airlie Adler * * Maximum profit, cooperatio of airlies Wei * * Aalyzig airlies based o the size of aircraft ad their service frequecy Zito * * Maximizig the profit i a o-cooperatio Zamarripaa * * Total cost, delays, ad patroage costs for cooperatio ad ocooperatio Kimms * * Profit, fair allocatio, cooperatio game ad the reveue sharig by the core Aggarwal * * Cost-effective, services for airlies, coalitio Shiao * * Profit optimizatio Saraswati * * Reveue sharig for the maximum beefit. Several airlies use cooperative airports Evas * * The payoff is Beefits ad airlies tryig to gai the market share Ricardo * Allocatio of profits betwee the players. o-cooperative Grauberger * Allocatio of profits betwee the players. o-cooperative Dae Ko * * Low-cost ad full-service airlies, fares, flight frequecy, No. of flights o specific routes for maximizig the profits Beheshtiia * Supp.ly chai, schedulig cooperatio Pagoi * * * Carbo emissios, cost, ad airfares Lu * * Hagma * * Tasi * * Sa Kilkis * * * Air pollutio idicators Saremi * Miimizig the trasportatio costs ad locatio costs. Miimizig the fuel costs Ghater Samai Tsui * * Majidi Miimizig the cost of fuel cosumptio ad GHG emissios of vehicles Abdoli Aghaei * Developig aircraft desig ad maufacturig idustry Daesh Asgari Efficiecy idicator i the trasportatio idustry This paper * * * * Three steps are itroduced to address the issues: (1) itroducig the compoets of a multi-attribute game to the multi-objective model, (2) multi-objective modelig by a sustaiable developmet app.roach, (3) solvig a multi-objective model by a developed method. 371 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... 2. Materials ad Methods 2.1 Game Theory Game theory is the study of mathematical models of coflict ad cooperatio betwee itelliget ratioal decisio-makers. Game theory is maily used i ecoomics, political sciece, psychology, logic, computer scieces, ad biology [Myerso, 1991]. It aalyzes situatios ivolved i the parties of coflictig iterests. It has two forms, amely sequetial or dyamic ad classical or ormal. Dyamic game theory covers two (or more) players that play sequetially with some kowledge, such as chess. I ormal game theory, players play simultaeously. O the other had, game theory has aother classificatio, amely cooperatio ad ocooperatio. I the o-cooperatio game, all players try to maximize their ow iterests idepedetly; however, i cooperatio games, players may be motivated to achieve their iterests with a agreed strategy. If there is o ay cooperatio betwee all the players, it is called a alliace. The game has three parts: players, player strategies that ca be discrete or cotiuous, ad pay-off or utility fuctio. First, we establish a set of utility fuctios defied o a decisio space for a group of idividuals. Yu itroduced the cocept of a utopia poit i the group decisio problems [Yu, 1973]. Let X be a decisio vector with x, ad use X to deote the set of all feasible x. The compact set X has a maximum value u, where u j is the utility fuctio for airlie j; thus, u j is the maximum utility. The players ca obtai thus u = (u 1, u 2,, u ) is the poit, i the utility space, i which everyoe is happ.y. Yu called it the utopia poit, where D idicates the distace betwee the utopia poit u ad utilities resultig from the decisio x. That distace will be miimized. Mi D = { u j u j p j=1 } 1 p 1 p (1) I the above method, there is oly oe payoff fuctio for each player; however, i this study, three types of pay-off fuctios were used for each player [Yu, 1973]. 2.2 Suggested Process for Solvig the Issue Cosiderig the issue of competig airlies with the cooperative app.roach i game theory ad sustaiable developmet, the followig three steps are suggested for ay limited No. of routes ad airlies that ca be used i other similar cases: Step 1: Itroducig the compoets of a multiattribute game to the multi-objective model. Step 2: Multi-objective modelig by a sustaiable developmet app.roach. Step 3: Solvig a multi-objective model by the developed method. 2.3 Step 1: Itroducig the compoets of multi-attribute game to the multi-objective model I each time period, the passeger s demad for each route is fiite, ad airlies compete for their market shares. I this research, airlies are the players ad they wat to maximize their profit, decrease the empty seats, ad miimize the total differece amog the No.s of flier passegers ad their demad o all routes ad flight times. These are the attribute or pay-off fuctios of the game. Airlie strategies are discrete ad the share of demads o each route ad flight schedulig of the game, which display by x ijk ad y ijk i the multi-objective model. I this research, the game type is ormal ad cooperative with multi-attribute fuctios ad discrete strategies. The game gets played oe time at the begiig of the programmig ad the cooperative results are used for scheduled flights for a specified time period. Durig the game, the No. of the players ad strategies must be idetified. Therefore, the game is complete iformatio. 2.4 Step 2: Multi-objective Modelig By A Sustaiable Developmet App.Roach 2.4.1 Notatios Decisio variables: Iteratioal Joural of Trasportatio Egieerig, 372
Sama Sorouri Ghareaghaj, Rami Sadeghia, Reza Tavakkoli-Moghaddam, Ahmad Makui y ijk : 1 if the airlie j at the flight time i was used for air route k; 0, otherwise x ijk : No. of passegers that fly at the flight time i by airlie j o the air route k Parameters: m jk : Maximum No. of flights for airlie j o air route k i a specific time period m: No. of competitor airlies (j idex) : No. of flight time (i idex) L: No. of air routes (k idex) H: No. of objective fuctios (h idex) f ijk : Fixed cost of airlie j at flight time i, o air route k v ijk : Variable cost of airlie j at flight time i ad o air route k D ik : Passeger demad for the air route k at flight time i t ijk : Airlie's share from the sale of tickets at flight time i for airlie j o air route k s ijk : Capacity of airlie j at flight time i ad for the air route k M: Very large No. u jh : Utility fuctio for airlie j ad objective fuctio h F ik : For air route k at the flight time i, the total differece amog the No.s of flier passegers ad their demad 2.4.2 Assumptios: The parameters of the model are wellkow for all players (i.e., airlies). The results of the cooperative model for a specified time period used for flight schedulig. The game is doe oe time at the begiig of the specific period. Airlies compete for a limited No. of routes. Demad forecast for each route is determied by airport iformatio, ad all demads ca be aswered by competitor airlies. The game type is ormal, cooperative ad multi-attribute. Strategies are discrete ad pure. The game is doe simultaeously ad did t exist domiate power i this problem that we survey. Accordig to the game's attribute (three objective or payoff fuctios) i the model, there is o domiat force amog airlies ad oly airlies decide o model variables (game strategies). 2.4.3. The multi-objective model: m L Max (t ijk x ijk v ijk x ijk ) i=1 j=1 k=1 m Mi y ijk L i=1 j=1 k=1 Mi 1 2 F ik s.t. L i=1 k=1 m L y ijk i=1 j=1 k=1 m f ijk s ijk x ijk L i=1 j=1 k=1 x ijk y ijk s ijk i, j, k (5) (2) (3) x ijk My ijk 0 i, j, k (6) 1 y ijk i=1 (4) j, k (7) y ijk m jk j, k (8) i=1 m x ijk = D ik i=1 j=1 m i=1 k (9) x ijk D ik = F ik i, k (10) j=1 y ijk = 0,1 i, j, k (11) 0 x ijk i, j, k (12) Objective fuctio (2) maximizes the airlies profit by calculatig the differece betwee the reveue of airlies from the sale of tickets ad costs. This objective itroduces the ecoomic dimesio of sustaiable developmet. 373 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... Objective fuctio (3) miimizes the total flight empty capacity. The use of seat coefficiet is a measure for prioritizig airlies. This objective ca elimiate extra flights ad costs, ad reduce fuel cosumptio ad air pollutio. This objective itroduces the ecoomic, evirometal, ad social factors of sustaiable developmet. The reduced capacity ca cause icreased dissatisfactio amog passegers from flight time, reducig the passegers ad profit for a airlie because some of the passegers are reallocated to the other airlies or other flight times. This cocers the coflict betwee the first ad third objectives. Objective fuctio (4) miimizes the total differece amog the No. of flier passegers ad their demad o all routes ad all flight times. The passeger s demad of o a route for each time is differet. Maybe, the demad is more tha the capacity of flights at a time for a route. I this mode, the remaiig passegers have to travel at other times, that dissatisfies passegers from flight time. Therefore, objective fuctio (4) tries to balace the betwee supp.ly ad passegers demad for all routes ad all times, ad decreases passeger dissatisfactio from flight time which is the social ad ecoomic dimesio of sustaiable developmet. This objective ca cause icreases i flights, empty seats, ad cost. Because of the absolute fuctio i (10), the total No. of F ik should be divided by two i this objective. Costrait (5) shows that the No. of allocated passegers that are flyig by airlie j at flight time i ad for air route k should ot be more tha the airlie capacity. Costrait (6) shows whe y is equal to zero, x is zero ad whe y is equal to oe, x is greater or equal to zero ad calculates the No. of passegers. Costraits (7) ad (8) show that, for each route ad each airlie at a specific period, the total No. of flights at all times should be at least oe ad maximized m jk. Costrait (9) shows that, for each route, the total No. of passegers o all flights should be equal to the total passeger demad. Demad forecast for each route is determied by airport iformatio ad all demads ca be aswered by competitor airlies. Costrait (10) calculates F ik by the differece amog the total No. of passegers that will fly by airlies from passeger demad at each time ad o each route. Costraits (11) ad (12) show that type of variables. 2.5. Step 3: Solvig the model by a multiobjective method This study is based o the cooperative game ad group decisio makig. Also, utopia values for airlies are available used by the similarity of Yu s method to solve the multi-objective model. This method is selected because it is used for multi-attribute game models. I the Yu s method, for each player, there was oly oe payoff fuctio. However, i this study, three types of a pay-off fuctio are used for each player. The alterative methods ca be aother multiobjective methods ad multi-attribute game theory methods, such as Nash methods. The solutios are determied for multi-attribute game model itroduced by (u jh ) utility fuctio for airlie j ad attribute h or objective h, ad is utility optimizatio. u jh H m Mi D = { u jh h=1 j=1 u jh p } 1 p j, h (13) For the cooperatio of the airlies, the objective fuctios 1, 2, ad 3 by h = 1, 2, ad 3 optimized with costraits separately ad u jh calculated. The placemet u jh i objective (13) with the uit off, the the mathematical model with objective fuctio (13) ad costraits (4) to (11) for p=1 is solved, ad the Nash equilibrium poit i a cooperative mode ca be obtaied. P ca be take each No. accordig to the Yu s method. I the Yu s method, a small amout of P is used to emphasize the utility of all players [Asgharpour, 2014]. Sice i the cooperatio game, players try to achieve more beefits simultaeously, so the results of the mathematical model suggest the best values of the variables (strategies) for ay airlie i the game ad airlies agreed with decisio variables. Iteratioal Joural of Trasportatio Egieerig, 374
Sama Sorouri Ghareaghaj, Rami Sadeghia, Reza Tavakkoli-Moghaddam, Ahmad Makui 3. Results Airlies should balace the passegers supp.ly (capacity of flights) ad demad. I other words, airlies should select the strategies that able to improve their operatios. Itegrated cotrol ad moitorig should be app.lied with a commo olie maagemet system. This problem is solved by the mathematical model for four airlies ad three air routes i a specified period. For validatio, the results of the airlie s cooperatio model prepared by usig Ligo software with the o-cooperatio are compared with Tables 2 to 4. Iformatio about the o-cooperative results are collected from airlies i the curret form. Tehra-Mashhad, Tehra-Shiraz ad Tehra- Kish routes are ivestigated for four airlies i the specified period. Iformatio about the parameters of the model such average costs ad capacity of airlies is well-kow ad are obtaied by iterviewig airlie maagers ad their website. The average of the forecasted demad o each route for the specific period by the iformatio about the Mehrabad airport is collected. Table 2 shows the profit of airlies ad No. of passegers i cooperative ad ocooperative modes. Table 3 ad Figure 1 show the empty seats ad the No. of flights decreased i a cooperative mode. Comparig the No. of flights for airlies o air routes i Table 4 ad comparig the total objectives with Table 6 are show i cooperative ad o-cooperative games. The results show that, i the cooperatio situatio, the total profit for airlies will be icreased. The aalysis of this issue shows that some airlies (i.e., first ad secod airlies) i a cooperative game, see a slight reductio i profits, removig extra flights ad decreasig empty seats. This demostrates the cocept of a o-domiat solutio by usig a multi-objective decisio-makig method. By removig extra flights, airlies ca develop the flights o other routes effectively ad ear more profit; however, other airlies lose profit. The No. of empty seats is a importat measure for evaluatig the airlies. Based o multiobjective mathematical model, by reducig the No. of flights, the No. of empty seats ca be reduced. The results show that the total No. of empty seats will be decreased from 1737 seats to just 87 seats. It shows a suitable use of resources ad help the airlie rakig. The total No. of flights will be decreased from 30 flights to 23. This leads to a reductio i evirometal pollutio, fuel usage, CO 2 emissios, ad costs. It also cotributes to the health ad welfare of society ad provides the ecoomic, evirometal, ad social dimesios of sustaiable developmet. Table 2. Profits ad No. of passegers Airlie No. Profit No. of Passegers Cooperative No-cooperative Cooperative No-cooperative 1 74,985 76,400 1103 1200 2 44,810 54,555 610 935 3 136,335 112,810 1565 1410 4 129,730 96,714 1580 1313 Total 385,860 340,479 4858 4858 Table 3. Empty seats ad No. of flights Airlie No. Empty Seats No. of Flights Cooperative No-cooperative Cooperative No-cooperative 1 77 570 6 8 2 10 235 4 7 3 0 465 6 7 4 0 467 7 8 Total 87 1737 23 30 375 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... Figure 1. Empty seats ad No. of flights Table 4. No. of flights for each airlie o each air route No. of Flights o No. of Flights o Secod No. of Flights o First Route Route Third Route Airlie Nocooperativcooperative No- No. Cooperative Cooperative Cooperative No-cooperative 1 1 2 2 3 3 3 2 2 3 1 2 1 2 3 1 2 2 2 3 3 4 3 3 1 2 3 3 Total 7 10 6 9 10 11 Routes Distace (Km) Table 5. CO2 emissio for routes i cooperative mode Average of Reduced Average fuel co2 emissio flights for cosumptio (Toe) all airlies Reduced average fuel cosumptio Total CO2 does ot emit (toe) Tehra-Mashhad 741 3705 (Kg) 11.48 3 11115 (Kg) 34.45 Tehra-Shiraz 682 3410 (Kg) 10.57 3 10230 (Kg) 31.71 Tehra-Kish 1043 5215 (Kg) 16.16 1 5215 (Kg) 16.16 Total for all routes 7 26560 (Kg) 82.32 Table 6. Comparig total objectives i cooperative game ad o-cooperative mode Objectives of Sustaiable Developmet Cooperative No-Cooperative Total profit for airlies (ecoomical goal) 385,860 340,479 Total No. of empty seat (social, evirometal, ad ecoomic goals) 87 1737 Total No. of flights (social, evirometal, ad ecoomic goals) 23 30 The total differece amog the No. of passegers that will fly by airlies from passeger demad (social ad ecoomic goals) 295 210 Iteratioal Joural of Trasportatio Egieerig, 376
Sama Sorouri Ghareaghaj, Rami Sadeghia, Reza Tavakkoli-Moghaddam, Ahmad Makui The passeger s demad o a route for each time is differet. It may be demad is more tha the capacity of flights at a specific time o a route. I this mode, the remaiig passegers will have to travel at other times, whose results are dissatisfied with a flight time. Therefore, miimizig the total differece amog the No.s of flier passegers ad their demad o all routes ad all flight times is used. Also, whe the demad is low at a time, this objective fuctio decreases the No. of flights. By reducig the No. of flights from 30 to 23, the empty seats are substatially reduced ad the total differece amog the No. of passegers that will fly by airlies from passeger demad o all routes ad all flight times icreases from 210 to 295. If this objective fuctio is ot used, the differece is very high, ad the No. of flights icreases iefficietly. Table 4 shows the No.s of flights for each airlie o each air route i a cooperative game model ad a o-cooperative mode (i.e., the existig mode). Aircraft egie emissios are directly related to fuel bur 1 kg of jet fuel bured geerates 3.16 kg of CO 2 [Cokorilo, 2016]. So, the key for airlies to miimize their evirometal impact is to use fuel efficietly. Table 5, for each route, shows the average of fuel cosumptio, average of CO 2 emissio, reduced flights for all airlies i a cooperative mode, reduced average fuel cosumptio ad total of CO 2 does ot emit. The average of the CO 2 emissio colum i Table 5 is calculated based o 1 kg of jet fuel bured geeratig 3.16 kg of CO 2. Due to the reduced flights for all routes, the total CO 2 is about 82.32 toes ad reduced average fuel cosumptio is 26560 Kg. This calculatio is based o the route distace ad average fuel cosumptio is achieved. The results are show i Table 6. Actually, through airlies cooperatio, a agreemet is established ad airlies achieve their iterests o the agreed strategy through the model decisio variables ad they will reach a Nash poit alog with a sustaiable developmet app.roach. Airlies use the other s iformatio for decreasig uecessary flights ad cost, improvig flight schedulig based o passeger demad, expadig flight etworks, balacig flight frequecy, improvig the maagemet ad seat usage coefficiet, decreasig costs of additioal flights, reducig air pollutio, ad fuel cosumptio. 4. Discussio ad Coclusios Sigificat developmets are i the field of air trasportatio. A large No. of coutries made remarkable strategies i iteratioal air trasport. Also, i airlie maagemet, there are some complex problems. This research evaluated the airlies cooperatio with game theory ad sustaiable developmet app.roaches. This research ca be used to help airlies by idetifyig the role of cooperatio i air trasportatio as a competitive strategy. The followig three steps are suggested for solvig the issue: (1) itroducig the compoets of multi-attribute game to the multi-objective model, (2) multi-objective modelig with a sustaiable developmet app.roach, ad (3) solvig the model by a multi-objective method. The three-step suggestio process for airlie cooperatio for optimal flight schedulig ad better utilizatio of the fleet that ca be used i other similar cases. The multi-attribute game theory was modeled o cooperative mode ad sustaiable developmet app.roach. The pay-off fuctios are to maximize the profit of airlies, miimize empty seats or maximize the seat usage coefficiet, ad miimize the total differece amog the No.s of flier passegers ad their demad o all routes ad all flight times. All above objectives will show all ecoomic, evirometal, ad social aspects of sustaiable developmet. I the cooperatio game, the results of the mathematical model suggest the best values of the variables or strategies for each airlie i the game; therefore, airlies agree with the decisio variables. This problem is solved i four airlies, three busy air routes, ad three flight times at a specific period. The results are show i the previous sectio, i which the total No. of empty seats ca be decreased from 1737 seats to just 87 seats. It 377 Iteratioal Joural of Trasportatio Egieerig,
Multi-Objective Modelig for Airlies Cooperatio by Game Theory ad... shows a suitable use of resources ad helps the airlie rakig. The total No. of flights ca be decreased from 30 flights to 23. Cooperatio betwee airlies makes it possible to icrease their profit ad use of seat coefficiet while decreasig passeger dissatisfactio from a flight time. Also, airlies cooperatio ca result i cacellig the o-required flights ad developig flights o other eeded routes. Therefore, this actio icreases the profit, reduces the air traffic rate ad iterrelated costs, ad also decreases the fuel cosumptio ad evirometal pollutio. These beefits lead to sustaiable developmet. Airlies play a crucial role i sustaiable developmet ad the cooperatio of the airlies ca have a effect o ecoomic, evirometal, ad social factors. Air trasportatio should be reliable, effective, ad safe. The passegers demad for each route is fiite. Airlies cooperatio ca be very iterestig for more market i competitio. Busiess cooperatio allows airlies to access a large air etwork ad provisio of ecessary services. Accordig to Table 5, the airlie cooperatio reduces the No. of flights. Cosequetly, it ca reduce Co 2 emissio or air pollutio ad fuel cosumptio. Total Co 2 emissio for all routes is about 82.32 toes ad reduced average fuel cosumptio is about 26560 Kg. Also, airlies are able to provide passegers with the varied flight schedules ad a wider choice of take-off ad ladig times. Despite all the features ad beefits from cooperatio with the air trasport idustry, which should be ecouraged airlies; there are some issues that eed to be addressed. Therefore, further research is ecessary to develop the other advatages effects of cooperatio. The cooperatio model has a complexity i terms of cooperatio frameworks ad has yet to udertake studies i this regard. Future research should cocer ew policies that eed to be developed for airlie cooperatio ad their impact o airlies, as well as the developmet ad use of other solvig methods of multi-attribute game theory. Author Cotributios: Sorouri ad Sadeghia preseted the cotributio of this paper. Sorouri wrote the paper, the model of the paper ad the umerical results of a case study. Sadeghia helped i the mathematical modelig ad game theory sectios. Tavakkoli-Moghaddam helped i modelig, solvig ad paper editig, ad Makui helped i the mathematical modelig ad game theory sectio. Coflicts of Iterest: The authors of this paper declare that there is o ay coflict of iterest amog them. 5. Refereces - Abdoli Aghaei, H., Beheshtiia, M. A., Amalick, M. S., Gholimotlagh, M. ad Fartash, K. (2015) "Studyig techology road mappig developmet ad selectig the appropriate model for aircraft desig ad maufacturig idustry", Iteratioal Joural of Scietific Studies, Volume 1, Issue 2, pp. 43-54. - Adler, N. (2001) "Competitio i a deregulated air trasportatio market", Europea Joural of Operatioal Research, Vol. 129, No. 2, pp. 337 345 - Adler, N. ad Smilowitz, K. (2007) "Hub-adspoke etwork alliaces ad mergers: pricelocatio competitio i the airlie idustry", Trasportatio Research Part B, Vol. 41, No. 4, pp. 394 409 - Aggarwal, A., Cha, F.T. S. ad Tiwari, M. K. (2013) "Developmet of a module based service family desig for mass customizatio of airlie sector usig the coalitio game", Computers & Idustrial Egieerig, Vol. 66. pp. 827 833 - Asgharpour, M. J. (2014) "Group decisio makig ad game theory i operatio research", Uiversity of Tehra Publicatios, 3rd Editio. - Beheshtiia, M. A. ad Ghasemi, A. (2017) "A multi-objective ad itegrated model for supp.ly chai schedulig optimizatio i a multi-site maufacturig system", Egieerig Optimizatio, Vol. 50, Issue 9, pp. 1415-1433 Iteratioal Joural of Trasportatio Egieerig, 378
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