Abstract
Minimum-cost capacitated fuzzy network is formulated as a fuzzy linear programming problem. A novel fuzzy linear programming formulation for minimum-cost capacitated fuzzy network where the total resource constraints are fuzzy is proposed. The proposed model is then implemented to minimize the operations cost of American Airlines. The research is helpful to identify the most profitable destinations for the American Airlines. Twelve origin/destination pairs are taken into considerations namely Atlantic (A), Latin American (L), Pacific (P) and Domestic (D). Flight operations capacity, Available Seat Miles ASM, is taken as a measure of capacity. The goal is to minimize the flight operations cost while ensuring maximum flight operations capacities to all destinations. This is followed by perspective data analytics for “What American Airline should do to be more profitable?” Perspective analytics suggest the airline to extend flight operations capacity in certain origin/destination pairs, whereas to maintain the previous approximate average capacity for those having high operations costs. The solution of the proposed fuzzy model suggests that flight operations capacity ASM can be significantly increased by 22345148 (000) with relatively small increase 1539356 (000) USD in operations cost. The fuzzy model is superior for it emphasizes to increase flight operations capacity ASM for the origin/destination pairs with minimum flight operations costs.
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Allahviranloo T, Lotfi FH, Kiasary MK, Kiani NA, Alizadeh L (2008) Solving full fuzzy linear programming problem by the ranking function. Appl Math Sci 2(1):19–32
Amiri NM, Nasseri SH (2007) Duality formulate dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets Syst 158(17):1961–1978. https://doi.org/10.1016/j.fss.2007.05.005
Arsenyeva O, Friedler F, Orosz A, Kapustenko PO (2019) Process network synthesis for energhy and cost minimization using the p-graph approach. Integr Technol Energy Sav. https://doi.org/10.20998/2078-5364.2019.4.09
Baykasoğlu A, Subulan K (2017) Constrained fuzzy arithmetic approach to fuzzy transportation problems with fuzzy decision variables. Expert Systs Appl 81:193–222. https://doi.org/10.1016/j.eswa.2017.03.040
Baykasoğlu A, Subulan K (2019) A direct solution approach based on constrained fuzzy arithmetic and metaheuristic for fuzzy transportation problems. Soft Comput 23(1):1667–1698. https://doi.org/10.1007/s00500-017-2890-2
Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164. https://doi.org/10.1287/mnsc.17.4.B141
Beltran-Royo C (2019) Fast scenario reduction by conditional scenarios in two-stage stochastic MILP problems. Optim Methods Softw. https://doi.org/10.1080/10556788.2019.1697696
Benhamiche A, Mahjoub AR, Perrot N, Uchoa E (2020) Capacitated multi-layer network design with unsplittable demands: polyhedra and branch-and-cut. Discrete Optim 35:100555. https://doi.org/10.1016/j.disopt.2019.100555
Birge JR, Chan T, Pavlin M, Zhu IY (2020) Spatial price integration in commodity markets with capacitated transportation networks. SSRN Electron J. https://doi.org/10.2139/ssrn.3544530
Borzabadi AH, Alemy H (2015) Dual simplex method for solving fully fuzzy linear programming problems. In: 4th Iranian joint congress on fuzzy and intelligent systems (CFIS). https://doi.org/10.1109/cfis.2015.7391653
Bouteggui M, Merazka F, Kurt GK (2020) Effective capacity of multi-unicast flows using network coded-ARQ. Electron Lett 56(9):464–467
Buckley JJ, Feuring T (2000) Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets Syst 109:35–53. https://doi.org/10.1016/S0165-0114(98)00022-0
Chen L, Peng J, Zhang B, Rosyida I (2017a) Diversified models for portfolio selection based on uncertain semivariance. Int J Syst Sci 48(3):637–648
Chen L, Peng J, Liu Z, Zhao R (2017b) Pricing and effort decisions for a supply chain with uncertain information. Int J Prod Res 55(1):264–284
Chen L, Peng J, Zhang B, Li S (2017c) Uncertain programming model for uncertain minimum weight vertex covering problem. J Intell Manuf 28:625–632
Chen L, Peng J, Zhang B (2017d) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59
Ciupala L, Deaconu A (2019) Minimum cost flow in a network with an overestimated arc capacity. Informatics 12(61): No. 1, Series III, ISSN 2065-6151, Print 2065-216X (CD-ROM). http://webbut.unitbv.ro/Bulletin/Series%20III/2019/BULETIN%20I%20PDF/9%20Ciupala%20Deaconu%201.pdf. Accessed 16 Apr 2019
Daneshrad R, Jafari D (2015) FFLP problem with symmetric trapezoidal fuzzy numbers. Decis Lett 4(2):117–124. https://doi.org/10.5267/j.dsl.2015.1.004
Das SK (2017) Modified method for solving fully fuzzy linear programming problem with triangular fuzzy numbers. Int J Res Ind Eng 6(4):293–311. https://doi.org/10.22105/riej.2017.101594.1024
Dehghan M, Hashemi B, Ghatee M (2006) Computational methods for solving fully fuzzy linear system. Appl Math Comput 179:328–343. https://doi.org/10.1016/j.amc.2005.11.124
Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292. https://doi.org/10.1109/ACCESS.2019.2897580
Deng W, Liu H, Xu J, Zhao H, Song Y (2020) An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2020.2983233
Dobruszkes F, Moyano A (2019) From transportation robustness to the robustness of modelling-based political decision making: a comment on ‘Managing reliever gateway airports with high-speed rail network’. Transp Res A Policy Pract 125:165–166. https://doi.org/10.1016/j.tra.2019.01.029
Ebrahimnejad A (2015) A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems. Int J Systs Sci 46(11):2048–2060. https://doi.org/10.1080/00207721.2013.844285
Ebrahimnejad A, Verdegay JL (2018) Linear programming with fuzzy parameters: simplex based approaches. In: Fuzzy sets-based methods and techniques for modern analytics, studies in fuzziness and soft computing. https://doi.org/10.1007/978-3-319-73903-8_3
Ganesan K, Veeramani P (2006) Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper Res 143:305–315. https://doi.org/10.1007/s10479-006-7390-1
Global Airline Industry Program, Airline Data Project, Massachusetts Institute of Technology, Provided by U.S Department of Transportation and Securities and Exchange Commission, http://web.mit.edu/airlinedata/www/American.html. Accessed 16 Apr 2019
Gong Z, Zhao W, Liu K (2018) A straight forward approach for solving fully fuzzy linear programming problem with LR-type fuzzy numbers. J Oper Res Soc Jpn 61(2):172–185. https://doi.org/10.15807/jorsj.61.172
Gowthami R, Prabakaran K (2019) Solution of multi objective transportation problem under fuzzy environment. J Phys: Conf Ser 1377(1):2038. https://doi.org/10.1088/1742-6596/1377/1/012038
Gupta S, Ali I, Ahmed A (2020) An extended multi-objective capacitated transportation problem with mixed constraints in fuzzy environment. Int J Oper Res 37(3):345–376. https://doi.org/10.1504/IJOR.2020.105443
Hashemi SH, Modarres M, Nasrabadi E, Nasrabadi MM (2006) Fully fuzzified linear programming, solution and duality. J Intell Fuzzy Syst 17(3):253–261. https://doi.org/10.1016/j.apm.2008.10.020
Hatami A, Kazemipoor H (2014) Solving fully fuzzy linear programming with symmetric trapezoidal fuzzy numbers using Mehar’s method. J Math Comput Sci 4(2):463–470
Hepzibah RI, Vidhya R (2015) Modified new operations for symmetric trapezoidal intuitionistic fuzzy numbers: an application of diet problem. Int J Fuzzy Math Arch 9(1):35–43
Hu Y, Zhao X, Liu J, Liang B, Ma C (2020) An efficient elgorithm for solving minimum cost flow problem with complementarity slack conditions. Math Probl Eng. https://doi.org/10.1155/2020/2439265
Hung HV, Chien TQ (2020) Implement and test algorithm finding maximal flow limited cost in extended multi commodity multicost network. IOSR J Comput Eng 22(2):34–44
Izaz UK, Karam FW (2019) Intelligent business analytics using proposed input/output oriented data envelopment analysis DEA and slack based DEA models for US-airlines. J Intell Fuzzy Syst 37(6):8207–8217
Izaz UK, Khan M (2016) The notion of duality in fully intuitionistic fuzzy linear programming (FIFLP) problems. Int J Fuzzy Syst Adv Appl 3:20–26
Izaz UK, Ahmad T, Maan N (2013) A simplified novel technique for solving fully fuzzy linear programming problems. J Optim Theory Appl 159:536–546. https://doi.org/10.1007/s10957-012-0215-2
Jiménez MA (2018) Nondominated solutions in a fully fuzzy linear programming problem. Math Methods Appl Sci. https://doi.org/10.1002/mma.4882
Jiménez MA, Blanco V (2019) On a fully fuzzy framework for minimax mixed integer linear programming. Comput Ind Eng 128:170–179. https://doi.org/10.1016/j.cie.2018.12.029
Khodayifar S, Raayatpanah MA, Pardalos PM (2019) A polynomial time algorithm for the minimum flow problem in time-varying networks. Ann Oper Res 272:29–39. https://doi.org/10.1007/s10479-017-2450-2
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2:3–16
Liu B (2009a) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin
Liu B (2009b) Some research problems in uncertainty theory. J Uncertain Syst 3:3–10
Liu B (2010a) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2010b) Uncertain risk analysis and uncertain reliability analysis. J Uncertain Syst 4:163–170
Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6:3–10
Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1:1
Lotfi FH, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33(7):3151–3156. https://doi.org/10.1016/j.apm.2008.10.020
Metropolitan Airport News, Certified MWBE-Woman-Owned Business Enterprise, New York USA, https://metroairportnews.com/2016-traffic-data-us-airlines-foreign-airlines-us-flights/. Accessed 16 Apr 2019
Mishmast NH, Maleki HR, Mashinchi M (2004) Solving fuzzy number linear programming problem by lexicographic ranking function. Ital J Pure Appl Math 15:9–20
Mollanoori H, Tavakkoli-Moghaddam R, Triki C, Hajiaghaei-Keshteli M, Sabouhi F (2019) Extending the solid step fixed-charge transportation problem to consider two-stage networks and multi-item shipments. Comput Ind Eng. https://doi.org/10.1016/j.cie.2019.106008
Murlidaran C, Venkateswarlu B (2018) Generalized ranking function for all symmetric fuzzy linear programming problems. J Intell Fuzzy Syst 35(1):1127–1131. https://doi.org/10.3233/JIFS-17917
Nasseri SH, Ardil E, Yazdani A, Zaefarian R (2005) Simplex method for solving linear programming problems with fuzzy numbers. Proc World Acad Sci Eng Technol 10(1):284–288
National Academies of Sciences, Engineering and Medicine (2020) Transportaion network companies (TNCs): Impacts to airport revenues and operations-reference guide. The National Academies Press, Washington. https://doi.org/10.17226/25759
Ozkok BA (2019) Finding fuzzy optimal and approximate fuzzy optimal solution of fully fuzzy linear programming problems with trapezoidal fuzzy numbers. J Intell Fuzzy Syst 36(1):1–12. https://doi.org/10.3233/JIFS-18016
Pathade P, Ghadle KP, Hamoud AA (2019) Optimal solution solved by triangular intuitionistic fuzzy transportation problem. Comput Eng Technol. https://doi.org/10.1007/978-981-32-9515-5-36
Pérez-Cañedo B, Concepción-Morales ER (2019a) A method to find the unique optimal fuzzy value of fully fuzzy linear programming problems with inequality constraints having unrestricted L-R fuzzy parameters and decision variables. Expert Syst Appl 123:256–269. https://doi.org/10.1016/j.eswa.2019.01.041
Pérez-Cañedo B, Concepción-Morales ER (2019b) On LR-type fully intuitionistic fuzzy linear programming with inequality constraints: solutions with unique optimal values. Expert Syst Appl 128:246–255. https://doi.org/10.1016/j.eswa.2019.03.035
Sallan JM, Lordan O (2019) Air route networks through complex networks theory. Elsevier B. V, Amsterdam. https://doi.org/10.1016/C2016-0-02288-X
Schaefer M, Čáp M, Mrkos J, Vokřínek J (2019) Routing a fleet of automated vehicles in a capacitated transportation network. In: IEEE/RSJ international conference on intelligent robots and systems (IROS) No. 19315105. https://doi.org/10.1109/iros40897.2019.8967723
Shiripour S, Mahdavi-Amiri N (2020a) An effective approach for aid planning on multi-type transportation networks after a disaster. Int J Ind Syst Eng 34(3):342–364
Shiripour S, Mahdavi-Amiri N (2020b) Disaster relief on destructive transportation networks using a circle-based approach. Transp Lett Int J Transp Res. https://doi.org/10.1080/19427867.2020.1742417
Sidhu SK, Kumar A (2016) Efficient methods for solving some mathematical programming problems with fuzzy parameters. Ph.D thesis School of Mathematics, Thapar Institute of Engineering and Technology, India. http://hdl.handle.net/10266/3871. Accessed 16 Apr 2019
Singh V, Yadav SP (2017) Development and optimization of unrestricted LR-type intuitionistic fuzzy mathematical programming problems. Expert Syst Appl 80:147–161. https://doi.org/10.1016/j.eswa.2017.03.015
Stanojević B, Stanojević M (2016) Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems. Fuzzy Optim Decis Mak 15(4):435–455. https://doi.org/10.1007/s10700-016-9232-1
Stanojević B, Dziţac I, Dziţac S (2015) On the ratio of fuzzy numbers–exact membership function computation and applications to decision making. Technol Econ Dev Econ 21:815–832. https://doi.org/10.3846/20294913.2015.1093563
Sundari M, Sundari S (2019) A novel shade to obtain an optimal solution to a fully fuzzy linear programming problem. https://www.researchgate.net/publication/331398088. Accessed 16 Apr 2019
Taha HA (1996) Operations research: an introduction, 6th edn. Pearson College Div, London, pp 248–256
Tanaka H, Asai K (1984) Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst 13:1–10. https://doi.org/10.1016/0165-0114(84)90022-8
Tavafoghi H, Shetty A, Poolla K, Varaiya PP (2019) Strategic information platforms in transportation networks. In: 57th Annual Allerton conference on communication, control, and computing (Allerton) USA. https://conf.papercept.net/conferences/conferences/ALLER19/program/ALLER19_ContentListWeb_3.html. Accessed 16 Apr 2019
Wang G, Peng J (2019) Fuzzy optimal solution of fuzzy number linear programming problems. Int J Fuzzy Syst 21(3):865–881. https://doi.org/10.1007/s40815-018-0594-0
Xi Z, Liu H, Liu H, Yang B (2014) Multiple object tracking using the shortest path faster association algorithm. Sci World J. https://doi.org/10.1155/2014/481719
Xi Z, Xu D, Song W, Zheng Y (2015a) A* algorithm with dynamic weights for multiple object tracking in video sequence. Optik 126(2):2500–2507. https://doi.org/10.1016/j.ijleo.2015.06.020
Xi Z, Tang S, Wu J, Zheng Y (2015b) Multiple object tracking using A* association algorithm with dynamic weights. J Intell Fuzzy Syst 29(5):2059–2072. https://doi.org/10.3233/IFS-151683
Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197
Zhao H, Liu H, Xu J, Deng W (2019) Performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2019.2948414
Zhao H, Zheng I, Deng W, Song Y (2020) Semi-supervised broad learning system based on manifold regularization and broad network. IEEE Trans Circ Syst 67(3):983–994
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55. https://doi.org/10.1016/0165-0114(78)90031-3
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Khan, I.U., Rafique, F. Minimum-cost capacitated fuzzy network, fuzzy linear programming formulation, and perspective data analytics to minimize the operations cost of American airlines. Soft Comput 25, 1411–1429 (2021). https://doi.org/10.1007/s00500-020-05228-5
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DOI: https://doi.org/10.1007/s00500-020-05228-5