Abstract
The flow tasks arising in the study of transportation networks are relevant due to their wide practical application.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Frank H, Frisch IT (1971) Communication, transmission, and transportation networks. Addison Wesley, Boston
Christofides N (1975) Graph theory: an algorithmic approach. Academic Press, New York
Bozhenyuk A, Gerasimenko E (2014) Flows finding in networks in fuzzy conditions. In: Kahraman C, Öztaysi B (eds) Supply chain management under fuzzines, studies in fuzziness and soft computing, vol 313, part III. Springer, Berlin, pp 269–291. doi:10.1007/978-3-642-53939-8_12
Rukovodstvo po otsenke propusknoy sposobnosti avtomobilnikh dorog (1982). Minavtodor RSFSR, Transport, Moskva
Kaufmann A (1975) Introduction to the theory of fuzzy subsets, vol 1. Academic Press, New York
Kofman A, Hilo Aluja H (1992) Introduction the theory of fuzzy sets in enterprise management. High School, Minsk
Zadeh LA, Fu KS, Tanaka K, Shimura M (eds) (1975) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York
Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164
Borisov AN, AlekseevA V, Merkuryeva GV, Slyadz NN, Glushkov VI (1989) Fuzzy information processing in decision-making systems. Radio and Communication Publisher, Moscow
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8(part I):199–249; Inf Sci 8(part II):301–335; Inf Sci 9(part III):43–80
Borisov AN, Alekseev AV, Krumberg OA et al (1982) Decision making models based on linguistic variable. Zinatne, Riga
Zimmermann HJ (1991) Fuzzy set theory and its applications, 2nd edn. Kluwer Academic Publishers, Boston
Bozhenyuk A, Rozenberg I, Starostina T (2006) Analiz i issledovaniye potokov i zhivuchesti v transportnykx setyakh pri nechetkikh dannykh. Nauchnyy Mir, Moskva
Bershtein LS, Dzuba TA (1998) Construction of a spanning subgraph in the fuzzy bipartite graph. In: Proceedings of EUFIT’98, Aachen, pp 47–51
Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9(6):613–626
Ford LR, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton
Minieka E (1978) Optimization algorithms for networks and graphs. Marcel Dekker Inc, New York and Basel
Goldberg AV, Tardos E, Tarjan RE (1990) Network flow algorithms. In: Korte B, Lovasz L, Proemel HJ, Schrijver A (eds) Paths, flows and VLSI-design. Springer, Berlin, pp 101–164
Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall Inc, New Jersey
Bozhenyuk A, Rozenberg I, Rogushina E (2011) The method of the maximum flow determination in the transportation network in fuzzy conditions. In: Proceedings of the congress on intelligent systems and information technologies «IS&IT’11», vol 4. Physmathlit, Moscow, pp 17–24 (Scientific Publication in 4 volumes)
Murty KG (1992) Network programming. Prentice Hall, Upper Saddle River
Even S (1979) Graph algorithms. Computer Science Press, Potomac
Lawler EL (1976) Combinatorial optimization: networks and matroids. Holt, Rinehart, and Winston, New York
Papadimitriouc H, Steiglitz K (1982) Combinatorial optimization: algorithms and complexity. Prentice-Hall, Englewood Cliffs
Tarjan RE (1983) Data structures and network algorithms. Society for Industrial and Applied Mathematics, Philadelphia
Hu TC (1969) Integer programming and network flows. Addison Wesley, Boston
Edmonds J, Karp RM (1972) Theoretical improvements in algorithmic efficiency for network flow problems. J Assoc Comput Mach 19(2):248–264
Dinic EA (1970) Algorithm for solution of a problem of maximal flow in a network with power estimation. Soviet Math Doklady 11:1277–1280
Karzanov AV (1974) Determining the maximum flow in the network by the method of preflows. Soviet Math Doklady 15:434–437
Cherkassky RV (1977) Algorithms of construction of maximal flow in networks with complexity \( O\left( {n^{ 2} \sqrt m } \right) \) operations. Math Methods Solut Econ Probl 7:112–125
Cherkassky BV (1979) A fast algorithm for computing maximum flow in a network. In: Karzanov AV (eds) Collected papers, combinatorial methods for flow problems. The Institute for Systems Studies, Moscow, vol 3, pp 90–96 (English translation appears in AMS Trans 158:23–30 (1994))
Orlin JB (2013) Max flows in O(nm) time or better. In: Proceedings of the 2013 symposium on the theory of computing, pp 765–774
Bozhenyuk AV, Rozenberg IN, Rogushina EM (2011) Approach of maximum flow determining for fuzzy transportation network. Izvestiya SFedU Eng Sci 5(118):83–88
Chanas S, Kolodziejczyk W (1982) Maximum flow in a network with fuzzy arc capacities. Fuzzy Sets Syst 8(2):165-153
Chanas S, Delgado M, Verdegay JL, Vila M (1995) Fuzzy optimal flow on imprecise structures. Eur J Oper Res 83(3):568–580
Kumar A, Kaur J, Singh P (2010) Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints. Int J Appl Math Comput Sci 6:37–41
Kumar A, Kaur J (2011) Solution of fuzzy maximal flow problems using fuzzy linear programming. Int J Comput Math Sci 5(2):62–66
Yi T, Murty KG (1991) Finding maximum flows in networks with nonzero lower bounds using Preflow methods. In: Technical report, IOE Department, University of Michigan, Ann Arbor, Mich
Garcia-Diaz A, Phillips DT (1981) Fundamentals of network analysis. Prentice-Hall, Englewood Cliffs
Busacker RG, Gowen P (1961) A procedure for determining a family of minimum-cost network flow patterns. In: Technical report 15, operations research office, John Hopkins University
Klein M (1967) A primal method for minimal cost flows with applications to the assignment and transportation problems. Manage Sci 14:205–220
Kovács P (2015) Minimum-cost flow algorithms: an experimental evaluation. Optim Methods Softw 30(1):94–127
Ahuja RK, Goldberg AV, Orlin JB, Tarjan RE (1992) Finding minimum-cost flows by double scaling. Mathematical Programming 53:243–266
Warshall S (1962) A theorem on boolean matrices. J ACM 9(1):11–12
Floyd RW (1962) Algorithm 97: shortest path. Commun ACM 5(6):345
Ganesan K, Veeramani P (2006) Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper Res 143:305–315
Thakre PA, Shelar DS, Thakre SP (2009) Solving fuzzy linear programming problem as multi objective linear programming problem. In: Proceedings of the world congress on engineering (WCE 2009), London, U.K
Dutta D, Murthy AS (2010) Multi-choice goal programming approaches for a fuzzy transportation problem. IJRRAS 2(2):132–139
Kumar A, Singh P, Kaur J (2010) Generalized simplex algorithm to solve fuzzy linear programming problems with ranking of generalized fuzzy numbers. Turkish J Fuzzy Syst (TJFS) 1(2):80–103
Maleki HR, Tata M, Mashinchi M (2000) Linear programming with fuzzy variables. Fuzzy Sets Syst 109:21–33
Maleki HR, Mashinchi M (2004) Fuzzy number linear programming: a probabilistic approach. J Appl Math Comput 15:333–341
Yoon KP (1996) A probabilistic approach to rank complex fuzzy numbers. Fuzzy Sets Syst 80:167–176
Allahviranloo T, Lotfi FH, Kiasary MK, Kiani NA, Alizadeh L (2008) Solving fully fuzzy linear programming problem by the ranking function. Appl Math Sci 2(1):19–32
Gerasimenko EM (2012) Minimum cost flow finding in the network by the method of expectation ranking of fuzzy cost functions. Izvestiya SFedU Eng Sci 4(129):247–251
Chanas S, Kuchta D (1994) Linear programming problem with fuzzy coefficients in the objective function. In: Delgado M et al (eds) Fuzzy Optimization, Physica-Verlag, Heidelberg, pp 148–157
Malyshev NG, Bershteyn LS, Bozhenyuk AV (1991) Nechetkiye modeli dlya ekspertnykh sistem v SAPR. Energoatomizdat, Moscow
Bozhenyuk A, Gerasimenko E (2013) Methods for maximum and minimum cost flow determining in fuzzy conditions. World Appl Sci J 22:76–81. doi:10.5829/idosi.wasj.2013.22.tt.22143 (Special Issue on Techniques and Technologies)
Tardos E (1985) A strongly polynomial minimum cost circulation algorithm. Combinatorica 5(3):247–255
Goldberg AV, Tarjan RE (1989) Finding minimum-cost circulations by canceling negative cycles. J ACM 36(4):873–886
Aronson JE (1989) A survey of dynamic network flows. Ann Oper Res 20:1–66
Ciurea E (1997) Two problems concerning dynamic flows in node and arc capacitated networks. Comput Sci J Moldova 5(3):15, 298–308
Silver MR, de Weck O (2006) Time-expanded decision network: a new framework for designing evolvable complex systems. In: Proceedings of 11th AIAA/ISSMO multidisciplinary analysis and optimization conference 6–8 September, Portsmouth, Virginia, pp 1–15
Lovetskii S, Melamed I (1987) Dynamic flows in networks. Autom Remote Control 48(11):1417–1434 (Translated from Avtomatika i Telemekhanika (1987), vol 11, pp 7–29)
Powell W, Jaillet P, Odoni A (1995) Stochastic and dynamic networks and routing. In: Ball MO, Magnanti TL, Monma CL, Nemhauser GL (eds) Handbook in operations research and management science, vol 8. Network Routing, Elsevier, Amsterdam, pp 141–296
Orlin JB (1983) Maximum-throughput dynamic network flows. Mathematical Programming 27:214–231
Fonoberova MA, Lozovanu DD (2004) The maximum flow in dynamic networks. Comput Sci J Moldova 12(3):36, 387–396
Fleischer L, Skutella M (2003) Minimum cost flows over time without intermediate storage. In: Proceedings of the 35th ACM/SIAM symposium on discrete algorithms (SODA), pp 66–75
Kotnyek B (2003) An annotated overview of dynamic network flows. In: Technical report, INRIA, Paris, No 4936, http://hal.inria.fr/inria-00071643/
Orlin JB (1984) Minimum convex cost dynamic network flows. Math Oper Res 9(2):190–207
Gale D (1959) Transient flows in networks. Michigan Math J 6:59–63
Halpern J (1979) A generalized dynamic flows problem. Networks 9:133–167
Cai X, Sha D, Wong CK (2001) Time-varying minimum cost flow-problems. Eur J Oper Res 131:352–374
Nasrabadi E, Hashemi SM (2010) Minimum cost time-varying network flow problems. Optim Methods Softw 25(3):429–447
Chalmet L, Francis R, Saunders P (1982) Network models for building evacuation. Manag Sci 28:86–105
Cooke L, Halsey E (1966) The shortest route through a network with time-dependent internodal transit times. J Math Anal Appl 14:492–498
Ahuja RK, Orlin JB, Pallottino S, Scutella MG (2003) Dynamic shortest paths minimizing travel times and costs. Networks 41:197–205
Chabini L (1998) Discrete dynamic shortest path problems in transportation applications: complexity and algorithms with optimal run time. Transp Res Rec 1645:170–175
Orda A, Rom R (1995) On continuous network flows. Oper Res Lett 17:27–36
Pallottino S, Scutellà MG (1998) Shortest path algorithms in transportation models: classical and innovative aspects. In: Marcotte P, Nguyen S (eds) Equilibrium and advanced transportation modelling, Kluwer, pp 245–281
Hall A, Langkau K, Skutella M (2007) An FPTAS for quickest multicommodity flows with inflow-dependent transit times. Algorithmica 47:299–321
Fleisher LK, Scutella M (2007) Quickest flows over time. SIAM J Comput 36:1600–1630
Glockner GD, Nemhauser GL, Tovey CA (2001) Dynamic network flow with uncertain arc capacities: decomposition algorithm and computational results. Comput Optim Appl 18(3):233–250
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bozhenyuk, A.V., Gerasimenko, E.M., Kacprzyk, J., Rozenberg, I.N. (2017). Flow Tasks in Networks in Crisp Conditions. In: Flows in Networks Under Fuzzy Conditions. Studies in Fuzziness and Soft Computing, vol 346. Springer, Cham. https://doi.org/10.1007/978-3-319-41618-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-41618-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41617-5
Online ISBN: 978-3-319-41618-2
eBook Packages: EngineeringEngineering (R0)