Minimum cost time-varying network flow problems

References

• Ahuja , R. K. , Magnanti , T. L. and Orlin , J. B. 1993 . Network Flows: Theory, Algorithms, and Applications , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Ahuja , R. K. , Orlin , J. B. , Pallottino , S. and Scutella , M. G. 2003 . Dynamic shortest paths minimizing travel times and costs . Networks , 41 : 197 – 205 .
   Web of Science ®Google Scholar
• Aronson , E. J. 1989 . A survey of dynamic network flows . Ann. Oper. Res. , 20 : 1 – 66 .
   Google Scholar
• Cai , X. , Kloks , T. and Wong , C. K. 1997 . Time-varying shortest path problems with constraints . Networks , 29 : 141 – 149 .
   Web of Science ®Google Scholar
• Cai , X. , Sha , D. and Wong , C. K. 2001 . Time-varying minimum cost flow problems . European J. Oper. Res. , 131 : 352 – 374 .
   Web of Science ®Google Scholar
• Chabini , L. 1998 . Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time . Transport. Res. Record , 1645 : 170 – 175 .
   Google Scholar
• Cheng , L. and Duran , M. A. 2004 . Logistics for world-wide crude oil transportation using discrete event simulation and optimal control . Comput. Chem. Eng. , 28 : 897 – 911 .
   Web of Science ®Google Scholar
• Cooke , L. and Halsey , E. 1966 . The shortest route through a network with time-dependent internodal transit times . J. Math. Anal. Appl. , 14 : 492 – 498 .
   Google Scholar
• Dijkstra , E. W. 1959 . A note on two problems in connection with graphs . Numer. Math. , 1 : 269 – 271 .
   Web of Science ®Google Scholar
• Dreyfus , S. E. 1969 . An appraisal of some shortest-path algorithms . Oper. Res. , 17 : 395 – 412 .
   Web of Science ®Google Scholar
• Fleischer , L. K. and Tardos , E. 1998 . Efficient continuous-time dynamic network flow algorithms . Oper. Res. Lett. , 23 : 71 – 80 .
   Web of Science ®Google Scholar
• Fleischer , L. and Skutella , M. Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms . Baltimore, MD. Minimum cost flows over time without intermediate storag , pp. 66 – 75 .
   Google Scholar
• Fleischer , L. K. and Skutella , M. 2007 . Quickest flows over time . SIAM J. Comput. , 36 : 1600 – 1630 .
   Web of Science ®Google Scholar
• Ford , L. R. and Fulkerson , D. R. 1958 . Constructing maximal dynamic flows from static flows . Oper. Res. , 6 : 419 – 433 .
   Web of Science ®Google Scholar
• Ford , L. and Fulkerson , D. 1962 . Flows in Networks , Princeton, NJ : Princeton University Press .
   Google Scholar
• Gale , D. 1959 . Transient fows in networks . Michigan Math. J. , 6 : 59 – 63 .
   Google Scholar
• Hall , A. , Hippler , S. and Skutella , M. 2003 . Multicommodity flows over time: Efficient algorithms and complexity . Theoret. Comput. Sci. , 2719 : 397 – 409 .
   Google Scholar
• Hoppe , B. 1995 . Efficient dynamic network flow algorithms . PhD thesis, Cornell University
   Google Scholar
• Hoppe , B. and Tardos , E. 2000 . The quickest transshipment problem . Math. Oper. Res. , 25 : 36 – 62 .
   Web of Science ®Google Scholar
• Kaufman , D. E. and Smith , R. L. 1993 . Fastest paths in time-dependent networks for intelligent vehicle-highway systems application . IVHS J , 1 : 1 – 11 .
   Google Scholar
• Klinz , B. and Woeginger , G. 2004 . Minimum cost dynamic flows: The series–parallel case . Network , 43 : 153 – 162 .
   Google Scholar
• Köhler , E. and Skutella , M. 2005 . Flows over time with load-dependent transit times . SIAM J. Optim. , 15 : 1185 – 1202 .
   Google Scholar
• Melkonian , V. 2007 . Flows in dynamic networks with aggregate arc capacities . Inform. Process. Lett. , 101 : 30 – 35 .
   Google Scholar
• Miller-Hooks , E. and Patterson , S. S. 2004 . On solving quickest time problems in time-dependent, dynamic networks . J. Math. Modell. Algorithms , 3 : 39 – 71 .
   Google Scholar
• Minieka , E. 1973 . Maximal, lexicographic, and dynamic network fows . Oper. Res. , 21 : 517 – 527 .
   Web of Science ®Google Scholar
• Orda , A. and Rom , R. 1990 . Shortest-path and minimum-delay algorithms in networks with time-dependent edge length . J. ACM , 37 : 607 – 625 .
   Web of Science ®Google Scholar
• Orda , A. and Rom , R. 1991 . Minimum weight paths in time-dependent networks . Networks , 21 : 295 – 320 .
   Web of Science ®Google Scholar
• Pallottino , S. and Scutella , M. G. 1998 . “ Shortest path algorithms in transportation models: Classical and innovative aspects ” . In Equilibrium and advanced transportation modelling , Edited by: Marcotte , P. and Nguyen , S. 245 – 281 . Norwell, MA : Kluwer .
   Google Scholar
• Powell , W. B. , Jaillet , P. and Odoni , A. 1995 . “ Stochastic and dynamic networks and routing ” . In Handbooks in OR and MS: Network Routing , Edited by: Ball , M. , Magnanti , T. , Monma , C. and Nemhauser , G. 141 – 295 . Amsterdam, , The Netherlands : North-Holland .
   Google Scholar
• Skutella , M. 2009 . “ An introduction to network flows over time ” . In Research Trends in Combinatorial Optimization , Edited by: Cook , W. , Lovász , L. and Vygen , J. 451 – 482 . Berlin : Springer .
   Google Scholar
• Wilkinson , W. L. 1971 . An algorithm for universal maximal dynamic fows in a network . Oper. Res. , 19 : 1602 – 1612 .
   Web of Science ®Google Scholar