Periodic Event Scheduling for Automated Production Systems

Published Online:https://doi.org/10.1287/ijoc.2021.1101

References

  • Bai L, Wu N, Li Z, Zhou M (2016) Optimal one-wafer cyclic scheduling and buffer space configuration for single-arm multicluster tools with linear topology. IEEE Trans. Systems Man Cybernics Systems 46(10):1456–1467.CrossrefGoogle Scholar
  • Borndörfer R, Lindner N, Roth S (2020a) A concurrent approach to the periodic event scheduling problem. J. Rail Transport Planning Management 15:100175.CrossrefGoogle Scholar
  • Borndörfer R, Hoppmann H, Karbstein M, Lindner N (2020b) Separation of cycle inequalities in periodic timetabling. Discrete Optim. 35:100552.CrossrefGoogle Scholar
  • Fischetti M, Lodi A (2007) Optimizing over the first Chvátal closure. Math. Programming 110(1):3–20.CrossrefGoogle Scholar
  • Goerigk M, Liebchen C (2017) An improved algorithm for the periodic timetabling problem. 17th Workshop Algorithmic Approaches Transportation Model. Optim. Systems (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany).Google Scholar
  • Goverde RMP (2007) Railway timetable stability analysis using max-plus system theory. Transportation Res. Part B: Methodological 41(2):179–201.CrossrefGoogle Scholar
  • Großmann P, Hölldobler S, Manthey N, Nachtigall K, Opitz J, Steinke P (2012) Solving periodic event scheduling problems with SAT. Internat. Conf. Industrial Engrg. Other Appl. Appl. Intelligent Systems (Springer, Berlin), 166–175.CrossrefGoogle Scholar
  • Hassin R (1996) A flow algorithm for network synchronization. Oper. Res. 44(4):570–579.LinkGoogle Scholar
  • Heidergott B, Olsder GJ, Van Der Woude J (2014) Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications, vol. 48 (Princeton University Press, Princeton, NJ).Google Scholar
  • Hofmann T, Wenzel D (2020) IPESP instance generator. Chemnitz University of Technology. Accessed August 24, 2021, https://www.tu-chemnitz.de/mathematik/discrete/projects/viRAL/index.php/#data.Google Scholar
  • Hofmann T, Wenzel D (2021) How to minimize cycle times of robot manufacturing systems. Optim. Engrg. 22:895–912.CrossrefGoogle Scholar
  • Karp RM (1972) Reducibility among combinatorial problems. Miller RE, Thatcher JW, Bohlinger JD, eds. Complexity of Computer Computations (Springer, Boston), 85–103.CrossrefGoogle Scholar
  • Kavitha T, Liebchen C, Mehlhorn K, Michail D, Rizzi R, Ueckerdt T, Zweig KA (2009) Cycle bases in graphs characterization, algorithms, complexity, and applications. Comput. Sci. Rev. 3(4):199–243.CrossrefGoogle Scholar
  • Liebchen C (2006) Periodic timetable optimization in public transport. Dissertation, Institut für Mathematik, Technische Universität Berlin, Berlin.Google Scholar
  • Liebchen C, Möhring RH (2007) The modeling power of the periodic event scheduling problem: Railway timetables—and beyond. Geraets F, Kroon L, Schoebel A, Wagner D, Zaroliagis CD, eds. Algorithmic Methods for Railway Optimization (Springer, Berlin), 3–40.CrossrefGoogle Scholar
  • Liebchen C, Peeters L (2002) On cyclic timetabling and cycles in graphs. Technical Report 761/2002, Technische Universität Berlin, Berlin.Google Scholar
  • Liebchen C, Peeters L (2009) Integral cycle bases for cyclic timetabling. Discrete Optim. 6(1):98–109.CrossrefGoogle Scholar
  • Liebchen C, Swarat E (2008) The second Chvátal closure can yield better railway timetables. Eighth Workshop Algorithmic Approaches Transportation Model. Optim. Systems (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany).Google Scholar
  • Lindner T (2000) Train Schedule Optimization in Public Rail Transport (Technische Universität Braunschweig, Braunschweig, Germany).Google Scholar
  • Lindner N, Liebchen C (2020) Determining all integer vertices of the PESP polytope by flipping arcs. Technical Report 20-19, Zuse Institute Berlin, Berlin.Google Scholar
  • Nachtigall K (1994) A Branch and Cut Approach for Periodic Network Programming (Institut für Mathematik, Universität Hildesheim, Hildesheim, Germany).Google Scholar
  • Nachtigall K (1996) Cutting planes for a polyhedron associated with a periodic network. German Aerospace Center report, Cologne.Google Scholar
  • Nachtigall K (1998) Periodic network optimization and fixed interval timetables. Report, German Aerospace Center, Cologne, Germany.Google Scholar
  • Nachtigall K, Opitz J (2008) A modulo network simplex method for solving periodic timetable optimisation problems. Oper. Res. Proc. 2007:461–466.CrossrefGoogle Scholar
  • Odijk MA (1994) Construction of Periodic Timetables. Part 1. A Cutting Plane Algorithm (TU Delft, Delft, Netherlands).Google Scholar
  • Serafini P, Ukovich W (1989) A mathematical model for periodic scheduling problems. SIAM J. Discrete Math. 2(4):550–581.CrossrefGoogle Scholar
  • Sparing D, Goverde RMP (2017) A cycle time optimization model for generating stable periodic railway timetables. Transportation Res. Part B: Methodological 98:198–223.CrossrefGoogle Scholar
  • Villumsen JC (2006) Construction of Timetables Based on Periodic Event Scheduling (Technical University of Denmark, Lyngby, Denmark).Google Scholar
  • Williams PH (2013) Model Building in Mathematical Programming (John Wiley & Sons, Chichester, UK).Google Scholar
  • Yang F, Wu N, Qiao Y, Su R (2017) Polynomial approach to optimal one-wafer cyclic scheduling of treelike hybrid multi-cluster tools via petri nets. IEEE/CAA J. Automatica Sinica 5(1):270–280.CrossrefGoogle Scholar
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