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Automation and Remote Control

, Volume 77, Issue 12, pp 2091–2109 | Cite as

Minimizing the maximal weighted lateness of delivering orders between two railroad stations

  • D. I. ArkhipovEmail author
  • A. A. Lazarev
Topical Issue
  • 44 Downloads

Abstract

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity O(qn 2 log n) operations, where q is the number of trains and n is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria wL max and C max in O(n 2 max{n log n, q log v}) operations, where v is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness wL max and total time of fulfilling freight delivery orders C max.

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References

  1. 1.
    Cordeau, J.-F., Toth, O., and Vigo, D., A Survey of Optimization Models for Train Routing and Scheduling, Transp. Sci., 2000, vol. 32 (4), pp. 380–396.CrossRefzbMATHGoogle Scholar
  2. 2.
    de Oliveira, E.S., Solving Single Track Railway Scheduling Problem Using Constraint Programming, PhD Thesis, Leeds: Univ. of Leeds, School of Computing, 2001.Google Scholar
  3. 3.
    Brucker, P., Heitmann, S., and Knust, S., Scheduling Railway Traffic at a Construction Site, OR Spectrum, 2002, 24 (1), pp. 19–30.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Sourd, F., Application of Scheduling Theory to Solve Real-life Railway Problems, Proc. Conf. on Optimization and Practices in Industry (COPI’11), Paris, 2011.Google Scholar
  5. 5.
    Gafarov, E., Dolgui, A., and Lazarev, A., Two-Station Single-Track Railway Scheduling Problem with Trains of Equal Speed, Comput. Ind. Eng., 2015, vol. 85, pp. 260–267.CrossRefGoogle Scholar
  6. 6.
    Disser, Y., Klimm, M., and Lubbecke, E., Bidirectional Scheduling on a Path, Matheon Preprint 1060, Berlin: Res. Cent. Matheon, Tech. Univ. Berlin, 2014.zbMATHGoogle Scholar
  7. 7.
    Lazarev, A.A., Musatova, E.G., and Arkhipov, D.I., The Problem of Minimization of the Maximal Weighted Lateness of Order Fulfillment for Two Stations, Tr. 3 Vseross. konf. s mezhd. uchastiem “Tekhnicheskie i programmnye sredstva sistem upravleniya, kontrolya i izmerenii” (Proc. 3rd Int. Conf. “Hardware and Software Means for Control, Testing, and Measurement Systems”) (UKI-2012), Moscow: Inst. Probl. Upravlen. RAN, 2012, pp. 1962–1967.Google Scholar
  8. 8.
    Arkhipov, D. and Lazarev, A., The Problem of Minimization Maximum Weighted Lateness of Orders for Two Railway Stations, EURO 2012, Vilnius, 2012, p. 151.Google Scholar
  9. 9.
    Arkhipov, D.I. and Lazarev, A.A., Minimizing the Maximal Weighted Time Delay for Delivering Freight Orders between Two Stations under Limited Train Motion, Tr. 3 Vseross. konf. s mezhd. uchastiem “Intellektual’nye sistemy upravleniya na zheleznodorozhnom transporte—ISUZhT-2014” (Proc. 3rd Int. Conf. Intelligent Control Systems on Railroad Transport) (ISUZhT-2014), Moscow: SJC “NIIAS,” 2014, pp. 7–10.Google Scholar
  10. 10.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., et al., Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey, Ann. Discret. Math., 1979, vol. 5, pp. 287–326.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Benson, H.P., An Outer Approximation Algorithm for Generating All Efficient Extreme Points in the Outcome Set of a Multiple Objective Linear Programming Problem, J. Glob. Optim., 1998, vol. 13, pp. 1–24.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lazarev, A.A., Teoriya raspisanii. Otsenki absolyutnoi pogreshnosti i skhema priblizhennykh reshenii zadach teorii raspisanii (Scheduling Theory. Estimates of Absolute Errors and Approximate Solution Schemes for Scheduling Theory Problems), Moscow: MIPT Press, 2008.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Lomonosov State UniversityMoscowRussia
  4. 4.Moscow Physical and Technical Institute (State University)DolgoprudnyiRussia

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