Parallelism for Perturbation Management and Robust Plans

  • Jan Ehrhoff
  • Sven Grothklags
  • Ulf Lorenz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3648)

Abstract

An important insufficiency of modern industrial plans is their lack of robustness. Disruptions prevent companies from operating as planned before and induce high costs for trouble shooting. The main reason for the severe impact of disruptions stems from the fact that planners do traditionally consider the precise input to be available at planning time.

The Repair Game is a formalization of a planning task, and playing it performs disruption management and generates robust plans with the help of game tree search. Technically, at each node of a search tree, a traditional optimization problem is solved such that large parts of the computation time are blocked by sequential computations. Nevertheless, there is enough node parallelism which we can make use of, in order to bring the running times onto a real-time level, and in order to increase the solution quality per minute significantly. Thus, we are able to present a planning application at the cutting-edge of Operations Research, heavily taking advantage of parallel game tree search. We present simulation experiments which show the benefits of the repair game, as well as speedup results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Althöfer, I.: Root evaluation errors: How they arise and propagate. ICCA Journal 11(3), 55–63 (1988)Google Scholar
  2. 2.
    Ballard, B.W.: The *-minimax search procedure for trees containing chance nodes. Artificial Intelligence 21(3), 327–350 (1983)MATHCrossRefGoogle Scholar
  3. 3.
    Ehrhoff, J., Grothklags, S., Lorenz, U.: Das Reparaturspiel als Formalisierung von Planung unter Zufallseinflüssen, angewendet in der Flugplanung. In: Proceedings of GOR conference: Entscheidungsunterstützende Systeme in Supply Chain Managment und Logistik, pp. 335–356. Physika-Verlag ,Heidelberg (2005)Google Scholar
  4. 4.
    Engell, S., Märkert, A., Sand, G., Schultz, R.: Production planning in a multiproduct batch plant under uncertainty. Preprint 495-2001, FB Mathematik, Gerhard-Mercator-Universität Duisburg (2001)Google Scholar
  5. 5.
    Feldmann, R., Mysliwietz, M., Monien, B.: Studying overheads in massively parallel min/max-tree evaluation. In: 6th ACM Annual symposium on parallel algorithms and architectures (SPAA 1994), pp. 94–104. ACM, New York (1994)CrossRefGoogle Scholar
  6. 6.
    Flemming, P.J., Wallace, J.J.: How not to lie with statistics: the correct way to summerize benchmark results. CACM 29(3), 218–221 (1986)Google Scholar
  7. 7.
    Hane, C.A., Barnhart, C., Johnson, E.L., Marsten, R.E., Nemhauser, G.L., Sigismondi, G.: The fleet assignment problem: solving a large-scale integer program. Mathematical Programming 70, 211–232 (1995)MathSciNetMATHGoogle Scholar
  8. 8.
    Kaindl, H., Scheucher, A.: The reason for the benefits of minmax search. In: Proc. of the 11 th IJCAI, Detroit, MI, pp. 322–327 (1989)Google Scholar
  9. 9.
    Knuth, D.E., Moore, R.W.: An analysis of alpha-beta pruning. Artificial Intelligence 6(4), 293–326 (1975)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Koenig, S., Furcy, D., Bauer, C.: Heuristic search-based replanning. In: Proceedings of the International Conference on Artificial Intelligence Planning and Scheduling, pp. 294–301 (2002)Google Scholar
  11. 11.
    Kouvelis, P., Daniels, R.L., Vairaktarakis, G.: Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Transactions 32(5), 421–432 (2000)Google Scholar
  12. 12.
    Leon, V.J., Wu, S.D., Storer, R.H.: A game-theoretic control approach for job shops in the presence of disruptions. International Journal of Production Research 32(6), 1451–1476 (1994)MATHCrossRefGoogle Scholar
  13. 13.
    Nau, D.S.: Pathology on game trees revisited, and an alternative to minimaxing. Artificial Intelligence 21(1-2), 221–244 (1983)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Papadimitriou, C.H.: Games against nature. Journal of Computer and System Science 31, 288–301 (1985)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Reinefeld, A.: An Improvement of the Scout Tree Search Algorithm. ICCA Journal 6(4), 4–14 (1983)Google Scholar
  16. 16.
    Römisch, W., Schultz, R.: Multistage stochastic integer programming: an introduction. Online Optimization of Large Scale Systems, 581–600 (2001)Google Scholar
  17. 17.
    Rosenberger, J.M., Schaefer, A.J., Goldsman, D., Johnson, E.L., Kleywegt, A.J., Nemhauser, G.L.: Simair: A stochastic model of airline operations. In: Winter Simulation Conference Proceedings (2000)Google Scholar
  18. 18.
    Russel, S., Norvig, P.: Artificial Intelligence, A Modern Approach. Prentice Hall Series in Artificial Intelligence (2003)Google Scholar
  19. 19.
    Shannon, C.E.: Programming a computer for playing chess. PhilosophicalMagazine 41, 256–275 (1950)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jan Ehrhoff
    • 2
  • Sven Grothklags
    • 1
  • Ulf Lorenz
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderborn
  2. 2.Lufthansa Systems Airline Services GmbH, Network Management SolutionsRaunheim

Personalised recommendations