Abstract

We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, an O(n 4) algorithm is proposed, which makes use of the preemptive mean busy time relaxation of the scheduling problem. The solution to this problem is used to test if an activity can start at each start time in its domain in solutions that respect the upper bound on the cost of the schedule. Empirical results show that the proposed global constraint significantly improves the performance of constraint-based approaches to single-machine scheduling for minimizing the total weighted completion time. Since our eventual goal is to use the global constraint as part of a larger optimization problem, we view this performance as very promising. We also sketch the application of the global constraint to cumulative resources and to problems with multiple machines.

Keywords

Schedule Problem Completion Time Single Machine Global Constraint Total Weighted Tardiness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Milis, I., Queyranne, M., Skutella, M., Stein, C., Sviridenko, M.: Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates. In: Proc. of the 40th IEEE Symposium on Foundations of Computer Science, pp. 32–44 (1999)Google Scholar
  2. 2.
    Akkan, C., Karabatı, S.: The Two-machine Flowshop Total Completion Time Problem: Improved Lower Bounds and a Branch-and-bound Algorithm. European Journal of Operational Research 159, 420–429 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    van den Akker, J.M., Hurkens, C.A.J., Savelsbergh, M.W.P.: Time-indexed Formulations for Machine Scheduling Problems: Column Generation. INFORMS Journal on Computing 12, 111–124 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Baptiste, P., Carlier, J., Jouglet, A.: A Branch-and-Bound Procedure to Minimize Total Tardiness on One Machine with Arbitrary Release Dates. European Journal of Operational Research 158, 595–608 (2004)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Baptiste, P., Peridy, L., Pinson, E.: A Branch and Bound to Mininimze the Number of Late Jobs on a Single Machine with Release Time Constraints. European Journal of Operational Research 144(1), 1–11 (2003)MATHMathSciNetGoogle Scholar
  6. 6.
    Belouadah, H., Posner, M.E., Potts, C.N.: Scheduling with Release Dates on a Single Machine to Minimize Total Weighted Completion Time. Discrete Applied Mathematics 36, 213–231 (1992)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chen, B., Potts, C.N., Woeginger, G.J.: A Review of Machine Scheduling: Complexity, Algorithms and Approximation. In: Handbook of Combinatorial Optimization, vol. 3, pp. 21–169. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  8. 8.
    Della Croce, F., Ghirardi, M., Tadei, R.: An Improved Branch-and-bound Algorithm for the Two Machine Total Completion Time Flow Shop Problem. European Journal of Operational Research 139, 293–301 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Dyer, M., Wolsey, L.A.: Formulating the Single Machine Sequencing Problem with Release Dates as Mixed Integer Program. Discrete Applied Mathematics 26, 255–270 (1990)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Focacci, F., Lodi, A., Milano, M.: Embedding Relaxations in Global Constraints for Solving TSP and TSPTW. Annals of Mathematics and Artificial Intelligence 34(4), 291–311 (2002)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Focacci, F., Lodi, A., Milano, M.: Optimization-Oriented Global Constraints. Constraints 7(3-4), 351–365 (2002)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Goemans, M.X., Queyranne, M., Schulz, A.S., Skutella, M., Wang, Y.: Single Machine Scheduling with Release Dates. SIAM Journal on Discrete Mathematics 15(2), 165–192 (2002)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jouglet, A., Baptiste, P., Carlier, J.: Branch-and-Bound Algorithms for Total Weighted Tardiness. In: Handbook of Scheduling: Algorithms, Models, and Performance Analysis, Chapman & Hall / CRC, Boca Raton (2004)Google Scholar
  14. 14.
    Kéri, A., Kis, T.: Primal-dual Combined with Constraint Propagation for Solving RCPSPWET. In: Proc. of the 2nd Multidisciplinary International Conference on Scheduling: Theory and Applications, pp. 748–751 (2005)Google Scholar
  15. 15.
    Nessah, R., Yalaoui, F., Chu, C.: A Branch-and-bound Algorithm to Minimize Total Weighted Completion Time on Identical Parallel Machines with Job Release Dates. Computers and Operations Research (in print)Google Scholar
  16. 16.
    Pan, Y.: Test Instances for the Dynamic Single-machine Sequencing Problem to Minimize Total Weighted Completion Time, Available at http://www.cs.wisc.edu/~yunpeng/test/sm/dwct/instances.htm
  17. 17.
    Pan, Y., Shi, L.: New Hybrid Optimization Algorithms for Machine Scheduling Problems. IEEE Transactions on Automation Science and Engineering (in print)Google Scholar
  18. 18.
    Schulz, A.S.: Scheduling to Minimize Total Weighted Completion Time: Performance Guarantees of LP-Based Heuristics and Lower Bounds. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 301–315. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • András Kovács
    • 1
    • 3
  • J. Christopher Beck
    • 2
  1. 1.Projet Contraintes, INRIA RocquencourtFrance
  2. 2.Dept. of Mechanical and Industrial Engineering, University of TorontoCanada
  3. 3.Computer and Automation Research Institute, Hungarian Academy of Sciences 

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