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.
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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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Focacci, F., Lodi, A., Milano, M.: Optimization-Oriented Global Constraints. Constraints 7(3-4), 351–365 (2002)
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)
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)
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)
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)
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
Pan, Y., Shi, L.: New Hybrid Optimization Algorithms for Machine Scheduling Problems. IEEE Transactions on Automation Science and Engineering (in print)
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)
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Kovács, A., Beck, J.C. (2007). A Global Constraint for Total Weighted Completion Time. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_9
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DOI: https://doi.org/10.1007/978-3-540-72397-4_9
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