Abstract
We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is a relaxation of the cumulative scheduling subproblem, which is critical to performance. We obtain substantial computational speedups relative to the state of the art in both MILP and CP. We also obtain much better solutions for problems that cannot be solved to optimality.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962)
Cambazard, H., Hladik, P.-E., Déplanche, A.-M., Jussien, N., Trinquet, Y.: Decomposition and learning for a hard real time task allocation algorithm. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 153–167. Springer, Heidelberg (2004)
Geoffrion, A.M.: Generalized Benders decomposition. Journal of Optimization Theory and Applications 10, 237–260 (1972)
Hooker, J.N.: Logic-based Methods for Optimization: Combining Optimization and Constraint Satisfaction. John Wiley & Sons, Chichester (2000)
Hooker, J.N.: A hybrid method for planning and scheduling. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 305–316. Springer, Heidelberg (2004)
Hooker, J.N.: A hybrid method for planning and scheduling. Constraints (to appear)
Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96, 33–60 (2003)
Hooker, J.N., Yan, H.: Logic circuit verification by Benders decomposition. In: Saraswat, V., Van Hentenryck, P. (eds.) Principles and Practice of Constraint Programming: The Newport Papers, pp. 267–288. MIT Press, Cambridge (1995)
Hooker, J.N., Yan, H.: A relaxation for the cumulative constraint. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 686–690. Springer, Heidelberg (2002)
Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing 13, 258–276 (2001)
Thorsteinsson, E.S.: Branch-and-Check: A hybrid framework integrating mixed integer programming and constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 16–30. Springer, Heidelberg (2001)
Türkay, M., Grossmann, I.E.: Logic-based MINLP algorithms for the optimal synthesis of process networks. Computers and Chemical Engineering 20, 959–978 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hooker, J.N. (2005). Planning and Scheduling to Minimize Tardiness. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_25
Download citation
DOI: https://doi.org/10.1007/11564751_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29238-8
Online ISBN: 978-3-540-32050-0
eBook Packages: Computer ScienceComputer Science (R0)