Abstract
This paper presents a new cumulatives constraint, which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way workload covering, producer-consumer, and scheduling problems. The introduction of negative heights has forced us to come up with new filtering algorithms and to revisit existing ones. The first filtering algorithm is derived from an idea called sweep, which is extensively used in computational geometry; the second algorithm is based on a combination of sweep and constructive disjunction; while the last is a generalization of task intervals to this new context. A real-life crew scheduling problem originally motivated this constraint which was implemented within the SICStus finite domain solver and evaluated against different problem patterns.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggoun, A., Beldiceanu, N.: Extending CHIP to solve Complex Scheduling and Packing Problems. Mathl. Comput. Modelling, 17(7), pages 57–73, (1993).
Artigues, C, Roubellat, F.: A polynomial activity insertion algorithm in a multiresource schedule with cumulative constraints and multiple modes. In European Journal of Operational Research (EJOR), 127, pages 297–316, (2000).
Barták, R.: Dynamic Constraint Models for Planning and Scheduling Problems. In New Trends in Constraints (Papers from the Joint ERCIM/Compulog-Net Workshop, Cyprus, October 25–27, 1999), LNAI 1865, Springer Verlag, (2000).
Baptiste, P., Le Pape, C, Nuijten, W.: Constraint-based Scheduling. Kluwer Academic Publishers, International Series in Operations Research & Management Science, (2001).
Beck, J. C, Fox, M. S.: Constraint-directed techniques for scheduling alternative activities. In Artificial Intelligence 121, pages 211–250, (2000).
Beldiceanu, N.: Pruning for the minimum Constraint Family and for the number of distinct values Constraint Family. In Proc. of the 7 th CP, 211–224, Paphos, (2001).
Beldiceanu, N., Carlsson, M.: Sweep as a Generic Pruning Technique Applied to the Non-Overlapping Rectangles Constraint. In Proc. of the 7 th CP, 377–391, Paphos, (2001).
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry–Algorithms and Applications. Springer, (1997).
Brucker, P., Drexl, A., Möhring, R., Neumann, K., Pesch, E.: Resource-constrained project scheduling: Notation, classification, models and methods, in EJOR 112, pages 3–41, (1999).
Carlsson, M., Ottosson G., Carlson, B.: An Open-Ended Finite Domain Constraint Solver. Proc. Programming Languages: Implementations, Logics, and Programs, vol. 1292 of Lecture Notes in Computer Science, pages 191–206, Springer-Verlag, (1997).
Caseau, Y., Laburthe, F.: Cumulative Scheduling with Task Intervals. In Proceedings of the Joint International Conference and Symposium on Logic Programming, MIT Press, (1996).
De Backer, B., Beringer, A.: A CLP Language Handling Disjunctions of Linear Constraints. In Proc. 10 th International Conference on Logic Programming, pages 550–563, (1993).
Erschler, J., Lopez, P.: Energy-based approach for task scheduling under time and resources constraints. In 2nd International Workshop on Project Management and Scheduling, pages 115–121, Compiègne (France), June 20–22, (1990).
Herroelen, W., Demeulemeester, E., De Reyck, B.: A Classification Scheme for Project Scheduling Problems. in: Weglarz J. (Ed.), Handbook on Recent advances in Project Scheduling, Kluwer Academic Publishers, (1998).
Lahrichi, A.: Scheduling: the Notions of Hump, Compulsory Parts and their Use in Cumulative Problems. in: C. R. Acad. Se. Paris, t. 294, pages 209–211, (1982).
Poder, E., Beldiceanu, N., Sanlaville, E.: Computing the Compulsory Part of a Task with Varying Duration and Varying Resource Consumption. Submitted to European Journal of Operational Research (EJOR), (February 2001).
Preparata, F. P., Shamos, M. I.: Computational geometry. An introduction. Springer-Verlag, (1985).
Simonis, H., Cornelissens, T.: Modelling Producer/Consumer Constraints. In Proc. of the 1 st CP, 449–462, Cassis, (1995).
Van Hentenryck, P., Saraswat, V., Deville, Y.: Design, Implementation and Evaluation of the Constraint Language cc(FD). In A. Podelski, ed., Constraints: Basics and Trends, vol. 910 of Lecture Notes in Computer Science, Springer-Verlag, (1995).
Würtz, J.: Oz Scheduler: A Workbench for Scheduling Problems. In Proceedings of the 8th IEEE International Conference on Tools with Artificial Intelligence, Nov l6–19 1996, IEEE Computer Society Press, (1996).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beldiceanu, N., Carlsson, M. (2002). A New Multi-resource cumulatives Constraint with Negative Heights. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-46135-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44120-5
Online ISBN: 978-3-540-46135-7
eBook Packages: Springer Book Archive