Abstract
Computing tight resource-level bounds is a fundamental problem in the construction of flexible plans with resource utilization. In this paper we describe an efficient algorithm that builds a resource envelope, the tightest possible such bound. The algorithm is based on transforming the temporal network of resource consuming and producing events into a flow network with nodes equal to the events and edges equal to the necessary predecessor links between events. A staged maximum flow problem on the network is then used to compute the time of occurrence and the height of each step of the resource envelope profile. Each stage has the same computational complexity of solving a maximum flow problem on the entire flow network. This makes this method computationally feasible and promising for use in the inner loop of flexible-time scheduling algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R.K. Ahuja, M. Kodialam, A.K. Mishra, J.B. Orlin. Computational Investigations of Maximum Flow Algorithms, European Journal of Operational Research, Vol 97(3), 1997.
K.R. Baker. Introduction to Sequencing and Scheduling. Wiley, New York, 1974.
J.C. Beck, A.J. Davenport, E.D. Davis, M.S. Fox. Beyond Contention: Extending Texture-Based Scheduling Heuristics. in Proceedings of AAAI 1997, Providence, RI, 1997.
A., Cesta, A. Oddi, S.F. Smith, A Constraint-Based Method for Resource Constrained Project Scheduling with Time Windows, CMU RI Technical Report, February 2000.
A. Cesta, C. Stella. A time and Resource Problem for Planning Architectures. Proceedings of the 4 th European Conference on Planning (ECP 97). Toulouse, France, 1997.
H. S.F. Cooper Jr., The Loneliness of the Long-Duration Astronaut, Air & Space/Smithsonian, June/July 1996, available at http://www.airspacemag.com/ASM/Mag/Index/1996/JJ/llda.html
T.H. Cormen, C.E. Leiserson, R.L. Rivest. Introduction to Algorithms. Cambridge, MA, 1990.
R. Dechter, I. Meiri, J. Pearl. Temporal Constraint Networks. Artificial Intelligence, 49:61–95, May 1991.
A.V. Goldberg, R.E. Tarjan. A New Approach to the Maximum-Flow Problem. Journal of the ACM, Vol. 35(4), 1988.
P. Laborie, Algorithms for Propagating Resource Constraints in AI Planning and Scheduling: Existing Approaches and New Results, Proceedings of ECP 2001, Toledo, Spain, 2001.
P. Morris, N. Muscettola, T. Vidal. Dynamic Control of Plans with Temporal Uncertainty, in Proceedings of IJCAI 2001, Seattle, WA, 2001
N. Muscettola. On the Utility of Bottleneck Reasoning for Scheduling. in Proceedings of AAAI 1994, Seattle, WA, 1994.
W.P.M. Nuijten. Time and Resource Constrained Scheduling: a Constraint Satisfaction Approach. PhD Thesis, Eindhoven University of Technology, 1994.
N. Sadeh. Look-ahead techniques for micro-opportunistic job-shop scheduling. PhD Thesis, Carnegie Mellon University, CMU-CS-91-102, 1991.
M. Zweben, M.S. Fox. Intelligent Scheduling. Morgan Kaufmann, San Francisco, 1994.
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
Muscettola, N. (2002). Computing the Envelope for Stepwise-Constant Resource Allocations. 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_10
Download citation
DOI: https://doi.org/10.1007/3-540-46135-3_10
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