Abstract
In this paper we show how the classical job-shop scheduling problem can be modeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to finding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniques for solving the optimization problem and, more importantly, it allows to model naturally more complex dynamic resource allocation problems which are not captured so easily in traditional models of operation research. We present several algorithms and heuristics for finding the shortest paths in timed automata and test their implementation in the tool Kronos on numerous benchmark examples.
Chapter PDF
References
R. Alur, S. La Torre and G.J. Pappas, Optimal Paths in Weighted Timed Automata, Proc. HSCC’01, 49–64, LNCS 2034, Springer 2001.
K. Altisen, G. Goessler, A. Pnueli, J. Sifakis, S. Tripakis and S. Yovine, A Framework for Scheduler Synthesis. Proc. RTSS’99, 154–163, IEEE, 1999.
R. Alur, C. Courcoubetis, and D.L. Dill, Model Checking in Dense Real Time, Information and Computation 104, 2–34, 1993.
R. Alur and D.L. Dill, A Theory of Timed Automata, Theoretical Computer Science 126, 183–235, 1994.
E. Asarin and O. Maler, As Soon as Possible: Time Optimal Control for Timed Automata, Proc. HSCC’99, 19–30, LNCS 1569, Springer, 1999.
E. Asarin, O. Maler and A. Pnueli, Symbolic Controller Synthesis for Discrete and Timed Systems, Hybrid Systems II, LNCS 999, Springer, 1995.
E. Asarin, O. Maler, A. Pnueli and J. Sifakis, Controller Synthesis for Timed Automata, Proc. IFAC Symposium on System Structure and Control, 469–474, Elsevier, 1998.
G. Behrmann, A. Fehnker T.S. Hune, K.G. Larsen, P. Pettersson and J. Romijn, Efficient Guiding Towards Cost-Optimality in UPPAAL, Proc. TACAS 2001, 174–188, LNCS 2031, Springer, 2001.
G. Behrmann, A. Fehnker T.S. Hune, K.G. Larsen, P. Pettersson, J. Romijn and F.W. Vaandrager, Minimum-Cost Reachability for Linearly Priced Timed Automata, Proc. HSCC’01, 147–161, LNCS 2034, Springer 2001.
R. Boel and G. Stremersch, VHS case study 5: Modelling and Verification of Scheduling for Steel Plant at SIDMAR, Draft, 1999.
M. Bozga, C. Daws, O. Maler, A. Olivero, S. Tripakis, and S. Yovine, Kronos: a Model-Checking Tool for Real-Time Systems, Proc. CAV’98, LNCS 1427, Springer, 1998.
S Campos, E. Clarke, W. Marrero, M. Minea and H. Hiraishi, Computing Quantitative Characteristics of Finite-state Real-time Systems, Proc. RTSS’94, IEEE, 1994.
C. Courcoubetis and M. Yannakakis, Minimum and Maximum Delay Problems in Real-time Systems, Proc. CAV’91, LNCS 575, 399–409, Springer, 1991.
C. Daws and S. Yovine, Reducing the Number of Clock Variables of Timed Automata, Proc. RTSS’96, 73–81, IEEE, 1996.
A. Fehnker, Scheduling a Steel Plant with Timed Automata, Proc. RTCSA’99, 1999.
T. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine, Symbolic Modelchecking for Real-time Systems, Information and Computation 111, 193–244, 1994.
A.S. Jain and S. Meeran, Deterministic Job-Shop Scheduling: Past, Present and Future, European Journal of Operational Research 113, 390–434, 1999.
O. Maler, On the Problem of Task Scheduling, Draft, February 1999.
O. Maler, A. Pnueli and J. Sifakis. On the Synthesis of Discrete Controllers for Timed Systems, Proc. STACS’95, 229–242, LNCS 900, Springer, 1995.
P. Niebert, S. Tripakis S. Yovine, Minimum-Time Reachability for Timed Automata, IEEE Mediteranean Control Conference, 2000.
P. Niebert and S. Yovine, Computing Optimal Operation Schemes for Chemical Plants in Multi-batch Mode, Proc. HSCC’2000, 338–351, LNCS 1790, Springer, 2000.
H. Wong-Toi and G. Hoffmann, The Control of Dense Real-Time Discrete Event Systems, Technical report STAN-CS-92-1411, Stanford University, 1992.
S. Yovine, Kronos: A Verification Tool for Real-time Systems, Int. J. of Software Tools for Technology Transfer 1, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abdeddaïm, Y., Maler, O. (2001). Job-Shop Scheduling Using Timed Automata?. In: Berry, G., Comon, H., Finkel, A. (eds) Computer Aided Verification. CAV 2001. Lecture Notes in Computer Science, vol 2102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44585-4_46
Download citation
DOI: https://doi.org/10.1007/3-540-44585-4_46
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42345-4
Online ISBN: 978-3-540-44585-2
eBook Packages: Springer Book Archive