Abstract
There are many systems and techniques that address stochastic planning and scheduling problems, based on distinct and sometimes opposite approaches, especially in terms of how generation and execution of the plan, or the schedule, are combined, and if and when knowledge about the uncertainties is taken into account. In many real-life problems, it appears that many of these approaches are needed and should be combined, which to our knowledge has never been done. In this paper, we propose a typology that distinguishes between proactive, progressive, and revision approaches. Then, focusing on scheduling and schedule execution, a theoretic model integrating those three approaches is defined. This model serves as a general template to implement a system that will fit specific application needs: we introduce and discuss our experimental prototypes which validate our model in part, and suggest how this framework could be extended to more general planning systems.
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References
Adams, J., Balas, E., & Zawack, D. (1988). The shifting bottleneck procedure for job-shop scheduling. Management Science, 34, 391–401.
Aktürk, M. S., & Yildirim, M. B. (1999). A new dominance rule for the total weighted tardiness problem. Production Planning and Control, 10(2), 138–149.
Applegate, D., & Cook, W. (1991). A computational study of the job-shop scheduling problem. ORSA Journal on Computing, 3(2), 149–156.
Baptiste, P., & Le Pape, C. (1996). Edge-finding constraint propagation algorithms for disjunctive and cumulative scheduling. In Proceedings of the fifteenth workshop of the UK planning special interest group, Liverpool, United Kingdom.
Beck, J. C. (1999). Texture measurements as a basis for heuristic commitment techniques in constraint-directed scheduling. Ph.D. dissertation, University of Toronto, Toronto, Canada.
Beck, J. C., & Fox, M. S. (2000). Constraint-directed techniques for scheduling with alternative activities. Artificial Intelligence, 121(1–2), 211–250.
Beck, J. C., & Wilson, N. (2007). Proactive algorithms for job shop scheduling with probabilistic durations. Journal of Artificial Intelligence Research, 28, 183–232.
Bidot, J., Laborie, P., Beck, J. C., & Vidal, T. (2003). Using simulation for execution monitoring and on-line rescheduling with uncertain durations. In Working notes of the ICAPS’03 workshop on plan execution, Trento, Italy, June 2003.
Bidot, J., Laborie, P., Beck, J. C., & Vidal, T. (2006). Using constraint programming and simulation for execution monitoring and progressive scheduling. In Proceedings of the twelfth IFAC symposium on information control problems in manufacturing (INCOM 2006) (pp. 595–600). Saint-Étienne, France, May 2006.
Bidot, J., Vidal, T., Laborie, P., & Beck, J. C. (2007). A general framework for scheduling in a stochastic environment. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI) (pp. 56–61). Hyderabad, India, January 2007.
Billaut, J.-C., Moukrim, A., & Sanlaville, E. (Eds.) (2007). Flexibility and robustness in scheduling. Control Systems, Robotics and Manufacturing. ISTE.
Branke, J., & Mattfeld, D. C. (2002). Anticipatory scheduling for dynamic job-shop problems. In G. Verfaillie (Ed.), Working notes of the AIPS’02 workshop on on-line planning and scheduling (pp. 3–10). Toulouse, France, April 2002.
Bresina, J. L., Dearden, R., Meuleau, N., Ramakrishnan, S., Smith, D. E., & Washington, R. (2002). Planning under continuous time and resource uncertainty: A challenge for AI. In Proceedings of the 18th conference on uncertainty in artificial intelligence (UAI) (pp. 77–84). Edmonton, Alberta, Canada, August 2002.
Chien, S. A., Knight, R., Stechert, A., Sherwood, R., & Rabideau, G. (2000). Using iterative repair to improve the responsiveness of planning and scheduling. In S. A. Chien, S. Kambhampati, & C. A. Knoblock (Eds.), Proceedings of the fifth international conference on artificial intelligence planning and scheduling (AIPS). Breckenridge, CO, USA, April 2000. (pp. 300–307). Menlo Park: AAAI Press.
Davenport, A. J., Gefflot, C., & Beck, J. C. (2001). Slack-based techniques for building robust schedules. In Proceedings of the sixth European conference on planning (ECP). Toledo, Spain, September 2001.
Drummond, M., Bresina, J. L., & Swanson, K. (1994). Just-In-Case scheduling. In Proceedings of the 12th national conference on artificial intelligence (AAAI) (pp. 1098–1104). Seattle, WA, USA, July 1994.
Dubois, D., Fargier, H., & Prade, H. (1993). The use of fuzzy constraints in job-shop scheduling. In Working notes of the IJCAI’93 workshop on knowledge-based production planning, scheduling, and control (pp. 101–112). Chambéry, France, August 1993.
Erschler, J. (1976). Analyse sous contraintes et aide à la décision pour certains problèmes d’ordonnancement. Ph.D. dissertation, Université Paul Sabatier, Toulouse, France.
Fargier, H., Lang, J., & Schiex, T. (1996). Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge. In Proceedings of the 13th national conference on artificial intelligence (AAAI) (pp. 175–180). Portland, OR, USA, August 1996.
Gao, H. (1995). Building robust schedules using temporal protection—an empirical study of constraint-based scheduling under machine failure uncertainty. Master’s thesis, Department of Industrial Engineering, University of Toronto, Toronto, Canada.
Geffner, H. (1998). Modeling intelligent behaviour: The Markov decision process approach. In H. Coelho (Ed.), Lecture notes in AI : Vol. 1484. Proceedings of iberamia 98 (pp. 1–12). New York: Springer. Invited talk.
Hagstrom, J. N. (1988). Computational complexity of PERT problems. Networks, 18, 139–147.
Herroelen, W. S., & Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165(2), 289–306.
Hildum, D. W. (1994). Flexibility in a knowledge-based system for solving dynamic resource-constrained scheduling problems. Ph.D. dissertation, Department of Computer Science, University of Massachusetts Amherst, September 1994.
ILOG S. A. (2002). ILOG scheduler 5.3: reference manual and user’s manual.
Kushmerick, N., Hanks, S., & Weld, D. S. (1995). An algorithm for probabilistic planning. Artificial Intelligence, 76(1–2), 239–286.
La, H. T. (2005). Utilisation d’ordres partiels pour la caractérisation de solutions robustes en ordonnancement. Ph.D. dissertation, Institut National des Sciences Appliquées de Toulouse, Toulouse, France, January 2005.
Lawrence, S. R. (1984). Resource-constrained project scheduling: an experimental investigation of heuristic scheduling techniques (supplement). Ph.D. dissertation, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, USA.
Lemai, S., & Ingrand, F. F. (2004). Interleaving temporal planning and execution in robotics domains. In Proceedings of the 19th national conference on artificial intelligence (AAAI). San Jose, CA, USA, July 2004.
Morris, P. H., Muscettola, N., & Vidal, T. (2001). Dynamic control of plans with temporal uncertainty. In Proceedings of the 17th international joint conference on artificial intelligence (IJCAI) (pp. 494–502). Seattle, WA, USA, August 2001.
Morton, T. E., & Pentico, D. W. (1993). Heuristic scheduling systems with applications to production systems and project management. New York: Wiley.
Muscettola, N. (1994). HSTS: Integrating planning and scheduling. In M. Zweben & M. S. Fox (Eds.), Intelligent scheduling (pp. 169–212). Morgan Kaufmann: San Mateo.
Muscettola, N. (2002). Computing the envelope for stepwise-constant resource allocations. In Proceedings of the eighth international conference on principles and practice of constraint programming (CP) (pp. 139–154). Cornell University, New York, USA, September 2002.
Nilsson, N. J. (1980). Principles of artificial intelligence. Morgan Kaufmann: San Mateo.
Nuijten, W. P. M. (1994). Time- and resource-constrained scheduling. A constraint-satisfaction approach. Ph.D. dissertation, Technische Universiteit Eindhoven, Eindhoven, Netherlands.
Policella, N., Oddi, A., Smith, S. F., & Cesta, A. (2004). Generating robust schedules through chaining. In Proceedings of the tenth international conference on principles and practice of constraint programming (CP) (pp. 496–511). Toronto, Canada, September 2004.
Puterman, M. L. (1994). Markov decision processes: discrete stochastic dynamic programming. New York: Wiley.
Sabuncuoglu, I., & Bayiz, M. (2000). Analysis of reactive scheduling problems in a job-shop environment. European Journal of Operational Research, 126, 567–586.
Sadeh, N. M. (1994). Micro-opportunistic scheduling: The Micro-Boss factory scheduler. In M. Zweben & M. S. Fox (Eds.), Intelligent scheduling (pp. 99–135). Morgan Kaufmann: San Mateo. Chap. 4.
Sadeh, N. M., Otsuka, S., & Schnelbach, R. (1993). Predictive and reactive scheduling with the Micro-Boss production scheduling and control system. In Working notes of the IJCAI’93 workshop on knowledge-based production planning, scheduling, and control (pp. 293–306). Chambéry, France, August 1993.
El Sakkout, H., & Wallace, M. (2000). Probe backtrack search for minimal perturbation in dynamic scheduling. Constraints, 5, 359–388.
Shafaei, R., & Brunn, P. (1999a). Workshop scheduling using practical (inaccurate) data. Part 1: The performance of heuristic scheduling rules in a dynamic job-shop environment using a rolling time horizon approach. International Journal of Production Research, 37(17), 3913–3925.
Shafaei, R., & Brunn, P. (1999b). Workshop scheduling using practical (inaccurate) data. Part 2: An investigation of the robustness of scheduling rules in a dynamic and stochastic environment. International Journal of Production Research, 37(18), 4105–4117.
Smith, S. F. (1994). OPIS: A methodology and architecture for reactive scheduling. In M. Zweben & M. S. Fox (Eds.), Intelligent scheduling (pp. 29–66). Morgan Kaufmann: San Mateo.
Smith, D. E., Frank, J., & Jónsson, A. K. (2000). Bridging the gap between planning and scheduling. Knowledge Engineering Review, 15(1), 61–94.
Tsamardinos, I., Vidal, T., & Pollack, M. E. (2003). CTP: A new constraint-based formalism for conditional, temporal planning. Constraints, 8(4), 365–388.
Vidal, T., Ghallab, M., & Alami, R. (1996). Incremental mission allocation to a large team of robots. In Proceedings of the IEEE international conference on robotics and automation (ICRA’96) (Vol. 2, pp. 1620–1625). Minneapolis, MN, USA.
Wang, X., & Chien, S. A. (1997). Replanning using hierarchical task network and operator-based planning. In Proceedings of the fourth European conference on planning (ECP) (pp. 427–439). Toulouse, France, September 1997.
Wu, S. D., Byeon, E.-S., & Storer, R. H. (1999). A graph-theoretic decomposition of the job-shop scheduling problem to achieve scheduling robustness. Operations Research, 47, 113–123.
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This article is a longer and extended version of a conference paper which appears at IJCAI’07 (Bidot et al. 2007).
J. Bidot is partially supported by Convention Industrielle de Formation par la REcherche 274/2001.
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Bidot, J., Vidal, T., Laborie, P. et al. A theoretic and practical framework for scheduling in a stochastic environment. J Sched 12, 315–344 (2009). https://doi.org/10.1007/s10951-008-0080-x
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DOI: https://doi.org/10.1007/s10951-008-0080-x