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A Constraint-Based Method for Project Scheduling with Time Windows

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Abstract

This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.

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References

  • Baptiste, P. and C. Le Pape. (1995). “A Theoretical and Experimental Comparison of Constraint Propagation Trchniques for Disjunctive Scheduling.” In Proceedings of the 14th International Joint Conference on Artificial Intelligence.

  • Baptiste, P., C. Le Pape, and W. Nuijten. (1999). “Satifiability Tests and Time-Bound Adjustments for Cumulative Scheduling Problems.” Technical Report, University of Compiégnie. Annals of Operations Research 92, 305–333.

    Google Scholar 

  • Bartusch, M., R.H. Mohring, and F.J. Radermacher. (1998). “Scheduling Project Networks with Resource Constraints and Time Windows.” Annals of Operations Research 16, 201–240.

    Google Scholar 

  • Brucker, P., A. Drexl, R. Mohring, K. Neumann, and E. Pesch, (1998). “Resource-Constrained Project Scheduling: Notation, Classification, Models, and Methods,” European Journal of Operations Research.

  • Caseau, Y. and F. Laburthe. (1994). “Improved CLP Scheduling with Task Intervals.” In P.V. Hentenryck (ed.), Logic Programming, Proceedings of the Eleventh International Conference on Logic Programming, Santa Margherita Ligure, Italy. Cambridge, MA: MIT Press, pp. 369–383.

    Google Scholar 

  • Caseau, Y. and F. Laburthe. (1996). “Cumulative Scheduling with Task Intervals.” In M. Maher (ed.), Logic Programming, Proceedings of the Joint International Conference and Symposium on Logic Programming, Bonn, Germany. Cambridge, MA: MIT Press.

    Google Scholar 

  • Cesta, A., A. Oddi, and S.F. Smith. (1998a). “Profile Based Algorithms to Solve Multiple Capacitated Metric Scheduling Problems.” In Proceedings of the Fourth Int. Conf. on Artificial Intelligence Planning Systems (AIPS-98).

  • Cesta, A., A. Oddi, and S.F. Smith. (1998b). “Scheduling Multi-Capacitated Resources under Complex Temporal Constraints.” Technical Report CMU-RI-TR-98-17, Robotics Institute, Carnegie Mellon University.

  • Cesta, A., A. Oddi, and S.F. Smith. (1999). “An Iterative Sampling Procedure for Resource Constrained Project Scheduling with Time Windows.” In Proceedings of the 16th Int. Joint Conference on Artificial Intelligence (IJCAI-99).

  • Cheng, C. and S.F. Smith. (1994). “Generating Feasible Schedules under Complex Metric Constraints.” In Proceedings 12th National Conference on AI (AAAI-94).

  • Cheng, C. and S.F. Smith. (1997). “Applying Constraint Satisfaction Techniques to Job Shop Scheduling.” Annals of Operations Research 70, 327–357.

    Google Scholar 

  • Crawford, J. (1996). “An Approach to Resource Constrained Project Scheduling.” In Proceedings of the 1996 Artificial Intelligence and Manufacturing Research Planning Workshop.

  • De Reyck, B. and W. Herroelen. (1998). “A Branch-and-Bound Procedure for the Resource-Constrained Project Scheduling Problem with Generalized Procedence Relations.” European Journal of Operations Research 111(1), 152–174.

    Google Scholar 

  • Dechter, R., I. Meiri, and J. Pearl. (1991). “Temporal Constraint Networks.” Artificial Intelligence 49, 61–95.

    Google Scholar 

  • Dorndorf, U., E. Pesch, and T. Phan Huy. (1998). “A Time-Oriented Branch-and-Bound Algorithm for Resource-Constrained Project Scheduling with Generalized Precedence Relations.” Technical Report, University of Bonn, Faculty of Economics.

  • Franck, B. and K. Neumann. (1998). “Resource Constrained Project Scheduling Problems with TimeWindows— Structural Questions and Priority-Rule Methods.” Technical Report WIOR-492, Universität Karlsruhe (Revised November 1998).

  • Harvey, W. and M. Ginsberg. (1995). “Limited Discrepancy Search.” In Proceedings of the 14th Int. Joint Conference on Artificial Intelligence (IJCAI-95).

  • Heilmann, R. and C. Schwindt. (1997). “Lower Bounds for RCPSP/max.” Technical Report WIOR-511, Universität Karlsruhe.

  • Kolisch, R., C. Schwindt, and A. Sprecher. (1998). “Benchmark Instances for Project Scheduling Problems.” In J. Weglarz (ed.), Handbook on Recent Advances in Project Scheduling. Dordrecht: Kluwer.

    Google Scholar 

  • Laborie, P. and M. Ghallab. (1995). “Planning with Sharable Resource Constraints.” In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-95).

  • Möhring, R., F. Stork, and M. Uetz. (1998). “Resource Constrained Project Scheduling with Time Windows: A Branching Scheme Based on Dynamic Release Dates.” Technical Report 596/1998, Fachbereich Mathematick, Technische Universität Berlin.

  • Montanari, U. (1974). “Networks of Constraints: Fundamental Properties and Applications to Picture Processing.” Information Sciences 7, 95–132.

    Google Scholar 

  • Neumann, K. and C. Schwindt. (1997). “Activity-on-Node Networks with Minimal and Maximal Time Lags and Their Application to Make-to-Order Production.” Operation Research Spektrum 19, 205–217.

    Google Scholar 

  • Neumann, K. and J. Zhan. (1995). “Heuristics for the Minimum Project-Duration Problem with Minimal and Maximal Time Lags under Fixed Resource Constraints.” Journal of Intelligent Manufacturing 6, 145–154.

    Google Scholar 

  • Nuijten, W. and E. Aarts. (1996). “A Computational Study of Constraint Satisfaction for Multiple Capacitated Job Shop Scheduling.” European Journal of Operational Research 90(2), 269–284.

    Google Scholar 

  • Nuijten, W. and C. Le Pape. (1998). “Constraint-Based Job Shop Scheduling with ILOG-SCHEDULER.” Journal of Heuristics 3, 271–286.

    Google Scholar 

  • Oddi, A. and S.F. Smith. (1997). “Stochastic Procedures for Generating Feasible Schedules.” In Proceedings 14th National Conference on AI (AAAI-97).

  • Sadeh, N. (1991). “Look-Ahead Techniques for Micro-opportunistic Job-Shop Scheduling.” Ph.D. Thesis, School of Computer Science, Carnegie Mellon University.

  • Schwindt, C. (1996). “Generation of Resource Constrained Project Scheduling Problems with Minimal and Maximal Time Lags.” Technical Report WIOR-489, Universität Karlsruhe.

  • Schwindt, C. (1998). “A Branch and Bound Algorithm for the Resource-Constrained Project Duration Problem Subject to Temporal Constraints.” Technical Report WIOR-544, Universität Karlsruhe.

  • Smith, S.F. and C. Cheng. (1993). “Slack-Based Heuristics for Constraint Satisfaction Scheduling.” In Proceedings 11th National Conference on AI (AAA1-93).

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Authors and Affiliations

  1. IP-CNR, National Research Council of Italy, Viale Marx 15, I-00137, Rome, Italy

    Amedeo Cesta & Angelo Oddi

  2. The Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Stephen F. Smith

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  1. Amedeo Cesta
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  2. Angelo Oddi
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  3. Stephen F. Smith
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Correspondence to Amedeo Cesta.

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Cesta, A., Oddi, A. & Smith, S.F. A Constraint-Based Method for Project Scheduling with Time Windows. Journal of Heuristics 8, 109–136 (2002). https://doi.org/10.1023/A:1013617802515

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