Skip to main content
SpringerLink
Log in

Synthesis and stochastic assessment of cost-optimal schedules

  • Regular Contribution
  • Published:
International Journal on Software Tools for Technology Transfer Aims and scope Submit manuscript

Abstract

We treat the problem of generating cost-optimal schedules for orders with individual due dates and cost functions based on earliness/tardiness. Orders can run in parallel in a resource-constrained manufacturing environment, where resources are subject to stochastic breakdowns. The goal is to generate schedules while minimizing the expected costs. First, we estimate the distribution of each order type by simulation (assuming a reasonable machine/load model) and derive from the cost-function an optimal offset from the due date of each individual order. Second, these optimal offsets are then used to guide the generation of schedules which are responsible to resolve resource conflicts. Third, we evaluate the generated schedules by simulation. The approach is demonstrated by means of a non-trivial case-study from lacquer production. Optimal offsets are derived with the Modest/Möbius tool, schedules are generated using Uppaal Cora. The experimental results show that our approach achieves good results in all considered scenarios, and better results than an approach based on adding slack to processing times.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdeddaïm Y., Asarin E., Maler O.: Scheduling with timed automata. Theor. Comput. Sci. 354(2), 272–300 (2006)

    Article  MATH  Google Scholar 

  2. Abdeddaïm Y., Maler O.: Job-shop scheduling using timed automata. In: Berry, G., Comon, H., Finkel, A. (eds) Computer Aided Verification. LNCS, vol. 2102, pp. 478–492. Springer, Berlin (2001)

    Chapter  Google Scholar 

  3. Alur R., Dill D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Alur R., Torre S., Pappas G.J.: Optimal paths in weighted timed automata. In: Di Benedetto , M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control 2001. LNCS, vol. 2034, Springer, Berlin (2001)

    Google Scholar 

  5. AMETIST, IST project ist-2001-35304. http://ametist.cs.utwente.nl/

  6. Amnell T., Behrmann G., Bengtsson J., D’Argenio P.R., David A., Fehnker A., Hune T., Jeannet B., Larsen K.G., Möller M.O., Pettersson P., Weise C., Yi W.: UPPAAL: Now, next, and future. In: Cassez, F., Jard, C., Rozoy, B., Ryan, M. (eds) MOVEP 2000. LNCS, vol. 2067, pp. 99–124. Springer, Berlin (2001)

    Google Scholar 

  7. Behrmann, G., Brinksma, H., Hendriks, M., Mader, A.: Production scheduling by reachability analysis: a case study. In: WPDRTS ’05. IEEE Computer Society, Los alamitos (2005)

  8. Behrmann, G., Brinksma, H., Hendriks, M., Mader, A.: Scheduling lacquer production by reachability analysis: a case study. In: Horacek, P., Simandl, M., Zitek, P. (eds.) 16th IFAC World Congress. International Federation of Automatic Control (2005)

  9. Behrmann G., David A., Larsen K.G.: A tutorial on Uppaal. In: Bernardo , M., Corradini, F. (eds) Formal Methods for the Design of Real-Time Systems 2004. LNCS, vol. 3185, pp. 200–236. Springer, Berlin (2004)

    Google Scholar 

  10. Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Petterson, P., Romijn, J.: Guiding and cost-optimality in Uppaal. In: Khatib, L., Pecheur, C., (eds.) Model-Based Validation of Intelligence: Papers from 2001 AAAI Spring Symposium. AAAI, Menlo Park (2001)

  11. Behrmann G., Larsen K.G., Rasmussen J.I.: Optimal scheduling using priced timed automata. SIGMETRICS Perform. Eval. Rev. 32(4), 34–40 (2005)

    Article  Google Scholar 

  12. Bohnenkamp H., d’Argenio P.R., Hermanns H., Katoen J.-P.: MoDeST: a compositional modeling formalism for real-time and stochastic systems. IEEE Trans. Soft. Eng. 32(10), 812–830 (2006)

    Article  Google Scholar 

  13. Bohnenkamp, H., Hermanns, H., Katoen, J.-P.: Motor: The MoDeST tool environment. In: Proceedings of TACAS ’07. LNCS, vol. 4424, pp. 500–504. Springer, Berlin (2007)

  14. Bohnenkamp H., Hermanns H., Katoen J.-P., Klaren R.: The Modest modeling tool and its implementation. In: Kemper, P., Sanders, W.H. (eds) TOOLS ’03. LNCS, vol. 2794, pp. 116–133. Springer, Berlin (2003)

    Google Scholar 

  15. Bohnenkamp, H., Hermanns, H., Klaren, R., Mader, A., Usenko, Y.S.: Synthesis and stochastic assessment of schedules for lacquer production. In: QEST ’04, pp. 28–37. IEEE Computer Society, Los Alamitos (2004)

  16. Butazzo G.C.: Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications. Kluwer, Dordrecht (1997)

    Google Scholar 

  17. Cai X.Q., Zhou X.: Stochastic scheduling with asymmetric earliness and tardiness penalties under random machine breakdowns. Probab. Eng. Inf. Sci. 20(4), 635–654 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  18. D’Argenio P.R., Hermanns H., Katoen J.-P., Klaren J.: MoDeST: a modelling and description language for stochastic timed systems. In: de alfaro, L., Gilmore, S. (eds) Process Algebra and Probabilistic Methods: … PAPM–PROBMIV. LNCS, vol. 2165, pp. 87–104. Springer, Berlin (2001)

    Google Scholar 

  19. Deavours D.D., Clark G., Courtney T., Daly D., Derasavi S., Doyle J.M., Sanders W.H., Webster P.G.: The Möbius framework and its implementation. IEEE Trans. Soft. Eng. 28(10), 956–969 (2002)

    Article  Google Scholar 

  20. Demeulemeester E.L., Herroelen W.S.: Project Scheduling: A Research Handbook. Kluwer, Boston (2002)

    MATH  Google Scholar 

  21. Fehnker, A.: Scheduling a steel plant with timed automata. In: Sixth International Conference on Real-Time Computing Systems and Applications: RTCSA, pp. 280–286. IEEE Computer Society, Los Alamitos (1999)

  22. Gao, H.: Building robust schedules using temporal protection—an empirical study of constrained based scheduling under machine failure uncertainty. Master’s thesis, Department of Industrial Engineering, University of Toronto (1995)

  23. Harrison P.G., Patel N.M.: Performance Modelling of Communication Networks and Computer Architectures. Addison-Wesley, Wokingham (1993)

    MATH  Google Scholar 

  24. Herroelen W., Leus R.: Robust and reactive project scheduling: a review and classification of procedures. Int. J. Prod. Res. 42(8), 1599–1620 (2004)

    Article  Google Scholar 

  25. Herroelen W., Leus R.: Project scheduling under uncertainty: survey and research potentials. Eur. J. Oper. Res. 165(2), 289–306 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  26. Holzmann G.J.: The SPIN Model Checker: Primer and Reference Manual. Addison-Wesley, Boston (2004)

    Google Scholar 

  27. Lambrechts O., Demeulemeester E., Herroelen W.: A tabu search procedure for developing robust predictive project schedules. Int. J. Prod. Econ. 111(2), 493–508 (2008)

    Article  MathSciNet  Google Scholar 

  28. Magee J., Kramer J.: Concurrency: State Models and Java Programs. Wiley, Chichester (1999)

    MATH  Google Scholar 

  29. Mehta S.V., Uzsoy R.M.: Predictable scheduling of a job shop subject to breakdowns. IEEE Trans. Robot. Autom. 14(3), 365–378 (1998)

    Article  Google Scholar 

  30. Mehta S.V., Uzsoy R.M.: Predictable scheduling of a single machine subject to breakdowns. Int. J. Comput. Integr. Manuf. 12(1), 15–38 (1999)

    Article  Google Scholar 

  31. MoDeST site. http://www.purl.com/net/modest

  32. Panek S., Engell S., Lessner C.: Scheduling of a pipeless multi-product batch plant using mixed-integer programming combined with heuristics. In: Puigjaner, L., Espuña, A. (eds) ESCAPE-15, A/B of Computer-aided chemical engineering, vol. 20, pp. 1033–1038. Elsevier, Amsterdam (2005)

    Google Scholar 

  33. Pinedo M.L.: Planning and Scheduling in Manufacturing and Services. Springer Series in Operations Research and Financial Engineering, New York (2005)

    MATH  Google Scholar 

  34. Stork, F.: Stochastic Resource-Constrained Project Scheduling. Ph.D. thesis, Technical University of Berlin (2001)

  35. UPPAAL CORA site. http://www.cs.aau.dk/~behrmann/cora/

  36. UPPAAL home page. http://www.uppaal.com

Download references

Author information

Authors and Affiliations

  1. Faculty EWI, University of Twente, 7500 AE, Enschede, The Netherlands

    Angelika Mader & Johann Hurink

  2. Modeling and Verification of Software, RWTH Aachen University, 52056, Aachen, Germany

    Henrik Bohnenkamp

  3. Centrum Wiskunde & Informatica Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Yaroslav S. Usenko

  4. Computing Science Institute, Radboud University Nijmegen, Nijmegen, The Netherlands

    David N. Jansen

  5. Dependable Systems and Software Group, Saarland University, 66041, Saarbrücken, Germany

    Holger Hermanns

Authors
  1. Angelika Mader
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henrik Bohnenkamp
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yaroslav S. Usenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David N. Jansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Johann Hurink
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Holger Hermanns
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Angelika Mader.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mader, A., Bohnenkamp, H., Usenko, Y.S. et al. Synthesis and stochastic assessment of cost-optimal schedules. Int J Softw Tools Technol Transfer 12, 305–318 (2010). https://doi.org/10.1007/s10009-009-0129-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10009-009-0129-y

Keywords

Search

Navigation