Skip to main content
SpringerLink
Log in

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

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

  • Baker, K. R., & Bertrand, J. W. M. (1982). A dynamic priority rule for scheduling against due-dates. Journal of Operations Management, 3, 37–42.

    Article  Google Scholar 

  • Bergamaschi, D., Cigolini, R., Perona, M., & Portioli, A. (1997). Order review and release strategies in a job shop environment: a review and a classification. International Journal of Production Research, 35, 399–420.

    Article  Google Scholar 

  • Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont: Athena Scientific.

    Google Scholar 

  • Du, J., & Leung, J. Y.-T. (1990). Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research, 15, 483–495.

    Article  Google Scholar 

  • de Farias, D. P., & Van Roy, B. (2003). The linear programming approach to approximate dynamic programming. Operations Research, 51, 850–865.

    Article  Google Scholar 

  • George, A., & Powell, W. B. (2006). Adaptive stepsizes for recursive estimation with applications in approximate dynamic programming. Machine Learning, 65, 167–198.

    Article  Google Scholar 

  • Kanet, J. J. (1986). Tactically delayed versus non-delay scheduling: an experimental investigation. European Journal of Operational Research, 24, 99–115.

    Article  Google Scholar 

  • Kanet, J. J., & Li, X. (2004). A weighted modified due date rule for sequencing to minimize weighted tardiness. Journal of Scheduling, 7, 261–276.

    Article  Google Scholar 

  • Kanet, J. J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48, 99–110.

    Article  Google Scholar 

  • Lee, J. H., & Lee, J. M. (2006). Approximate dynamic programming based approach to process control and scheduling. Computer and Chemical Engineering, 30, 1603–1618.

    Article  Google Scholar 

  • Powell, W. B., & Van Roy, B. (2004). Approximate dynamic programming for high dimensional resource allocation problems. In J. Si, A. G. Barto, & W. B. Powell II (Eds.), Handbook of learning and approximate dynamic programming. New York: IEEE Press.

    Google Scholar 

  • Powell, W. B. (2007). Approximate dynamic programming: solving the curses of dimensionality. Hoboken: Wiley.

    Book  Google Scholar 

  • Pinedo, M. (2002). Scheduling: theory, algorithms, and systems. Upper Saddle River: Prentice-Hall.

    Google Scholar 

  • Sen, T., & Gupta, S. K. (1984). State-of-art survey of static scheduling research involving due dates. OMEGA, 12, 63–76.

    Article  Google Scholar 

  • Sen, T., Sulek, J. M., & Dileepan, P. (2003). Static scheduling research to minimize weighted and unweighted tardiness: a state-of-the-art survey. International Journal of Production Economics, 83, 1–12.

    Article  Google Scholar 

  • Sridharan, V., & Zhou, Z. (1996). Dynamic non-preemptive single machine scheduling. Computers and Operations Research, 23, 1183–1190.

    Article  Google Scholar 

  • Spivey, M. Z., & Powell, W. B. (2004). The dynamic assignment problem. Transportation Science, 38, 339–419.

    Article  Google Scholar 

  • Sutton, R., & Barto, A. (1998). Reinforcement learning. Cambridge: MIT Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Engenharia de Produção, Escola Politécnica, Universidade de São Paulo, Av. Prof. Almeida Prado, 128, Cidade Universitária, 05508-900, São Paulo, SP, Brazil

    Débora P. Ronconi

  2. Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 08544, USA

    Warren B. Powell

Authors
  1. Débora P. Ronconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Warren B. Powell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Débora P. Ronconi.

Additional information

D.P. Ronconi was supported by CNPq (Grants 486124/2007-0 and 307399/2006-0) and FAPESP (Grants 06/03496-3 and 06/53440-4).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ronconi, D.P., Powell, W.B. Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming. J Sched 13, 597–607 (2010). https://doi.org/10.1007/s10951-009-0160-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-009-0160-6

Keywords

Search

Navigation