Journal of Scheduling

, Volume 13, Issue 6, pp 597–607 | Cite as

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

  • Débora P. Ronconi
  • Warren B. Powell


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.


Tardiness Approximate dynamic programming Single machine Scheduling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baker, K. R., & Bertrand, J. W. M. (1982). A dynamic priority rule for scheduling against due-dates. Journal of Operations Management, 3, 37–42. CrossRefGoogle Scholar
  2. 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. CrossRefGoogle Scholar
  3. Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont: Athena Scientific. Google Scholar
  4. Du, J., & Leung, J. Y.-T. (1990). Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research, 15, 483–495. CrossRefGoogle Scholar
  5. de Farias, D. P., & Van Roy, B. (2003). The linear programming approach to approximate dynamic programming. Operations Research, 51, 850–865. CrossRefGoogle Scholar
  6. George, A., & Powell, W. B. (2006). Adaptive stepsizes for recursive estimation with applications in approximate dynamic programming. Machine Learning, 65, 167–198. CrossRefGoogle Scholar
  7. Kanet, J. J. (1986). Tactically delayed versus non-delay scheduling: an experimental investigation. European Journal of Operational Research, 24, 99–115. CrossRefGoogle Scholar
  8. Kanet, J. J., & Li, X. (2004). A weighted modified due date rule for sequencing to minimize weighted tardiness. Journal of Scheduling, 7, 261–276. CrossRefGoogle Scholar
  9. Kanet, J. J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48, 99–110. CrossRefGoogle Scholar
  10. Lee, J. H., & Lee, J. M. (2006). Approximate dynamic programming based approach to process control and scheduling. Computer and Chemical Engineering, 30, 1603–1618. CrossRefGoogle Scholar
  11. 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
  12. Powell, W. B. (2007). Approximate dynamic programming: solving the curses of dimensionality. Hoboken: Wiley. CrossRefGoogle Scholar
  13. Pinedo, M. (2002). Scheduling: theory, algorithms, and systems. Upper Saddle River: Prentice-Hall. Google Scholar
  14. Sen, T., & Gupta, S. K. (1984). State-of-art survey of static scheduling research involving due dates. OMEGA, 12, 63–76. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. Sridharan, V., & Zhou, Z. (1996). Dynamic non-preemptive single machine scheduling. Computers and Operations Research, 23, 1183–1190. CrossRefGoogle Scholar
  17. Spivey, M. Z., & Powell, W. B. (2004). The dynamic assignment problem. Transportation Science, 38, 339–419. CrossRefGoogle Scholar
  18. Sutton, R., & Barto, A. (1998). Reinforcement learning. Cambridge: MIT Press. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Departamento de Engenharia de Produção, Escola PolitécnicaUniversidade de São PauloSão PauloBrazil
  2. 2.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations