Journal of Scheduling

, Volume 18, Issue 3, pp 305–309 | Cite as

Trading off due-date tightness and job tardiness in a basic scheduling model

  • Kenneth R. BakerEmail author
  • Dan Trietsch


We consider a scheduling problem in which the criterion for assigning due dates is to make them as tight as possible, while the criterion for sequencing jobs is to minimize their tardiness. Because these two criteria conflict, we examine the trade-off between the tightness of the due dates and the tardiness of the jobs. We formulate a version of this trade-off in the case of a stochastic single-machine model with normally distributed processing times. Using lower bounds and dominance properties to curtail the enumeration, we develop a branch-and- bound procedure that is capable of solving large versions of the problem, and we report the results of computational experiments involving several hundred test problems.


Sequencing Stochastic scheduling Tardiness Due-date assignment Single machine 


  1. Baker, K., & Trietsch, D. (2009a). Principles of Sequencing and Scheduling. New York: John Wiley & Sons.CrossRefGoogle Scholar
  2. Baker, K., & Trietsch, D. (2009b). Safe scheduling: Setting due dates in single-machine problems. European Journal of Operational Research, 196, 69–77.CrossRefGoogle Scholar
  3. Balut, S. (1973). Scheduling to minimize the number of late jobs when set-up and processing times are uncertain. Management Science, 19, 1283–1288. Google Scholar
  4. Cheng, T., & Gupta, M. (1989). Survey of scheduling research involving due date determination decisions. European Journal of Operational Research, 38, 156–166.CrossRefGoogle Scholar
  5. Cai, X., & Zhou, S. (1997). Scheduling stochastic jobs with asymmetric earliness and tardiness penalties. Naval Research Logistics, 44, 531–557.CrossRefGoogle Scholar
  6. Gordon, V., Proth, J.-M., & Chu, C. (2002). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139, 1–25.Google Scholar
  7. Jang, W. (2002). Dynamic scheduling of stochastic jobs on a single machine. European Journal of Operational Research, 138, 518–530.CrossRefGoogle Scholar
  8. Portougal, V., & Trietsch, D. (2006). Setting due dates in a stochastic single machine environment. Computers & Operations Research, 33, 1681–1694.CrossRefGoogle Scholar
  9. Sarin, S., Erdel, E., & Steiner, G. (1991). Sequencing jobs on a single machine with a common due date and stochastic processing times. European Journal of Operational Research, 27, 188–198.CrossRefGoogle Scholar
  10. Seo, D., Klein, C., & Jang, W. (2005). Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models. Computers & Industrial Engineering, 48, 153–161.CrossRefGoogle Scholar
  11. Soroush, H. (1999). Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs. European Journal of Operations Research, 113, 450–468.CrossRefGoogle Scholar
  12. Soroush, H., & Fredendall, L. (1994). The stochastic single machine scheduling problem with earliness and tardiness costs. European Journal of Operational Research, 77, 287–302.CrossRefGoogle Scholar
  13. Wein, L. M. (1991). Due-date setting and priority sequencing in a multiclass M/G/1 queue. Management Science, 37, 834–850.CrossRefGoogle Scholar
  14. Wu, C., Brown, K., & Beck, J. (2009). Scheduling with uncertain durations: Modeling \(\beta \)-robust scheduling with constraints. Computers & Operations Research, 36, 2348–2356.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Tuck SchoolDartmouth CollegeHanoverUSA
  2. 2.College of EngineeringAmerican University of ArmeniaYerevanArmenia

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