Skip to main content
Log in

The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We study the earliness-tardiness scheduling problem on a single machine with due date assignment and controllable processing times. We analyze the problem with three different due date assignment methods and two different processing time functions. For each combination of these, we provide a polynomial-time algorithm to find the optimal job sequence, due date values and resource allocation minimizing an objective function which includes earliness, tardiness, due date assignment, makespan and total resource consumption costs.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adamopoulos, G. I., & Pappis, C. P. (1996). Single machine scheduling with flow allowances. Journal of the Operational Research Society, 47, 1280–1285.

    Article  Google Scholar 

  • Alidaee, B., & Ahmadian, A. (1993). Two parallel machine sequencing problems involving controllable job processing times. European Journal of Operational Research, 70, 335–341.

    Article  Google Scholar 

  • Armstrong, R., Gu, S., & Lei, L. (1995). An algorithm for the two-resource allocation problem with a non-differentiable convex objective function. Journal of the Operational Research Society, 46, 116–122.

    Article  Google Scholar 

  • Armstrong, R., Gu, S., & Lei, L. (1997). Solving a class of two-resource allocation problem by equivalent load method. Journal of the Operational Research Society, 48, 818–825.

    Article  Google Scholar 

  • Baker, K. R., & Scudder, G. D. (1990). Sequencing with earliness and tardiness penalties: a review. Operations Research, 38, 22–36.

    Google Scholar 

  • Biskup, D., & Jahnke, H. (2001). Common due date assignment for scheduling on a single machine with jointly reducible processing times. International Journal of Production Economics, 69, 317–322.

    Article  Google Scholar 

  • Cheng, T. C. E., Oğaz, C., & Qi, X. D. (1996). Due-date assignment and single machine scheduling with compressible processing times. International Journal of Production Economics, 43, 29–35.

    Article  Google Scholar 

  • Daniels, R. L. (1990). A multi-objective approach to resource allocation in single machine scheduling. European Journal of Operational Research, 48, 226–241.

    Article  Google Scholar 

  • Gordon, V., Proth, J. M., & Chu, C. B. (2002a). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139, 1–25.

    Article  Google Scholar 

  • Gordon, V., Proth, J. M., & Chu, C. B. (2002b). Due date assignment and scheduling: SLK, TWK and other due date assignment models. Production Planning and Control, 13(2), 117–132.

    Article  Google Scholar 

  • Gupta, Y. P., Bector, C. R., & Gupta, M. C. (1990). Optimal schedule on a single machine using various due date determination methods. Computers in Industry, 15(3), 245–253.

    Article  Google Scholar 

  • Hall, N. G., & Posner, M. (1991). Earliness-tardiness scheduling problems, I: weighted deviation of completion times about a common due date. Operations Research, 39(5), 836–846.

    Google Scholar 

  • Hardy, G. H., Littlewood, J. E., & Polya, G. (1934). Inequalities. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hoogeveen, H., & Woeginger, G. J. (2002). Some comments on sequencing with controllable processing times. Computing, 68, 181–192.

    Article  Google Scholar 

  • Janiak, A. (1987). One-machine scheduling with allocation of continuously-divisible resource and with no precedence constraints. Kybernetika, 23(4), 289–293.

    Google Scholar 

  • Monma, C.L., Schrijver, A., Todd, M. J., & Wei, V. K. (1990). Convex resource allocation problems on directed acyclic graphs: duality, complexity, special cases and extensions. Mathematics of Operations Research, 15, 736–748.

    Google Scholar 

  • Ng, C. T. D., Cheng, T. C. E., Kovalyov, M. Y., & Lam, S. S. (2003). Single machine scheduling with a variable common due date and resource-dependent processing times. Computers and Operations Research, 30, 1173–1185.

    Article  Google Scholar 

  • Nowicki, E., & Zdrzalka, S. (1990). A survey of results for sequencing problems with controllable processing times. Discrete Applied Mathematics, 26, 271–287.

    Article  Google Scholar 

  • Panwalkar, S. S., Smith, M. L., & Seidmann, A. (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research, 30, 391–399.

    Article  Google Scholar 

  • Panwalkar, S. S., & Rajagopalan, R. (1992). Single-machine sequencing with controllable processing times. European Journal of Operational Research, 59, 298–302.

    Article  Google Scholar 

  • Papadimitriou, C. H., & Steiglitz, K. (1982). Combinatorial optimization: algorithms and complexity. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Scott, S. C., & Jefferson, T. R. (1995). Allocation of resources in project management. International Journal of Systems Science, 26(2), 413–420.

    Article  Google Scholar 

  • Seidmann, A., Panwalkar, S. S., & Smith, M. L. (1981). Optimal assignment of due dates for a single processor scheduling problem. International Journal of Production Research, 19, 393–399.

    Article  Google Scholar 

  • Shabtay, D. (2004). Single and a two-resource allocation algorithms for minimizing the maximal lateness in a single machine-scheduling problem. Computers and Operations Research, 31(8), 1303–1315.

    Article  Google Scholar 

  • Shabtay, D., & Kaspi, M. (2004). Minimizing the total weighted flow time in a single machine with controllable processing times. Computers and Operations Research, 31(13), 2279–2289.

    Article  Google Scholar 

  • Shabtay, D., & Steiner, G. (2006). Two due date assignment problems in scheduling a single machine. Operations Research Letters, 34(6), 683–691.

    Article  Google Scholar 

  • Shabtay, D., & Steiner, G. (2007). A survey of scheduling with controllable processing times. Discrete Applied Mathematics, 155(13), 1643–1666.

    Article  Google Scholar 

  • Slotnick, S. A., & Sobel, M. J. (2005). Manufacturing lead-time rules: Customer retention versus tardiness costs. European Journal of Operational Research, 169, 825–856.

    Article  Google Scholar 

  • Van Wassenhove, L., & Baker, K. R. (1982). A bicriterion approach to time/cost trade-offs in sequencing. European Journal of Operational Research, 11, 48–54.

    Article  Google Scholar 

  • Vickson, R. G. (1980). Two single machine sequencing problems involving controllable job processing times. AIIE Transactions, 12(3), 258–262.

    Google Scholar 

  • Wan, G., Yen, B. P. C., & Li, C. L. (2001). Single machine scheduling to minimize total compression plus weighted flow cost is \(\mathcal{NP}\) -hard. Information Processing Letters, 79, 273–280.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dvir Shabtay.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shabtay, D., Steiner, G. The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times. Ann Oper Res 159, 25–40 (2008). https://doi.org/10.1007/s10479-007-0269-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-007-0269-y

Keywords

Navigation