Skip to main content
SpringerLink
Log in

Due date assignment for multistage assembly systems

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

This paper is concerned with the study of the constant due-date assignment policy in a multistage assembly system. The multistage assembly system is modeled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite machine with exponentially distributed processing time. The transport times between every pair of service stations are independent random variables with generalized Erlang distributions. It is assumed that each product has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order arrives. This constant value is the constant lead time that a product might expect between time of placing the order and time of delivery. By applying the longest path analysis in queueing networks, we obtain the distribution function of manufacturing lead time. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per product. Finally, the results are verified by Monte Carlo simulation.

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. Azaron, A.: Multiobjective optimal control in stochastic and dynamic networks with applications using shortest path and longest path approaches. Ph.D. Thesis, Hiroshima University, Hiroshima, Japan (2005)

  2. Azaron A., Modarres M.: Distribution function of the shortest path in networks of queues. OR Spectrum 27, 123–144 (2005). doi:10.1007/s00291-004-0169-3

    Article  MATH  MathSciNet  Google Scholar 

  3. Azaron A., Katagiri H., Kato K., Sakawa M.: Modelling complex assemblies as a queueing network for lead time control. Eur. J. Oper. Res. 174, 150–168 (2006). doi:10.1016/j.ejor.2005.01.025

    Article  MATH  MathSciNet  Google Scholar 

  4. Azaron A., Fatemi Ghomi S.M.T.: Optimal control of service rates and arrivals in Jackson networks. Eur. J. Oper. Res. 147, 17–31 (2003). doi:10.1016/S0377-2217(02)00177-7

    Article  MATH  MathSciNet  Google Scholar 

  5. Charnes A., Cooper W., Thompson G.: Critical path analysis via chance constrained and stochastic programming. Oper. Res. 12, 460–470 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cheng T.C.E., Gupta M.C.: Survey of scheduling research involving due date determination decisions. Eur. J. Oper. Res. 38, 156–166 (1989). doi:10.1016/0377-2217(89)90100-8

    Article  MATH  MathSciNet  Google Scholar 

  7. Elmaghraby S.E., Ferreira A.A., Tavares L.V.: Optimal start time under stochastic activity durations. Int. J. Prod. Econ. 64, 153–164 (2000). doi:10.1016/S0925-5273(99)00054-7

    Article  Google Scholar 

  8. Gold H.: A Markovian single server with upstream job and downstream demand arrival stream. Queueing Syst. 30, 435–455 (1998). doi:10.1023/A:1019137626073

    Article  MATH  MathSciNet  Google Scholar 

  9. Harrison J.M.: Assembly-like queues. J. Appl. Probab. 10, 354–367 (1973). doi:10.2307/3212352

    Article  MATH  MathSciNet  Google Scholar 

  10. Haskose A., Kingsman B.G., Worthington D.: Modelling flow and jobbing shops as a queueing network for workload control. Int. J. Prod. Econ. 78, 271–285 (2002). doi:10.1016/S0925-5273(01)00117-7

    Article  Google Scholar 

  11. Hemachandra N., Eedupuganti S.K.: Performance analysis and buffer allocations in some open assembly systems. Comput. Oper. Res. 30, 695–704 (2003). doi:10.1016/S0305-0548(02)00034-5

    Article  MATH  Google Scholar 

  12. Kapadia A.S., His B.P.: Steady state waiting time in a multicenter job shop. Nav. Res. Logistics Q. 25, 149–154 (1978). doi:10.1002/nav.3800250112

    Article  MATH  Google Scholar 

  13. Kulkarni V., Adlakha V.: Markov and Markov-regenerative PERT networks. Oper. Res. 34, 769–781 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lipper E.H., Sengupta B.: Assembly-like queues with finite capacity: bounds, asympototics and approximations. Queueing Syst. 1, 67–83 (1986). doi:10.1007/BF01149328

    Article  MATH  MathSciNet  Google Scholar 

  15. Martin J.: Distribution of the time through a directed acyclic network. Oper. Res. 13, 46–66 (1965)

    Article  MATH  Google Scholar 

  16. Papadopoulos H.T., Heavey C.: Queueing theory in manufacturing systems analysis and design: a classification of models for production and transfer lines. Eur. J. Oper. Res. 92, 1–27 (1996). doi:10.1016/0377-2217(95)00378-9

    Article  MATH  Google Scholar 

  17. Seidman A., Smith M.L.: Due date assignment for production systems. Manage. Sci. 27, 571–581 (1981)

    Article  Google Scholar 

  18. Shanthikumar J.G., Sumita U.: Approximations for the time spent in a dynamic job shop with application to due-date assignment. Int. J. Prod. Res. 26, 1329–1352 (1988). doi:10.1080/00207548808947949

    Article  MATH  Google Scholar 

  19. Song D.P., Hicks C., Earl C.F.: Product due date assignment for complex assemblies. Int. J. Prod. Econ. 76, 243–256 (2002). doi:10.1016/S0925-5273(01)00170-0

    Article  Google Scholar 

  20. Soroush H.M.: Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs. Eur. J. Oper. Res. 113, 450–468 (1999). doi:10.1016/S0377-2217(98)00003-4

    Article  MATH  Google Scholar 

  21. Vandaele N., Boeck L.D., Callewier D.: An open queueing network for lead time analysis. IIE Trans. 34, 1–9 (2002)

    Google Scholar 

  22. Walpole R.E., Myers R.H., Myers S.L., Ye K.: Probability and statistics for engineers and scientists, 8th edn. Prentice Hall, Englewood Cliffs, NJ, USA (2002)

    Google Scholar 

  23. Yano C.A.: Stochastic lead-time in two-level assembly systems. IIE Trans. 19, 371–378 (1987). doi:10.1080/07408178708975409

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Fördertechnik und Logistiksysteme (IFL), Universität Karlsruhe (TH), Karlsruhe, Germany

    Amir Azaron

  2. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

    Farhad Kianfar

Authors
  1. Amir Azaron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farhad Kianfar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amir Azaron.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Azaron, A., Kianfar, F. Due date assignment for multistage assembly systems. Optim Lett 3, 199–210 (2009). https://doi.org/10.1007/s11590-008-0101-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-008-0101-x

Keywords

Search

Navigation