Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Dynamic scheduling to minimize lost sales subject to set-up costs

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We consider scheduling a shared server in a two-class, make-to-stock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without set-ups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal. We also develop and test a heuristic policy for a model in which the shared resource is part of a series network under a CONWIP release policy.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  1. D.P. Bertsekas, Dynamic Programming: Deterministic and Stochastic Models (Prentice-Hall, Englewood Cliffs, NJ, 1987).

    Google Scholar 

  2. D. Bertsimas and J. Niño-Mora, Conservation laws, extended polymatroids and mult-armed bandit problems; a unified approach to indexable systems, Math. Oper. Res. 21 (1996) 257–306.

    Article  Google Scholar 

  3. M. Elhafsi and S. Bai, Optimal and near optimal control of a two-part-type stochastic manufacturing system with dynamic set-ups, Preprint (1996).

  4. A. Federgruen and Z. Katalan, Determining production schedules under base-stock policies in single facility multi-item production systems, preprint (1995).

  5. A. Federgruen and Z. Katalan, The stochastic economic lot scheduling problem: Cyclical base-stock policies with idle times, Managm. Sci. 42(6) (1996) 783–796.

    Google Scholar 

  6. J.C. Gittins, Multi-Armed Bandit Allocation Indices (Wiley, New York, 1989).

    Google Scholar 

  7. A.Y. Ha, Optimal dynamic scheduling policy for a make-to-stock production system, Oper. Res. 45 (1997) 42–53.

    Google Scholar 

  8. W.J. Hopp and M.L. Spearman, Factory Physics: Foundations of Manufacturing Management (Irwin, Chicago, 1996).

    Google Scholar 

  9. E. Kim and M.P. Van Oyen, Beyond the rule: Dynamic scheduling of a two-class loss queue, Math. Methods Oper. Res. 48(1) (1998).

  10. E. Kim, M.P. Van Oyen and M. Rieders, General dynamic programming algorithms applied to polling systems, Working paper, Northwestern University, Evanston, IL (1996).

    Google Scholar 

  11. G.P. Klimov, Time sharing service systems I, Theory Probab. Appl. 19 (1974) 532–551.

    Article  Google Scholar 

  12. H. Levy and M. Sidi, Polling systems: applications, modelling, and optimization, IEEE Trans. Commun. 38 (1990) 1750–1760.

    Article  Google Scholar 

  13. D.M. Markowitz and L. Wein, Heavy traffic analysis of dynamic cyclic policies: A unified treatment of the single machine scheduling problem, Working paper 3925–96-MSA, MIT Sloan School of Management, Cambridge (1996).

    Google Scholar 

  14. J. Qiu and R. Loulou, Multiproduct production/inventory control under random demands, IEEE Trans. Automat. Control 40(2) (1995) 350–356.

    Article  Google Scholar 

  15. S.M. Ross, Introduction to Stochastic Dynamic Programming (Academic Press, New York, 1983).

    Google Scholar 

  16. S.M. Ross, Stochastic Processes (Wiley, New York, 1983).

    Google Scholar 

  17. M.L. Spearman, D.L. Woodruff and W.J. Hopp, CONWIP: A pull alternatives to KANBAN, Internat. J. Production Res. 28(5) (1989) 879–894.

    Google Scholar 

  18. M.L. Spearman and M.A. Zazanis, Push and pull production systems: Issues and comparisons, Oper. Res. 40(3) (1992) 521–532.

    Google Scholar 

  19. H. Takagi, Queueing analysis of polling models: Progress in 1990–1993, in: Frontiers in Queueing: Models, Methods and Problems, ed. J.H. Dshalalow (CRC Press, 1994).

  20. M.H. Veatch and L.M. Wein, Optimal control of a two-station tandem production/inventory system, Oper. Res. 42(2) (1994) 337–350.

    Google Scholar 

  21. M.H. Veatch and L.M. Wein, Scheduling a make-to-stock queue: Index policies and hedging points, Oper. Res. 44(4) (1996) 634–647.

    Google Scholar 

  22. L.M. Wein, Dynamic scheduling of a multiclass make-to-stock queue, Oper. Res. 40(4) (1992) 724–735.

    Google Scholar 

  23. P. Whittle, Restless bandits: activity allocation in a changing world, in: A Celebration of Applied Probability, ed. J. Gani, J. Appl. Probab. 25A (1988) 287–298.

  24. Y. Zheng and P. Zipkin, A queueing model to analyze the value of centralized inventory information, Oper. Res. 38(2) (1990) 296–307.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, E., Van Oyen, M.P. Dynamic scheduling to minimize lost sales subject to set-up costs. Queueing Systems 29, 193–229 (1998). https://doi.org/10.1023/A:1019136231100

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019136231100

Navigation