Skip to main content
SpringerLink
Log in

Multi-product lot-sizing and sequencing on a single imperfect machine

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

A problem of lot-sizing and sequencing several products on a single machine is studied. The machine is imperfect in two senses: it can produce defective items and it can breakdown. The number of defective items for each product is given as an integer valued non-decreasing function of the manufactured quantity. The total machine breakdown time is given as a real valued non-decreasing function of the manufactured quantities of all the products. A sequence-dependent setup time is required to switch the machine from manufacturing one product to another. Two problem settings are considered. In the first, the objective is to minimize the completion time of the last item, provided that all the product demands for the good quality items are satisfied. In the second, the goal is to minimize the total cost of demand dissatisfaction, subject to an assumption that the completion time of the last item does not exceed a given upper bound. Computational complexity and algorithmic results are presented, including an FPTAS for a special case of the cost minimization problem, and computer experiments with the FPTAS.

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. Allahverdi, A., Ng, C.T., Cheng, T.C.E., Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187, 985–1032 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Buscher, U., Lindner, G.: Optimizing a production system with rework and equal sized batch shipments. Comput. Oper. Res. 34, 515–535 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cheng, T.C.E., Kovalyov, M.Y.: An unconstrained optimization problem is NP-hard given an oracle representation of its objective function: a technical note. Comput. Oper. Res. 29, 2087–2091 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chiu, S.W., Ting, C.-K., Chiu, Y.-S.P.: Optimal production lot sizing with rework, scrap rate, and service level constraint. Math. Comput. Model. 46, 535–549 (2007)

    Article  Google Scholar 

  5. Chubanov, S., Kovalyov, M.Y., Pesch, E.: An FPTAS for a single-item capacitated economic lot-sizing problem. Math. Program., Ser. A 106, 453–466 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dolgui, A., Levin, G., Louly, M.-A.: Decomposition approach for a problem of lot-sizing and sequencing under uncertainties. Int. J. Comput. Integr. Manuf. 18, 376–385 (2005)

    Article  Google Scholar 

  7. Dolgui, A., Kovalyov, M., Shchamialiova, K.: Lot-sizing and sequencing on a single imperfect machine. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) Communications in Computer and Information Science, vol. 14, pp. 117–125. Springer, Berlin (2008)

    Google Scholar 

  8. Flapper, S.D.P., Fransoo, J.C., Broekmeulen, R.A.C.M., Inderfurth, K.: Planning and control of rework in the process industries: a review. Prod. Plan. Control 1, 26–34 (2002)

    Google Scholar 

  9. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  10. Gerchak, Y., Wang, Y., Yano, C.A.: Lot-sizing in assembly systems with random yields. IIE Trans. 26(2), 19–24 (1994)

    Article  Google Scholar 

  11. Gitlow, H., Gitlow, S., Oppenheim, A., Oppenheim, R.: Tools and Methods for the Improvement of Quality. Irwin, Boston (1989)

    MATH  Google Scholar 

  12. Groenevelt, H., Pintelon, L., Seidmann, A.: Production lot sizing with machine breakdowns. Manag. Sci. 38, 104–120 (1992)

    Article  MATH  Google Scholar 

  13. Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. J. Soc. Ind. Appl. Math. 10, 196–210 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  14. Inderfurth, K., Lindner, G., Rahaniotis, N.P.: Lotsizing in a production system with rework and product deterioration. Preprint 1/2003, Faculty of Economics and Management, Otto-von-Guericke-University Magdeburg, Germany (2003)

  15. Inderfurth, K., Janiak, A., Kovalyov, M.Y., Werner, F.: Batching work and rework processes with limited deterioration of reworkables. Comput. Oper. Res. 33, 1595–1605 (2006)

    Article  MATH  Google Scholar 

  16. Inderfurth, K., Kovalyov, M.Y., Ng, C.T., Werner, F.: Cost minimizing scheduling of work and rework processes on a single facility under deterioration of reworkables. Int. J. Prod. Econ. 105, 345–356 (2007)

    Article  Google Scholar 

  17. Kovalyov, M.Y.: A rounding technique to construct approximation algorithms for knapsack and partition type problems. Appl. Math. Comput. Sci. 6, 101–113 (1996)

    MathSciNet  Google Scholar 

  18. Potts, C.N., Kovalyov, M.Y.: Scheduling with batching: a review. Eur. J. Oper. Res. 120, 228–249 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Potts, C.N., Van Wassenhove, L.N.: Integrating scheduling with batching and lot-sizing: a review of algorithms and complexity. J. Oper. Res. Soc. 43, 395–406 (1992)

    MATH  Google Scholar 

  20. Rosenblatt, M.J., Lee, H.L.: Economic production cycles with imperfect production processes. IIE Trans. 18, 48–55 (1986)

    Article  Google Scholar 

  21. Tanaev, V.S., Kovalyov, M.Y., Shafransky, Y.M.: Scheduling Theory. Group Technologies. IEC NANB, Minsk (1998). (in Russian)

    Google Scholar 

  22. Teunter, R.H., Flapper, S.D.P.: Lot-sizing for a single-stage single-product production system with rework of perishable production defectives. OR Spectrum 25, 85–96 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yano, C.A., Lee, H.L.: Lot-sizing with random yields: a review. Oper. Res. 43(2), 311–333 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Industrial Engineering and Computer Science Centre (G2I), Ecole des Mines de Saint-Etienne, 158, cours Fauriel, 42023, Saint-Etienne Cedex 2, France

    A. Dolgui, M. Y. Kovalyov & K. Shchamialiova

  2. United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganova 6, 220012, Minsk, Belarus

    M. Y. Kovalyov

Authors
  1. A. Dolgui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Y. Kovalyov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Shchamialiova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Dolgui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dolgui, A., Kovalyov, M.Y. & Shchamialiova, K. Multi-product lot-sizing and sequencing on a single imperfect machine. Comput Optim Appl 50, 465–482 (2011). https://doi.org/10.1007/s10589-010-9346-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-010-9346-2

Keywords

Search

Navigation